Global Index A B C D E F G H I J K L M N O P Q R S T U V W X Y Z _ other (3805 entries)
Notation Index A B C D E F G H I J K L M N O P Q R S T U V W X Y Z _ other (13 entries)
Module Index A B C D E F G H I J K L M N O P Q R S T U V W X Y Z _ other (14 entries)
Variable Index A B C D E F G H I J K L M N O P Q R S T U V W X Y Z _ other (25 entries)
Library Index A B C D E F G H I J K L M N O P Q R S T U V W X Y Z _ other (142 entries)
Lemma Index A B C D E F G H I J K L M N O P Q R S T U V W X Y Z _ other (2837 entries)
Constructor Index A B C D E F G H I J K L M N O P Q R S T U V W X Y Z _ other (19 entries)
Projection Index A B C D E F G H I J K L M N O P Q R S T U V W X Y Z _ other (123 entries)
Inductive Index A B C D E F G H I J K L M N O P Q R S T U V W X Y Z _ other (8 entries)
Section Index A B C D E F G H I J K L M N O P Q R S T U V W X Y Z _ other (182 entries)
Instance Index A B C D E F G H I J K L M N O P Q R S T U V W X Y Z _ other (51 entries)
Definition Index A B C D E F G H I J K L M N O P Q R S T U V W X Y Z _ other (374 entries)
Record Index A B C D E F G H I J K L M N O P Q R S T U V W X Y Z _ other (17 entries)

Global Index

A

aah__hpp [lemma, in GeoCoq.Meta_theory.Parallel_postulates.szmielew]
absolute_exterior_angle_theorem [lemma, in GeoCoq.Tarski_dev.Annexes.saccheri]
Acute [definition, in GeoCoq.Tarski_dev.Ch11_angles]
acute_col_out [lemma, in GeoCoq.Tarski_dev.Ch13_3_angles]
acute_not_bet [lemma, in GeoCoq.Tarski_dev.Ch13_3_angles]
acute_col_perp__out [lemma, in GeoCoq.Tarski_dev.Ch12_parallel]
acute_sac__aah [lemma, in GeoCoq.Tarski_dev.Annexes.saccheri]
acute_sac__lt [lemma, in GeoCoq.Tarski_dev.Annexes.saccheri]
acute_comp_not_acute [lemma, in GeoCoq.Tarski_dev.Ch13_4_cos]
acute_not_obtuse [lemma, in GeoCoq.Tarski_dev.Ch13_4_cos]
acute_archi_aux2 [lemma, in GeoCoq.Meta_theory.Parallel_postulates.angle_archimedes]
acute_archi_aux1 [lemma, in GeoCoq.Meta_theory.Parallel_postulates.angle_archimedes]
acute_archi_aux [lemma, in GeoCoq.Meta_theory.Parallel_postulates.angle_archimedes]
acute_not_per [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
acute_trivial [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
acute_chara [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
acute_obtuse__lta [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
acute_per__lta [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
acute_conga__acute [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
acute_distincts [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
acute_distinct [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
acute_lea_acute [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
acute_sym [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
acute_bet_obtuse [lemma, in GeoCoq.Tarski_dev.Ch13_1]
acute_suma__nbet [lemma, in GeoCoq.Tarski_dev.Annexes.suma]
acute__isi [lemma, in GeoCoq.Tarski_dev.Annexes.suma]
AddF [definition, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
addF_morphism [instance, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
addition [projection, in GeoCoq.Axioms.hilbert_axioms]
addition_betH [lemma, in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
allButLastCP [definition, in GeoCoq.Utils.arity]
allButLastCPTl [lemma, in GeoCoq.Utils.arity]
all_eqaa [lemma, in GeoCoq.Tarski_dev.Ch13_3_angles]
all_eqa [lemma, in GeoCoq.Tarski_dev.Ch13_3_angles]
all_one_side_par_strict [lemma, in GeoCoq.Tarski_dev.Ch12_parallel]
all_equiv_under [definition, in GeoCoq.Utils.all_equiv]
all_equiv_equiv [lemma, in GeoCoq.Utils.all_equiv]
all_equiv' [definition, in GeoCoq.Utils.all_equiv]
all_equiv [definition, in GeoCoq.Utils.all_equiv]
all_coplanar_upper_dim [lemma, in GeoCoq.Meta_theory.Dimension_axioms.upper_dim]
all_coplanar_implies_upper_dim [lemma, in GeoCoq.Meta_theory.Dimension_axioms.upper_dim]
all_coplanar_axiom [definition, in GeoCoq.Meta_theory.Dimension_axioms.upper_dim]
all_eql [lemma, in GeoCoq.Tarski_dev.Ch13_2_length]
all_coplanar [lemma, in GeoCoq.Tarski_dev.Ch10_line_reflexivity_2D]
all_equiv [library]
alternate_interior__triangle [lemma, in GeoCoq.Meta_theory.Parallel_postulates.alternate_interior_angles_triangle]
alternate_interior_angles_postulate_triangle [section, in GeoCoq.Meta_theory.Parallel_postulates.alternate_interior_angles_triangle]
alternate_interior__playfair_bis [lemma, in GeoCoq.Meta_theory.Parallel_postulates.alternate_interior_angles_playfair_bis]
alternate_interior__playfair_aux [lemma, in GeoCoq.Meta_theory.Parallel_postulates.alternate_interior_angles_playfair_bis]
alternate_interior_angles_playfair_bis [section, in GeoCoq.Meta_theory.Parallel_postulates.alternate_interior_angles_playfair_bis]
alternate_interior__proclus [lemma, in GeoCoq.Meta_theory.Parallel_postulates.alternate_interior_angles_proclus]
alternate_interior_angles_proclus [section, in GeoCoq.Meta_theory.Parallel_postulates.alternate_interior_angles_proclus]
alternate_interior__consecutive_interior [lemma, in GeoCoq.Meta_theory.Parallel_postulates.alternate_interior_angles_consecutive_interior_angles]
alternate_interior_angles_consecutive_interior_angles [section, in GeoCoq.Meta_theory.Parallel_postulates.alternate_interior_angles_consecutive_interior_angles]
alternate_interior_angles_postulate [definition, in GeoCoq.Meta_theory.Parallel_postulates.Euclid_def]
alternate_interior_angles_proclus [library]
alternate_interior_angles_consecutive_interior_angles [library]
alternate_interior_angles_playfair_bis [library]
alternate_interior_angles_triangle [library]
alternative_proclus_postulate [definition, in GeoCoq.Meta_theory.Parallel_postulates.Euclid_def]
alternative_strong_parallel_postulate [definition, in GeoCoq.Meta_theory.Parallel_postulates.Euclid_def]
alternative_playfair_s_postulate [definition, in GeoCoq.Meta_theory.Parallel_postulates.Euclid_def]
altitude_intersect [lemma, in GeoCoq.Highschool.orthocenter]
altitude_is_perp_bisect [lemma, in GeoCoq.Highschool.orthocenter]
AM_CongAL [definition, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
AM_perp_AM_Par_AM_perp [lemma, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
AM_Perp_triv2 [lemma, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
AM_Perp_triv1 [lemma, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
AM_Perp_AM_Perp_AM_Par [lemma, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
AM_lower_dim [lemma, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
AM_Par_ratio_AM_Par [lemma, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
AM_on_foot [definition, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
AM_Par [definition, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
AM_Perp [definition, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
AM_Per [definition, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
AM_Col [definition, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
AM_Cong [definition, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
Ang [definition, in GeoCoq.Tarski_dev.Ch13_3_angles]
anga_col_null [lemma, in GeoCoq.Tarski_dev.Ch13_3_angles]
anga_not_lg_null [lemma, in GeoCoq.Tarski_dev.Ch13_3_angles]
anga_col_out [lemma, in GeoCoq.Tarski_dev.Ch13_3_angles]
anga_out_anga [lemma, in GeoCoq.Tarski_dev.Ch13_3_angles]
anga_conga_anga [lemma, in GeoCoq.Tarski_dev.Ch13_3_angles]
anga_const_o [lemma, in GeoCoq.Tarski_dev.Ch13_3_angles]
anga_not_flat [lemma, in GeoCoq.Tarski_dev.Ch13_3_angles]
anga_acute [lemma, in GeoCoq.Tarski_dev.Ch13_3_angles]
anga_const [lemma, in GeoCoq.Tarski_dev.Ch13_3_angles]
anga_distincts [lemma, in GeoCoq.Tarski_dev.Ch13_3_angles]
anga_not_null_lg [lemma, in GeoCoq.Tarski_dev.Ch13_3_angles]
anga_sym [lemma, in GeoCoq.Tarski_dev.Ch13_3_angles]
anga_distinct [lemma, in GeoCoq.Tarski_dev.Ch13_3_angles]
anga_conga [lemma, in GeoCoq.Tarski_dev.Ch13_3_angles]
anga_is_ang [lemma, in GeoCoq.Tarski_dev.Ch13_3_angles]
anga_exists [lemma, in GeoCoq.Tarski_dev.Ch13_3_angles]
Angles_5 [section, in GeoCoq.Tarski_dev.Ch13_3_angles]
Angles_4 [section, in GeoCoq.Tarski_dev.Ch13_3_angles]
Angles_3 [section, in GeoCoq.Tarski_dev.Ch13_3_angles]
Angles_2 [section, in GeoCoq.Tarski_dev.Ch13_3_angles]
Angles_1 [section, in GeoCoq.Tarski_dev.Ch13_3_angles]
angles_archi_aux1 [lemma, in GeoCoq.Meta_theory.Parallel_postulates.angle_archimedes]
angles_archi_aux [lemma, in GeoCoq.Meta_theory.Parallel_postulates.angle_archimedes]
Angle_archimedes [section, in GeoCoq.Meta_theory.Parallel_postulates.angle_archimedes]
angle_bisector [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
angle_partition [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
angle_construction_3 [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
angle_construction_2 [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
angle_construction_1 [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
angle_archimedes [library]
ang_not_lg_null [lemma, in GeoCoq.Tarski_dev.Ch13_3_angles]
ang_cong_ang [lemma, in GeoCoq.Tarski_dev.Ch13_3_angles]
ang_const_o [lemma, in GeoCoq.Tarski_dev.Ch13_3_angles]
ang_distincts [lemma, in GeoCoq.Tarski_dev.Ch13_3_angles]
ang_not_null_lg [lemma, in GeoCoq.Tarski_dev.Ch13_3_angles]
ang_sym [lemma, in GeoCoq.Tarski_dev.Ch13_3_angles]
ang_const [lemma, in GeoCoq.Tarski_dev.Ch13_3_angles]
Ang_Flat [definition, in GeoCoq.Tarski_dev.Ch13_3_angles]
Ang_Acute [definition, in GeoCoq.Tarski_dev.Ch13_3_angles]
ang_distinct [lemma, in GeoCoq.Tarski_dev.Ch13_3_angles]
ang_conga [lemma, in GeoCoq.Tarski_dev.Ch13_3_angles]
ang_exists [lemma, in GeoCoq.Tarski_dev.Ch13_3_angles]
another_point [lemma, in GeoCoq.Meta_theory.Models.tarski_to_beeson]
another_point [lemma, in GeoCoq.Tarski_dev.Ch03_bet]
app [definition, in GeoCoq.Utils.arity]
app_2_n_app_eq [lemma, in GeoCoq.Utils.arity]
app_app_2_n_default [lemma, in GeoCoq.Utils.arity]
app_app_2_n [lemma, in GeoCoq.Utils.arity]
app_2_n_app_default [lemma, in GeoCoq.Utils.arity]
app_2_n_app [lemma, in GeoCoq.Utils.arity]
app_2_n [definition, in GeoCoq.Utils.arity]
app_1_n_app_eq [lemma, in GeoCoq.Utils.arity]
app_app_1_n [lemma, in GeoCoq.Utils.arity]
app_1_n_app [lemma, in GeoCoq.Utils.arity]
app_1_n [definition, in GeoCoq.Utils.arity]
app_n_1_app_eq [lemma, in GeoCoq.Utils.arity]
app_app_n_1 [lemma, in GeoCoq.Utils.arity]
app_n_1_app [lemma, in GeoCoq.Utils.arity]
app_n_1 [definition, in GeoCoq.Utils.arity]
Archimedes [section, in GeoCoq.Meta_theory.Parallel_postulates.archimedes]
archimedes [library]
archimedes_postulate [definition, in GeoCoq.Meta_theory.Parallel_postulates.archimedes]
archi__gradaexp_destruction [lemma, in GeoCoq.Meta_theory.Parallel_postulates.angle_archimedes]
archi__grada_destruction [lemma, in GeoCoq.Meta_theory.Parallel_postulates.angle_archimedes]
archi_in_angles [lemma, in GeoCoq.Meta_theory.Parallel_postulates.angle_archimedes]
archi_in_acute_angles [lemma, in GeoCoq.Meta_theory.Parallel_postulates.angle_archimedes]
archi__acute_or_right [lemma, in GeoCoq.Meta_theory.Parallel_postulates.archimedes]
archi__obtuse_case_elimination [lemma, in GeoCoq.Meta_theory.Parallel_postulates.archimedes]
aristotle__greenberg [lemma, in GeoCoq.Meta_theory.Parallel_postulates.aristotle_greenberg]
aristotle_greenberg [section, in GeoCoq.Meta_theory.Parallel_postulates.aristotle_greenberg]
aristotle_s_postulate [definition, in GeoCoq.Meta_theory.Parallel_postulates.Euclid_def]
aristotle_greenberg [library]
Arity [record, in GeoCoq.Tactics.Coinc.tactics_axioms]
arity [definition, in GeoCoq.Utils.arity]
arity [library]
Ar1 [definition, in GeoCoq.Tarski_dev.Ch14_sum]
Ar2 [definition, in GeoCoq.Tarski_dev.Ch14_sum]
Ar2_4 [definition, in GeoCoq.Tarski_dev.Ch14_prod]
aux [library]
axiom_A2a [lemma, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
axiom_A2b [lemma, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
axiom_euclid_uniqueness [lemma, in GeoCoq.Meta_theory.Models.tarski_to_hilbert]
axiom_conga_refl [lemma, in GeoCoq.Meta_theory.Models.tarski_to_hilbert]
axiom_inter_dec [lemma, in GeoCoq.Meta_theory.Models.tarski_to_hilbert]
axiom_conga_permlr [lemma, in GeoCoq.Meta_theory.Models.tarski_to_hilbert]
axiom_congaH_outH_congaH [lemma, in GeoCoq.Meta_theory.Models.tarski_to_hilbert]
axiom_cong_permr [lemma, in GeoCoq.Meta_theory.Models.tarski_to_hilbert]
axiom_conga_comm [lemma, in GeoCoq.Meta_theory.Models.tarski_to_hilbert]
axiom_hcong_4_uniqueness [lemma, in GeoCoq.Meta_theory.Models.tarski_to_hilbert]
axiom_hcong_4_existence [lemma, in GeoCoq.Meta_theory.Models.tarski_to_hilbert]
axiom_cong_5' [lemma, in GeoCoq.Meta_theory.Models.tarski_to_hilbert]
axiom_hcong_3 [lemma, in GeoCoq.Meta_theory.Models.tarski_to_hilbert]
axiom_hcong_refl [lemma, in GeoCoq.Meta_theory.Models.tarski_to_hilbert]
axiom_hcong_trans [lemma, in GeoCoq.Meta_theory.Models.tarski_to_hilbert]
axiom_hcong_scott [lemma, in GeoCoq.Meta_theory.Models.tarski_to_hilbert]
axiom_hcong_1_uniqueness [lemma, in GeoCoq.Meta_theory.Models.tarski_to_hilbert]
axiom_hcong_1_existence [lemma, in GeoCoq.Meta_theory.Models.tarski_to_hilbert]
axiom_pasch [lemma, in GeoCoq.Meta_theory.Models.tarski_to_hilbert]
axiom_between_one [lemma, in GeoCoq.Meta_theory.Models.tarski_to_hilbert]
axiom_between_only_one [lemma, in GeoCoq.Meta_theory.Models.tarski_to_hilbert]
axiom_between_out [lemma, in GeoCoq.Meta_theory.Models.tarski_to_hilbert]
axiom_between_comm [lemma, in GeoCoq.Meta_theory.Models.tarski_to_hilbert]
axiom_between_diff [lemma, in GeoCoq.Meta_theory.Models.tarski_to_hilbert]
axiom_between_col [lemma, in GeoCoq.Meta_theory.Models.tarski_to_hilbert]
axiom_plan' [lemma, in GeoCoq.Meta_theory.Models.tarski_to_hilbert]
axiom_plan [lemma, in GeoCoq.Meta_theory.Models.tarski_to_hilbert]
axiom_two_points_on_line [lemma, in GeoCoq.Meta_theory.Models.tarski_to_hilbert]
axiom_line_uniqueness [lemma, in GeoCoq.Meta_theory.Models.tarski_to_hilbert]
axiom_Incid_dec [lemma, in GeoCoq.Meta_theory.Models.tarski_to_hilbert]
axiom_Incid_morphism [lemma, in GeoCoq.Meta_theory.Models.tarski_to_hilbert]
axiom_line_existence [lemma, in GeoCoq.Meta_theory.Models.tarski_to_hilbert]
axiom_five_segmentsH [lemma, in GeoCoq.Meta_theory.Models.hilbert_to_tarski]


B

bachmann_s_lotschnittaxiom__existential_inverse_projection_postulate [lemma, in GeoCoq.Meta_theory.Parallel_postulates.bachmann_s_lotschnittaxiom_existential_inverse_projection_postulate]
bachmann_s_lotschnittaxiom_existential_inverse_projection_postulate [section, in GeoCoq.Meta_theory.Parallel_postulates.bachmann_s_lotschnittaxiom_existential_inverse_projection_postulate]
bachmann_s_lotschnittaxiom__weak_triangle_circumscription_principle [lemma, in GeoCoq.Meta_theory.Parallel_postulates.bachmann_s_lotschnittaxiom_weak_triangle_circumscription_principle]
bachmann_s_lotschnittaxiom_weak_triangle_circumscription_principle [section, in GeoCoq.Meta_theory.Parallel_postulates.bachmann_s_lotschnittaxiom_weak_triangle_circumscription_principle]
bachmann_s_lotschnittaxiom [definition, in GeoCoq.Meta_theory.Parallel_postulates.Euclid_def]
bachmann_s_lotschnittaxiom_existential_inverse_projection_postulate [library]
bachmann_s_lotschnittaxiom_weak_triangle_circumscription_principle [library]
Beeson_follows_from_Tarski [instance, in GeoCoq.Meta_theory.Models.tarski_to_beeson]
Beeson_2.Bet_stability [variable, in GeoCoq.Tarski_dev.Ch03_bet]
Beeson_2 [section, in GeoCoq.Tarski_dev.Ch03_bet]
Beeson_1.Cong_stability [variable, in GeoCoq.Tarski_dev.Ch03_bet]
Beeson_1 [section, in GeoCoq.Tarski_dev.Ch03_bet]
beeson_s_axioms [library]
Bet [projection, in GeoCoq.Axioms.tarski_axioms]
Bet [definition, in GeoCoq.Meta_theory.Counter_models.counter_model_segment_construction]
Bet [definition, in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
Bet [definition, in GeoCoq.Meta_theory.Counter_models.counter_model_bet_identity]
BetG [projection, in GeoCoq.Axioms.independent_tarski_axioms]
BetH [definition, in GeoCoq.Meta_theory.Models.tarski_to_beeson]
BetH [projection, in GeoCoq.Axioms.hilbert_axioms]
BetH_Bet [lemma, in GeoCoq.Meta_theory.Models.tarski_to_beeson]
betH_congH2__False [lemma, in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
betH_outH2__betH [lemma, in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
betH_outH__outH [lemma, in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
betH_congH3_outH_betH [lemma, in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
betH_not_congH [lemma, in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
betH_dec [lemma, in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
betH_trans0 [lemma, in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
betH_trans [lemma, in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
betH_trans2 [lemma, in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
betH_trans1 [lemma, in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
betH_expand [lemma, in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
betH_colH [lemma, in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
betH_line [lemma, in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
betH_to_bet [lemma, in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
betH_distincts [lemma, in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
betH2_out [lemma, in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
BetM [projection, in GeoCoq.Axioms.makarios_variant_axioms]
BetS [definition, in GeoCoq.Meta_theory.Parallel_postulates.Euclid_def]
BetSEq [lemma, in GeoCoq.Meta_theory.Parallel_postulates.Euclid_def]
BetT [definition, in GeoCoq.Meta_theory.Models.tarski_to_beeson]
BetT_id [lemma, in GeoCoq.Meta_theory.Models.tarski_to_beeson]
BetT_symmetry [lemma, in GeoCoq.Meta_theory.Models.tarski_to_beeson]
between_identity [projection, in GeoCoq.Axioms.tarski_axioms]
between_symmetry_B [lemma, in GeoCoq.Meta_theory.Models.tarski_to_beeson]
between_inner_transitivity_B [lemma, in GeoCoq.Meta_theory.Models.tarski_to_beeson]
between_identity_B [lemma, in GeoCoq.Meta_theory.Models.tarski_to_beeson]
between_cong_3 [lemma, in GeoCoq.Tarski_dev.Ch05_bet_le]
between_cong_2 [lemma, in GeoCoq.Tarski_dev.Ch05_bet_le]
between_cong [lemma, in GeoCoq.Tarski_dev.Ch05_bet_le]
between_only_one [projection, in GeoCoq.Axioms.hilbert_axioms]
between_out [projection, in GeoCoq.Axioms.hilbert_axioms]
between_comm [projection, in GeoCoq.Axioms.hilbert_axioms]
between_diff [projection, in GeoCoq.Axioms.hilbert_axioms]
between_col [projection, in GeoCoq.Axioms.hilbert_axioms]
between_exchange4 [lemma, in GeoCoq.Tarski_dev.Ch03_bet]
between_exchange2 [lemma, in GeoCoq.Tarski_dev.Ch03_bet]
between_inner_transitivity [lemma, in GeoCoq.Tarski_dev.Ch03_bet]
between_exchange3 [lemma, in GeoCoq.Tarski_dev.Ch03_bet]
between_equality [lemma, in GeoCoq.Tarski_dev.Ch03_bet]
between_trivial2 [lemma, in GeoCoq.Tarski_dev.Ch03_bet]
between_symmetry [lemma, in GeoCoq.Tarski_dev.Ch03_bet]
between_trivial [lemma, in GeoCoq.Tarski_dev.Ch03_bet]
between_trivialT [lemma, in GeoCoq.Meta_theory.Models.independent_tarski_to_tarski]
between_identityT [lemma, in GeoCoq.Meta_theory.Models.independent_tarski_to_tarski]
between_identity [lemma, in GeoCoq.Meta_theory.Counter_models.counter_model_segment_construction]
between_symmetry [lemma, in GeoCoq.Meta_theory.Models.tarski_to_makarios]
between_trivial [lemma, in GeoCoq.Meta_theory.Models.tarski_to_makarios]
between_symmetric [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
between_one [lemma, in GeoCoq.Meta_theory.Models.tarski_to_hilbert]
Between_H [definition, in GeoCoq.Meta_theory.Models.tarski_to_hilbert]
between_one [lemma, in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
between_only_one' [lemma, in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
between_identity_independent [section, in GeoCoq.Meta_theory.Counter_models.counter_model_bet_identity]
bet_flat_ang [lemma, in GeoCoq.Tarski_dev.Ch13_3_angles]
bet_id [lemma, in GeoCoq.Meta_theory.Models.tarski_to_beeson]
Bet_T [lemma, in GeoCoq.Meta_theory.Models.tarski_to_beeson]
bet_stability [lemma, in GeoCoq.Meta_theory.Models.tarski_to_beeson]
bet_half_bet [lemma, in GeoCoq.Highschool.orientation]
bet_double_bet [lemma, in GeoCoq.Highschool.orientation]
bet_le_le [lemma, in GeoCoq.Highschool.orientation]
bet_le_eq [lemma, in GeoCoq.Tarski_dev.Ch05_bet_le]
bet__le2313 [lemma, in GeoCoq.Tarski_dev.Ch05_bet_le]
bet__le1213 [lemma, in GeoCoq.Tarski_dev.Ch05_bet_le]
bet_cong_eq [lemma, in GeoCoq.Tarski_dev.Ch05_bet_le]
bet_dec [lemma, in GeoCoq.Tarski_dev.Ch05_bet_le]
bet_dec_eq_dec_b [lemma, in GeoCoq.Tarski_dev.Ch03_bet]
Bet_4 [definition, in GeoCoq.Tarski_dev.Ch03_bet]
bet_neq32__neq [lemma, in GeoCoq.Tarski_dev.Ch03_bet]
bet_neq23__neq [lemma, in GeoCoq.Tarski_dev.Ch03_bet]
bet_neq21__neq [lemma, in GeoCoq.Tarski_dev.Ch03_bet]
bet_neq12__neq [lemma, in GeoCoq.Tarski_dev.Ch03_bet]
Bet_perm [lemma, in GeoCoq.Tarski_dev.Ch03_bet]
Bet_cases [lemma, in GeoCoq.Tarski_dev.Ch03_bet]
bet_col [lemma, in GeoCoq.Tarski_dev.Ch03_bet]
bet_inner_transitivityG [projection, in GeoCoq.Axioms.independent_tarski_axioms]
bet_symmetryG [projection, in GeoCoq.Axioms.independent_tarski_axioms]
bet_decG [lemma, in GeoCoq.Meta_theory.Models.independent_tarski_to_tarski]
bet_leP [lemma, in GeoCoq.Tarski_dev.Ch15_lengths]
bet_lt21_le31 [lemma, in GeoCoq.Tarski_dev.Ch14_order]
bet_lt21_le32 [lemma, in GeoCoq.Tarski_dev.Ch14_order]
bet_lt12_le13 [lemma, in GeoCoq.Tarski_dev.Ch14_order]
bet_lt12_le23 [lemma, in GeoCoq.Tarski_dev.Ch14_order]
bet_cong3 [lemma, in GeoCoq.Tarski_dev.Ch02_cong]
bet_col1 [lemma, in GeoCoq.Tarski_dev.Ch07_midpoint]
bet_le__lt [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
bet_obtuse__acute [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
bet_acute__obtuse [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
bet__obtuse [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
bet_lea__bet [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
bet_in_angle_bet [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
bet_conga_bet [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
bet_out_out_bet [lemma, in GeoCoq.Tarski_dev.Ch06_out_lines]
bet_out [lemma, in GeoCoq.Tarski_dev.Ch06_out_lines]
Bet_Between_H [lemma, in GeoCoq.Meta_theory.Models.tarski_to_hilbert]
bet_betCood [lemma, in GeoCoq.Tarski_dev.Ch16_coordinates]
bet_betCood_aux [lemma, in GeoCoq.Tarski_dev.Ch16_coordinates]
bet_trans [lemma, in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
bet_comm [lemma, in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
bet_cong3_bet [lemma, in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
bet_disjoint [lemma, in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
bet_colH [lemma, in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
bet_identity [lemma, in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
bet_same_dir2 [lemma, in GeoCoq.Tarski_dev.Annexes.vectors]
bet_same_dir1 [lemma, in GeoCoq.Tarski_dev.Annexes.vectors]
Bet_tagged_Bet [lemma, in GeoCoq.Tarski_dev.Annexes.Tagged_predicates]
Bet_Bet_tagged [lemma, in GeoCoq.Tarski_dev.Annexes.Tagged_predicates]
Bet_tagged [definition, in GeoCoq.Tarski_dev.Annexes.Tagged_predicates]
bet_dec_eq_dec [lemma, in GeoCoq.Meta_theory.Decidability.equivalence_between_decidability_properties_of_basic_relations]
bet_cong_bet [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals]
bet_half_bet [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals]
bet_double_bet [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals]
bet_le_le [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals]
bet_suma__per [lemma, in GeoCoq.Tarski_dev.Annexes.suma]
bet_per_suma__per123 [lemma, in GeoCoq.Tarski_dev.Annexes.suma]
bet_per_suma__per456 [lemma, in GeoCoq.Tarski_dev.Annexes.suma]
bet_suma__isi [lemma, in GeoCoq.Tarski_dev.Annexes.suma]
Bet_stability [projection, in GeoCoq.Axioms.beeson_s_axioms]
bet2_lta__lta [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
bet2_out_out [lemma, in GeoCoq.Tarski_dev.Ch06_out_lines]
bet2_le2__le1245 [lemma, in GeoCoq.Tarski_dev.Ch06_out_lines]
bet2_le2__le2356 [lemma, in GeoCoq.Tarski_dev.Ch06_out_lines]
bet2_le2__le1346 [lemma, in GeoCoq.Tarski_dev.Ch06_out_lines]
bet2_cong_bet [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals]
bet3_cong3_bet [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals]
Bisector [section, in GeoCoq.Highschool.bisector]
bisector [library]
bisector_perp_equality [lemma, in GeoCoq.Highschool.bisector]
Bisector_2 [section, in GeoCoq.Highschool.bisector]
bisector_foot_out_out [lemma, in GeoCoq.Highschool.bisector]
bisector_existence [lemma, in GeoCoq.Highschool.bisector]
build_couple [constructor, in GeoCoq.Utils.aux]
build_triple [constructor, in GeoCoq.Utils.aux]


C

cartesianPower [definition, in GeoCoq.Utils.arity]
cartesianPowerAux [definition, in GeoCoq.Utils.arity]
ccw [definition, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
Cd [definition, in GeoCoq.Tarski_dev.Ch16_coordinates]
Cd_Cd_EqF [lemma, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
Cd_Col [lemma, in GeoCoq.Tarski_dev.Ch16_coordinates]
centroid_theorem [lemma, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
change_grid_prod [lemma, in GeoCoq.Tarski_dev.Ch14_prod]
change_grid_prod1 [lemma, in GeoCoq.Tarski_dev.Ch14_prod]
change_grid_prod_l_O [lemma, in GeoCoq.Tarski_dev.Ch14_prod]
change_grid_sum [lemma, in GeoCoq.Tarski_dev.Ch14_sum]
change_grid_sum_0 [lemma, in GeoCoq.Tarski_dev.Ch14_sum]
characterization_of_perpendicularity_F [lemma, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
characterization_of_perpendicularity_F_bis [lemma, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
characterization_of_parallelism_F [lemma, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
characterization_of_parallelism_F_bis [lemma, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
characterization_of_parallelism_F_aux [lemma, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
characterization_of_right_triangle_F [lemma, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
characterization_of_midpoint_F [lemma, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
characterization_of_neq_F [lemma, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
characterization_of_equality_F_bis [lemma, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
characterization_of_equality_F_aux [lemma, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
characterization_of_neq_F_bis [lemma, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
characterization_of_equality_F [lemma, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
characterization_of_collinearity_F [lemma, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
characterization_of_betweenness_F [lemma, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
characterization_of_congruence_F [lemma, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
characterization_of_collinearity [lemma, in GeoCoq.Tarski_dev.Ch16_coordinates]
characterization_of_betweenness [lemma, in GeoCoq.Tarski_dev.Ch16_coordinates]
characterization_of_betweenness_aux [lemma, in GeoCoq.Tarski_dev.Ch16_coordinates]
characterization_of_congruence [lemma, in GeoCoq.Tarski_dev.Ch16_coordinates]
chasles [lemma, in GeoCoq.Tarski_dev.Annexes.vectors]
chasles_ratios [lemma, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
Ch02_cong [library]
Ch03_bet [library]
Ch04_cong_bet [library]
Ch04_col [library]
Ch05_bet_le [library]
Ch06_out_lines [library]
Ch07_midpoint [library]
Ch08_orthogonality [library]
Ch09_plane [library]
Ch10_line_reflexivity_2D [library]
Ch10_line_reflexivity [library]
Ch11_angles [library]
Ch12_parallel_inter_dec [library]
Ch12_parallel [library]
Ch13_4_cos [library]
Ch13_6_Desargues_Hessenberg [library]
Ch13_3_angles [library]
Ch13_5_Pappus_Pascal [library]
Ch13_2_length [library]
Ch13_1 [library]
Ch14_order [library]
Ch14_sum [library]
Ch14_prod [library]
Ch15_lengths [library]
Ch15_pyth_rel [library]
Ch16_coordinates [library]
Ch16_coordinates_with_functions [library]
circPermNConsOK [lemma, in GeoCoq.Utils.arity]
circPermNConsTlOK [lemma, in GeoCoq.Utils.arity]
circPermNCP [definition, in GeoCoq.Utils.arity]
circPermNCPOK [lemma, in GeoCoq.Utils.arity]
circPermNCP0 [lemma, in GeoCoq.Utils.arity]
circPermNId [lemma, in GeoCoq.Utils.arity]
circPermNIdAux [lemma, in GeoCoq.Utils.arity]
circPermNIdFirst [lemma, in GeoCoq.Utils.arity]
circPermPerm [lemma, in GeoCoq.Utils.arity]
Circumcenter [section, in GeoCoq.Highschool.circumcenter]
circumcenter [library]
circumcenter_per [lemma, in GeoCoq.Highschool.circumcenter]
circumcenter_intersect [lemma, in GeoCoq.Highschool.circumcenter]
circumcenter_perp_all [lemma, in GeoCoq.Highschool.circumcenter]
circumcenter_perp [lemma, in GeoCoq.Highschool.circumcenter]
circumcenter_cong [lemma, in GeoCoq.Highschool.circumcenter]
Circumcenter2 [section, in GeoCoq.Highschool.circumcenter]
Circumcenter3 [section, in GeoCoq.Highschool.circumcenter]
CoappDup [lemma, in GeoCoq.Tactics.Coinc.CoincR]
CoappDupAux [lemma, in GeoCoq.Tactics.Coinc.CoincR]
CoappDupPerm [lemma, in GeoCoq.Tactics.Coinc.CoincR]
coinc [projection, in GeoCoq.Tactics.Coinc.tactics_axioms]
COINCpoint [projection, in GeoCoq.Tactics.Coinc.tactics_axioms]
CoincR [library]
CoincR_for_col [section, in GeoCoq.Tactics.Coinc.CoincR_for_col]
CoincR_for_col [library]
coinc_n [projection, in GeoCoq.Tactics.Coinc.tactics_axioms]
coinc_bd [projection, in GeoCoq.Tactics.Coinc.tactics_axioms]
coinc_perm_2 [projection, in GeoCoq.Tactics.Coinc.tactics_axioms]
coinc_perm_1 [projection, in GeoCoq.Tactics.Coinc.tactics_axioms]
Coinc_theory [record, in GeoCoq.Tactics.Coinc.tactics_axioms]
Coinc_predicates [record, in GeoCoq.Tactics.Coinc.tactics_axioms]
Coinc_refl [section, in GeoCoq.Tactics.Coinc.CoincR]
col [definition, in GeoCoq.Tactics.Coinc.tarski_to_coinc_theory_for_col]
Col [definition, in GeoCoq.Tarski_dev.Ch03_bet]
Col [definition, in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
ColB [definition, in GeoCoq.Meta_theory.Models.tarski_to_beeson]
ColB_Col [lemma, in GeoCoq.Meta_theory.Models.tarski_to_beeson]
ColG [definition, in GeoCoq.Meta_theory.Models.independent_tarski_to_tarski]
ColH_bets [lemma, in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
colH_trans [lemma, in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
colH_dec [lemma, in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
colH_trivial121 [lemma, in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
colH_trivial122 [lemma, in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
colH_trivial112 [lemma, in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
colH_trivial111 [lemma, in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
colH_permut_321 [lemma, in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
colH_permut_132 [lemma, in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
colH_permut_213 [lemma, in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
colH_permut_312 [lemma, in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
colH_permut_231 [lemma, in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
collect_diffs [lemma, in GeoCoq.Tactics.Coinc.ColR]
collect_cols [lemma, in GeoCoq.Tactics.Coinc.ColR]
collect_wds [lemma, in GeoCoq.Tactics.Coinc.CoincR]
collect_coincs [lemma, in GeoCoq.Tactics.Coinc.CoincR]
collect_wds_for_col [lemma, in GeoCoq.Tactics.Coinc.CoincR_for_col]
collect_coincs_for_col [lemma, in GeoCoq.Tactics.Coinc.CoincR_for_col]
ColR [library]
cols_coincide [lemma, in GeoCoq.Meta_theory.Models.tarski_to_hilbert]
cols_coincide_2 [lemma, in GeoCoq.Meta_theory.Models.tarski_to_hilbert]
cols_coincide_1 [lemma, in GeoCoq.Meta_theory.Models.tarski_to_hilbert]
Col_refl [section, in GeoCoq.Tactics.Coinc.ColR]
Col_dec [lemma, in GeoCoq.Meta_theory.Models.tarski_to_beeson]
col_proj_proj [lemma, in GeoCoq.Highschool.orientation]
col_proj_col [lemma, in GeoCoq.Highschool.orientation]
Col_dec [lemma, in GeoCoq.Tarski_dev.Ch05_bet_le]
col_3 [lemma, in GeoCoq.Tactics.Coinc.tarski_to_coinc_theory_for_col]
col_bd [lemma, in GeoCoq.Tactics.Coinc.tarski_to_coinc_theory_for_col]
col_perm_2 [lemma, in GeoCoq.Tactics.Coinc.tarski_to_coinc_theory_for_col]
col_perm_1 [lemma, in GeoCoq.Tactics.Coinc.tarski_to_coinc_theory_for_col]
col_par [lemma, in GeoCoq.Tarski_dev.Ch12_parallel]
col_not_col_not_par [lemma, in GeoCoq.Tarski_dev.Ch12_parallel]
Col_decG [lemma, in GeoCoq.Meta_theory.Models.independent_tarski_to_tarski]
col_permut321 [lemma, in GeoCoq.Tarski_dev.Annexes.midpoint_theorems]
col_permut312 [lemma, in GeoCoq.Tarski_dev.Annexes.midpoint_theorems]
col_permut231 [lemma, in GeoCoq.Tarski_dev.Annexes.midpoint_theorems]
col_permut213 [lemma, in GeoCoq.Tarski_dev.Annexes.midpoint_theorems]
col_permut132 [lemma, in GeoCoq.Tarski_dev.Annexes.midpoint_theorems]
Col_theory [record, in GeoCoq.Tactics.Coinc.tactics_axioms]
Col_AM_Col [lemma, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
col_defect__out [lemma, in GeoCoq.Meta_theory.Parallel_postulates.legendre]
col_2_le_or_ge [lemma, in GeoCoq.Tarski_dev.Ch14_order]
col_pos_or_neg [lemma, in GeoCoq.Tarski_dev.Ch14_order]
col_coplanar [lemma, in GeoCoq.Tarski_dev.Coplanar_perm]
col_perp_perp_col [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
col_conga_col [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
col_in_angle_out [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
col_in_angle [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
col_per_perp [lemma, in GeoCoq.Tarski_dev.Ch08_orthogonality]
col_col_per_per [lemma, in GeoCoq.Tarski_dev.Ch08_orthogonality]
col_out2_col [lemma, in GeoCoq.Tarski_dev.Ch06_out_lines]
col_transitivity_2 [lemma, in GeoCoq.Tarski_dev.Ch06_out_lines]
col_transitivity_1 [lemma, in GeoCoq.Tarski_dev.Ch06_out_lines]
col_incident [lemma, in GeoCoq.Meta_theory.Models.tarski_to_hilbert]
col_disjoint_bet [lemma, in GeoCoq.Meta_theory.Models.tarski_to_hilbert]
Col_H [definition, in GeoCoq.Meta_theory.Models.tarski_to_hilbert]
col_upper_dim [lemma, in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
col_2_par_projp2_cong [lemma, in GeoCoq.Tarski_dev.Annexes.project]
col_par_projp2_eq [lemma, in GeoCoq.Tarski_dev.Annexes.project]
col_projp_eq [lemma, in GeoCoq.Tarski_dev.Annexes.project]
Col_tagged_Col [lemma, in GeoCoq.Tarski_dev.Annexes.Tagged_predicates]
Col_Col_tagged [lemma, in GeoCoq.Tarski_dev.Annexes.Tagged_predicates]
Col_tagged [definition, in GeoCoq.Tarski_dev.Annexes.Tagged_predicates]
col_two_sides_bet [lemma, in GeoCoq.Tarski_dev.Ch09_plane]
col_one_side_out [lemma, in GeoCoq.Tarski_dev.Ch09_plane]
col_one_side [lemma, in GeoCoq.Tarski_dev.Ch09_plane]
col_two_sides [lemma, in GeoCoq.Tarski_dev.Ch09_plane]
col_eq [lemma, in GeoCoq.Tarski_dev.Ch09_plane]
col_preserves_two_sides [lemma, in GeoCoq.Tarski_dev.Ch09_plane]
col_cong_cong [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals_inter_dec]
col_cong_mid2 [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals]
col_cong_mid1 [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals]
col_bet2_cong2 [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals]
col_bet2_cong1 [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals]
col_cong2_bet4 [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals]
col_cong2_bet3 [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals]
col_cong2_bet2 [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals]
col_cong2_bet1 [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals]
col_cong_bet [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals]
col_not_plgs [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals]
col_cong_mid [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals]
col_trisuma__bet [lemma, in GeoCoq.Tarski_dev.Annexes.suma]
col_par_par_col [lemma, in GeoCoq.Tarski_dev.Ch12_parallel_inter_dec]
col_cong_3_cong_3_eq [lemma, in GeoCoq.Tarski_dev.Ch04_col]
col_trivial_3 [lemma, in GeoCoq.Tarski_dev.Ch04_col]
col_trivial_2 [lemma, in GeoCoq.Tarski_dev.Ch04_col]
col_trivial_1 [lemma, in GeoCoq.Tarski_dev.Ch04_col]
Col_perm [lemma, in GeoCoq.Tarski_dev.Ch04_col]
Col_cases [lemma, in GeoCoq.Tarski_dev.Ch04_col]
col_permutation_5 [lemma, in GeoCoq.Tarski_dev.Ch04_col]
col_permutation_4 [lemma, in GeoCoq.Tarski_dev.Ch04_col]
col_permutation_3 [lemma, in GeoCoq.Tarski_dev.Ch04_col]
col_permutation_2 [lemma, in GeoCoq.Tarski_dev.Ch04_col]
col_permutation_1 [lemma, in GeoCoq.Tarski_dev.Ch04_col]
col123_124__col234 [lemma, in GeoCoq.Tarski_dev.Annexes.midpoint_theorems]
col123_124__col134 [lemma, in GeoCoq.Tarski_dev.Annexes.midpoint_theorems]
col123__nos [lemma, in GeoCoq.Tarski_dev.Ch09_plane]
col124__nos [lemma, in GeoCoq.Tarski_dev.Ch09_plane]
col2_os__os [lemma, in GeoCoq.Tarski_dev.Ch09_plane]
col3 [lemma, in GeoCoq.Tarski_dev.Ch06_out_lines]
compareList [definition, in GeoCoq.Utils.sets]
compareListSpec [lemma, in GeoCoq.Utils.sets]
compareST [definition, in GeoCoq.Utils.sets]
compare_spec [lemma, in GeoCoq.Utils.sets]
compatibility_of_prod_with_order [lemma, in GeoCoq.Tarski_dev.Ch14_order]
compatibility_of_sum_with_order [lemma, in GeoCoq.Tarski_dev.Ch14_order]
concy [definition, in GeoCoq.Tactics.Coinc.tarski_to_coinc_theory_for_concyclic]
Concyclic [definition, in GeoCoq.Highschool.concyclic]
Concyclic [section, in GeoCoq.Highschool.concyclic]
concyclic [library]
concyclic_1123 [lemma, in GeoCoq.Highschool.concyclic]
concyclic_perm_23 [lemma, in GeoCoq.Highschool.concyclic]
concyclic_perm_22 [lemma, in GeoCoq.Highschool.concyclic]
concyclic_perm_21 [lemma, in GeoCoq.Highschool.concyclic]
concyclic_perm_20 [lemma, in GeoCoq.Highschool.concyclic]
concyclic_perm_19 [lemma, in GeoCoq.Highschool.concyclic]
concyclic_perm_18 [lemma, in GeoCoq.Highschool.concyclic]
concyclic_perm_17 [lemma, in GeoCoq.Highschool.concyclic]
concyclic_perm_16 [lemma, in GeoCoq.Highschool.concyclic]
concyclic_perm_15 [lemma, in GeoCoq.Highschool.concyclic]
concyclic_perm_14 [lemma, in GeoCoq.Highschool.concyclic]
concyclic_perm_13 [lemma, in GeoCoq.Highschool.concyclic]
concyclic_perm_12 [lemma, in GeoCoq.Highschool.concyclic]
concyclic_perm_11 [lemma, in GeoCoq.Highschool.concyclic]
concyclic_perm_10 [lemma, in GeoCoq.Highschool.concyclic]
concyclic_perm_9 [lemma, in GeoCoq.Highschool.concyclic]
concyclic_perm_8 [lemma, in GeoCoq.Highschool.concyclic]
concyclic_perm_7 [lemma, in GeoCoq.Highschool.concyclic]
concyclic_perm_6 [lemma, in GeoCoq.Highschool.concyclic]
concyclic_perm_5 [lemma, in GeoCoq.Highschool.concyclic]
concyclic_perm_4 [lemma, in GeoCoq.Highschool.concyclic]
concyclic_perm_3 [lemma, in GeoCoq.Highschool.concyclic]
concyclic_perm_2 [lemma, in GeoCoq.Highschool.concyclic]
concyclic_perm_1 [lemma, in GeoCoq.Highschool.concyclic]
concyclic_trans [lemma, in GeoCoq.Highschool.concyclic]
concyclic_gen_pseudo_trans [lemma, in GeoCoq.Tactics.Coinc.tarski_to_coinc_theory_for_concyclic]
concyclic_gen_1123 [lemma, in GeoCoq.Tactics.Coinc.tarski_to_coinc_theory_for_concyclic]
concyclic_gen_2134 [lemma, in GeoCoq.Tactics.Coinc.tarski_to_coinc_theory_for_concyclic]
concyclic_gen_2341 [lemma, in GeoCoq.Tactics.Coinc.tarski_to_coinc_theory_for_concyclic]
Concyclic_gen [definition, in GeoCoq.Tactics.Coinc.tarski_to_coinc_theory_for_concyclic]
concyclic_not_col_or_eq [lemma, in GeoCoq.Highschool.Euler_line]
concyclic_not_col_or_eq_aux [lemma, in GeoCoq.Highschool.Euler_line]
concy_3 [lemma, in GeoCoq.Tactics.Coinc.tarski_to_coinc_theory_for_concyclic]
concy_trans_1 [lemma, in GeoCoq.Tactics.Coinc.tarski_to_coinc_theory_for_concyclic]
concy_bd [lemma, in GeoCoq.Tactics.Coinc.tarski_to_coinc_theory_for_concyclic]
concy_perm_2 [lemma, in GeoCoq.Tactics.Coinc.tarski_to_coinc_theory_for_concyclic]
concy_perm_1 [lemma, in GeoCoq.Tactics.Coinc.tarski_to_coinc_theory_for_concyclic]
Cond [projection, in GeoCoq.Utils.aux]
Cong [projection, in GeoCoq.Axioms.tarski_axioms]
Cong [definition, in GeoCoq.Meta_theory.Counter_models.counter_model_segment_construction]
Cong [definition, in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
Cong [definition, in GeoCoq.Meta_theory.Counter_models.counter_model_bet_identity]
CongA [definition, in GeoCoq.Tarski_dev.Ch11_angles]
CongaH [projection, in GeoCoq.Axioms.hilbert_axioms]
congaH_outH_congaH [projection, in GeoCoq.Axioms.hilbert_axioms]
congaH_permlr [projection, in GeoCoq.Axioms.hilbert_axioms]
congaH_commr [lemma, in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
congaH_sym [lemma, in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
congaH_existence_congH [lemma, in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
conga_comm [projection, in GeoCoq.Axioms.hilbert_axioms]
conga_refl [projection, in GeoCoq.Axioms.hilbert_axioms]
conga_per2_os__cong [lemma, in GeoCoq.Tarski_dev.Annexes.saccheri]
conga_bet_conga [lemma, in GeoCoq.Tarski_dev.Ch15_lengths]
conga_defect__defect [lemma, in GeoCoq.Meta_theory.Parallel_postulates.legendre]
conga_distinct [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
conga_dec [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
conga_sym_equiv [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
conga_preserves_gta [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
conga_preserves_lta [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
conga__lea456123 [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
conga__lea [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
conga_preserves_in_angle [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
conga_ex_cong3 [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
conga_line [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
conga_comm [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
conga_left_comm [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
conga_right_comm [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
conga_trivial_1 [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
conga_pseudo_refl [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
conga_trans [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
conga_diff56 [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
conga_diff45 [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
conga_diff2 [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
conga_diff1 [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
conga_sym [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
conga_refl [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
conga_preserves_obtuse [lemma, in GeoCoq.Tarski_dev.Ch13_1]
CongA_3 [definition, in GeoCoq.Tarski_dev.Annexes.project]
conga_to_par_os [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals_inter_dec]
conga_to_par_ts [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals_inter_dec]
conga_trisuma__trisuma [lemma, in GeoCoq.Tarski_dev.Annexes.suma]
conga_isi_nos__nts [lemma, in GeoCoq.Tarski_dev.Annexes.suma]
conga2_grada__grada [lemma, in GeoCoq.Meta_theory.Parallel_postulates.angle_archimedes]
conga2_isi__isi [lemma, in GeoCoq.Tarski_dev.Annexes.suma]
conga3_defect__defect [lemma, in GeoCoq.Meta_theory.Parallel_postulates.legendre]
conga3_trisuma__trisuma [lemma, in GeoCoq.Tarski_dev.Annexes.suma]
conga3_suma__suma [lemma, in GeoCoq.Tarski_dev.Annexes.suma]
CongG [projection, in GeoCoq.Axioms.independent_tarski_axioms]
CongH [projection, in GeoCoq.Axioms.hilbert_axioms]
congH_colH_betH [lemma, in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
congH_perml [lemma, in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
congH_perms [lemma, in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
congH_permlr [lemma, in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
congH_sym [lemma, in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
congH_refl [lemma, in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
congH_perm [lemma, in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
CongM [projection, in GeoCoq.Axioms.makarios_variant_axioms]
cong_identity [projection, in GeoCoq.Axioms.tarski_axioms]
cong_inner_transitivity [projection, in GeoCoq.Axioms.tarski_axioms]
cong_pseudo_reflexivity [projection, in GeoCoq.Axioms.tarski_axioms]
cong_stability_eq_stability [lemma, in GeoCoq.Meta_theory.Models.tarski_to_beeson]
cong_stability [lemma, in GeoCoq.Meta_theory.Models.tarski_to_beeson]
cong_le_le [lemma, in GeoCoq.Highschool.orientation]
cong_identity_inv [lemma, in GeoCoq.Highschool.orientation]
cong__le [lemma, in GeoCoq.Tarski_dev.Ch05_bet_le]
Cong_dec [lemma, in GeoCoq.Tarski_dev.Ch05_bet_le]
cong_preserves_le [definition, in GeoCoq.Tarski_dev.Ch05_bet_le]
cong_5 [projection, in GeoCoq.Axioms.hilbert_axioms]
cong_existence [projection, in GeoCoq.Axioms.hilbert_axioms]
cong_pseudo_transitivity [projection, in GeoCoq.Axioms.hilbert_axioms]
cong_permr [projection, in GeoCoq.Axioms.hilbert_axioms]
cong_dec_eq_dec_b [lemma, in GeoCoq.Tarski_dev.Ch03_bet]
cong_conga_perp [lemma, in GeoCoq.Tarski_dev.Ch12_parallel]
cong_identityG [projection, in GeoCoq.Axioms.independent_tarski_axioms]
cong_inner_transitivityG [projection, in GeoCoq.Axioms.independent_tarski_axioms]
cong_pseudo_reflexivityG [projection, in GeoCoq.Axioms.independent_tarski_axioms]
cong_trivial_identityT [lemma, in GeoCoq.Meta_theory.Models.independent_tarski_to_tarski]
cong_inner_transitivityT [lemma, in GeoCoq.Meta_theory.Models.independent_tarski_to_tarski]
cong_inner_transitivity [lemma, in GeoCoq.Meta_theory.Counter_models.counter_model_segment_construction]
cong_identity [lemma, in GeoCoq.Meta_theory.Counter_models.counter_model_segment_construction]
cong_pseudo_reflexivity [lemma, in GeoCoq.Meta_theory.Counter_models.counter_model_segment_construction]
cong_mid__suma [lemma, in GeoCoq.Tarski_dev.Annexes.saccheri]
cong_sac__per [lemma, in GeoCoq.Tarski_dev.Annexes.saccheri]
Cong_AM_Cong [lemma, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
cong_pseudo_reflexivity [lemma, in GeoCoq.Meta_theory.Models.tarski_to_makarios]
cong_left_commutativity [lemma, in GeoCoq.Meta_theory.Models.tarski_to_makarios]
cong_symmetry [lemma, in GeoCoq.Meta_theory.Models.tarski_to_makarios]
cong_reflexivity [lemma, in GeoCoq.Meta_theory.Models.tarski_to_makarios]
Cong_perm [lemma, in GeoCoq.Tarski_dev.Ch02_cong]
Cong_cases [lemma, in GeoCoq.Tarski_dev.Ch02_cong]
cong_3_swap_2 [lemma, in GeoCoq.Tarski_dev.Ch02_cong]
cong_3_swap [lemma, in GeoCoq.Tarski_dev.Ch02_cong]
cong_3_sym [lemma, in GeoCoq.Tarski_dev.Ch02_cong]
Cong_3 [definition, in GeoCoq.Tarski_dev.Ch02_cong]
cong_diff_4 [lemma, in GeoCoq.Tarski_dev.Ch02_cong]
cong_diff_3 [lemma, in GeoCoq.Tarski_dev.Ch02_cong]
cong_diff_2 [lemma, in GeoCoq.Tarski_dev.Ch02_cong]
cong_diff [lemma, in GeoCoq.Tarski_dev.Ch02_cong]
cong_commutativity [lemma, in GeoCoq.Tarski_dev.Ch02_cong]
cong_reverse_identity [lemma, in GeoCoq.Tarski_dev.Ch02_cong]
cong_trivial_identity [lemma, in GeoCoq.Tarski_dev.Ch02_cong]
cong_4321 [lemma, in GeoCoq.Tarski_dev.Ch02_cong]
cong_4312 [lemma, in GeoCoq.Tarski_dev.Ch02_cong]
cong_3421 [lemma, in GeoCoq.Tarski_dev.Ch02_cong]
cong_right_commutativity [lemma, in GeoCoq.Tarski_dev.Ch02_cong]
cong_left_commutativity [lemma, in GeoCoq.Tarski_dev.Ch02_cong]
cong_transitivity [lemma, in GeoCoq.Tarski_dev.Ch02_cong]
cong_symmetry [lemma, in GeoCoq.Tarski_dev.Ch02_cong]
cong_reflexivity [lemma, in GeoCoq.Tarski_dev.Ch02_cong]
cong_mid2__cong13 [lemma, in GeoCoq.Tarski_dev.Ch07_midpoint]
cong_cong_half_2 [lemma, in GeoCoq.Tarski_dev.Ch07_midpoint]
cong_cong_half_1 [lemma, in GeoCoq.Tarski_dev.Ch07_midpoint]
cong_col_mid [lemma, in GeoCoq.Tarski_dev.Ch07_midpoint]
cong_perp_conga [lemma, in GeoCoq.Tarski_dev.Ch13_1]
cong_preserves_bet [lemma, in GeoCoq.Tarski_dev.Ch06_out_lines]
cong_3_3_cong_5 [lemma, in GeoCoq.Tarski_dev.Ch16_coordinates]
Cong_5 [definition, in GeoCoq.Tarski_dev.Ch16_coordinates]
cong_3_2_cong_4 [lemma, in GeoCoq.Tarski_dev.Ch16_coordinates]
Cong_4 [definition, in GeoCoq.Tarski_dev.Ch16_coordinates]
cong_permT [lemma, in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
cong_transitivity [lemma, in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
cong_preserves_bet [lemma, in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
cong_preserves_col_stronger [lemma, in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
cong_preserves_col [lemma, in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
cong_trans [lemma, in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
cong_sym [lemma, in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
cong_distincts [lemma, in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
cong_inner_transitivity [lemma, in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
cong_identity [lemma, in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
cong_aux_6 [lemma, in GeoCoq.Meta_theory.Counter_models.counter_model_bet_identity]
cong_aux_5 [lemma, in GeoCoq.Meta_theory.Counter_models.counter_model_bet_identity]
cong_aux_4 [lemma, in GeoCoq.Meta_theory.Counter_models.counter_model_bet_identity]
cong_aux_3 [lemma, in GeoCoq.Meta_theory.Counter_models.counter_model_bet_identity]
cong_aux_2 [lemma, in GeoCoq.Meta_theory.Counter_models.counter_model_bet_identity]
cong_aux [lemma, in GeoCoq.Meta_theory.Counter_models.counter_model_bet_identity]
cong_sym [lemma, in GeoCoq.Meta_theory.Counter_models.counter_model_bet_identity]
cong_inner_transitivity [lemma, in GeoCoq.Meta_theory.Counter_models.counter_model_bet_identity]
cong_identity [lemma, in GeoCoq.Meta_theory.Counter_models.counter_model_bet_identity]
cong_pseudo_reflexivity [lemma, in GeoCoq.Meta_theory.Counter_models.counter_model_bet_identity]
cong_conga3_cong3 [lemma, in GeoCoq.Tarski_dev.Annexes.project]
cong_perp_bisect_col [lemma, in GeoCoq.Tarski_dev.Annexes.perp_bisect]
cong_perp_bisect [lemma, in GeoCoq.Tarski_dev.Annexes.perp_bisect]
Cong_tagged_Cong [lemma, in GeoCoq.Tarski_dev.Annexes.Tagged_predicates]
Cong_Cong_tagged [lemma, in GeoCoq.Tarski_dev.Annexes.Tagged_predicates]
Cong_tagged [definition, in GeoCoq.Tarski_dev.Annexes.Tagged_predicates]
cong_dec_eq_dec [lemma, in GeoCoq.Meta_theory.Decidability.equivalence_between_decidability_properties_of_basic_relations]
cong_le_le [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals]
cong_identity_inv [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals]
cong_sum [lemma, in GeoCoq.Tarski_dev.Ch14_sum]
Cong_stability [projection, in GeoCoq.Axioms.beeson_s_axioms]
cong2_lt__lt [lemma, in GeoCoq.Tarski_dev.Ch05_bet_le]
cong2_sac2__cong [lemma, in GeoCoq.Tarski_dev.Annexes.saccheri]
cong2_lam2__conga [lemma, in GeoCoq.Tarski_dev.Annexes.saccheri]
cong2_lam2__cong [lemma, in GeoCoq.Tarski_dev.Annexes.saccheri]
cong2_conga_cong [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
cong3_symmetry [lemma, in GeoCoq.Tarski_dev.Ch05_bet_le]
cong3_bet_eq [lemma, in GeoCoq.Tarski_dev.Ch04_cong_bet]
cong3_transitivity [lemma, in GeoCoq.Tarski_dev.Ch02_cong]
cong3_preserves_out [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
cong3_conga2 [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
cong3_conga [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
cong3_diff2 [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
cong3_diff [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
cong3_par2_par [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals_inter_dec]
cong3_id [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals]
consecutive_interior__alternate_interior [lemma, in GeoCoq.Meta_theory.Parallel_postulates.consecutive_interior_angles_alternate_interior_angles]
consecutive_interior_angles_alternate_interior_angles [section, in GeoCoq.Meta_theory.Parallel_postulates.consecutive_interior_angles_alternate_interior_angles]
consecutive_interior_angles_postulate [definition, in GeoCoq.Meta_theory.Parallel_postulates.Euclid_def]
consecutive_interior_angles_alternate_interior_angles [library]
consHdInterpOK [lemma, in GeoCoq.Tactics.Coinc.CoincR]
consHdTlTlHd [lemma, in GeoCoq.Utils.arity]
consHeadCP [definition, in GeoCoq.Utils.arity]
consHeadCPHd [lemma, in GeoCoq.Utils.arity]
consHeadCPOK [lemma, in GeoCoq.Utils.arity]
consHeadCPTl [lemma, in GeoCoq.Utils.arity]
consTailCP [definition, in GeoCoq.Utils.arity]
consTailCPAbl [lemma, in GeoCoq.Utils.arity]
consTailCPLast [lemma, in GeoCoq.Utils.arity]
consTailCPOK [lemma, in GeoCoq.Utils.arity]
consTailCPTl [lemma, in GeoCoq.Utils.arity]
consTailCPTlD [lemma, in GeoCoq.Utils.arity]
consTailOK [lemma, in GeoCoq.Utils.arity]
consTailPerm [lemma, in GeoCoq.Utils.arity]
consTlHdHdTl [lemma, in GeoCoq.Utils.arity]
construction_uniquenessT [lemma, in GeoCoq.Meta_theory.Models.independent_tarski_to_tarski]
construction_uniqueness [lemma, in GeoCoq.Tarski_dev.Ch02_cong]
construction_uniqueness [lemma, in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
construct_triangle [lemma, in GeoCoq.Highschool.orthocenter]
construct_intersection [lemma, in GeoCoq.Highschool.orthocenter]
coordinates_of_point_F [lemma, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
coordinates_of_point_f [lemma, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
coordinates_of_point [lemma, in GeoCoq.Tarski_dev.Ch16_coordinates]
coord_exchange_axes [lemma, in GeoCoq.Tarski_dev.Ch16_coordinates]
cop [definition, in GeoCoq.Tactics.Coinc.tarski_to_coinc_theory_for_cop]
Coplanar [definition, in GeoCoq.Tarski_dev.Coplanar_perm]
coplanar_pseudo_trans [lemma, in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1 [lemma, in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4 [lemma, in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_3 [lemma, in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_3_3 [lemma, in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_3_3_3 [lemma, in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_3_3_2 [lemma, in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_3_3_2_3 [lemma, in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_3_3_2_2 [lemma, in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_3_3_2_1 [lemma, in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_3_3_1 [lemma, in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_3_2 [lemma, in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_3_2_3 [lemma, in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_3_2_3_3 [lemma, in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_3_2_3_2 [lemma, in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_3_2_3_1 [lemma, in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_3_2_2 [lemma, in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_3_2_1 [lemma, in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_3_2_1_3 [lemma, in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_3_2_1_2 [lemma, in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_3_2_1_1 [lemma, in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_3_1 [lemma, in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_3_1_3 [lemma, in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_3_1_3_3 [lemma, in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_3_1_3_2 [lemma, in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_3_1_3_1 [lemma, in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_3_1_2 [lemma, in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_3_1_1 [lemma, in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_3_1_1_3 [lemma, in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_3_1_1_2 [lemma, in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_3_1_1_1 [lemma, in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_2 [lemma, in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_2_3 [lemma, in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_2_3_3 [lemma, in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_2_3_2 [lemma, in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_2_3_2_3 [lemma, in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_2_3_2_2 [lemma, in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_2_3_2_1 [lemma, in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_2_3_1 [lemma, in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_2_2 [lemma, in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_2_2_3 [lemma, in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_2_2_3_3 [lemma, in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_2_2_3_2 [lemma, in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_2_2_3_1 [lemma, in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_2_2_2 [lemma, in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_2_2_1 [lemma, in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_2_2_1_3 [lemma, in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_2_2_1_2 [lemma, in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_2_2_1_1 [lemma, in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_2_1 [lemma, in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_2_1_3 [lemma, in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_2_1_3_3 [lemma, in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_2_1_3_2 [lemma, in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_2_1_3_1 [lemma, in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_2_1_2 [lemma, in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_2_1_2_3 [lemma, in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_2_1_2_2 [lemma, in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_2_1_2_1 [lemma, in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_2_1_1 [lemma, in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_2_1_1_3 [lemma, in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_2_1_1_2 [lemma, in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_2_1_1_1 [lemma, in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_1 [lemma, in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_1_3 [lemma, in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_1_3_3 [lemma, in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_1_3_3_3 [lemma, in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_1_3_3_2 [lemma, in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_1_3_3_1 [lemma, in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_1_3_2 [lemma, in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_1_3_2_3 [lemma, in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_1_3_2_2 [lemma, in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_1_3_2_1 [lemma, in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_1_3_1 [lemma, in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_1_3_1_3 [lemma, in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_1_3_1_2 [lemma, in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_1_3_1_1 [lemma, in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_1_2 [lemma, in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_1_2_3 [lemma, in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_1_2_2 [lemma, in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_1_2_2_3 [lemma, in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_1_2_2_2 [lemma, in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_1_2_2_1 [lemma, in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_1_2_1 [lemma, in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_1_1 [lemma, in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_1_1_3 [lemma, in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_1_1_2 [lemma, in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_1_1_2_3 [lemma, in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_1_1_2_2 [lemma, in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_1_1_2_1 [lemma, in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_1_1_1 [lemma, in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_3 [lemma, in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_3_3_3 [lemma, in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_3_3_3_3 [lemma, in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_3_3_3_3_3 [lemma, in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_3_3_3_3_2 [lemma, in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_3_3_3_3_1 [lemma, in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_3_3_3_2 [lemma, in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_3_3_3_2_3 [lemma, in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_3_3_3_2_2 [lemma, in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_3_3_3_2_1 [lemma, in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_3_3_3_1 [lemma, in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_3_3_3_1_3 [lemma, in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_3_3_3_1_2 [lemma, in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_3_3_3_1_1 [lemma, in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_3_2_3 [lemma, in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_3_2_2 [lemma, in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_3_1_3 [lemma, in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_3_1_2 [lemma, in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_3_1_2_3 [lemma, in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_3_1_2_3_3 [lemma, in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_3_1_2_3_2 [lemma, in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_3_1_2_3_1 [lemma, in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_3_1_2_2 [lemma, in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_3_1_2_2_3 [lemma, in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_3_1_2_2_2 [lemma, in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_3_1_2_2_1 [lemma, in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_3_1_2_1 [lemma, in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_3_1_2_1_3 [lemma, in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_3_1_2_1_2 [lemma, in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_3_1_2_1_1 [lemma, in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_3_1_1 [lemma, in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_2 [lemma, in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_2_3_3 [lemma, in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_2_3_3_2_2 [lemma, in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_2_3_3_1_3 [lemma, in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_2_3_3_1_2 [lemma, in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_2_3_3_1_1 [lemma, in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_2_2_3 [lemma, in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_2_2_2 [lemma, in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_2_2_2_2_2 [lemma, in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_2_2_2_1_3 [lemma, in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_2_2_2_1_2 [lemma, in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_2_2_2_1_1 [lemma, in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_2_1_3 [lemma, in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_2_1_3_3_3 [lemma, in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_2_1_3_2_3 [lemma, in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_2_1_3_2_2 [lemma, in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_2_1_3_1_3 [lemma, in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_2_1_3_1_2 [lemma, in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_2_1_3_1_1 [lemma, in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_2_1_2 [lemma, in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_2_1_1 [lemma, in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_2_1_1_2_2 [lemma, in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_2_1_1_1_3 [lemma, in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_2_1_1_1_2 [lemma, in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_2_1_1_1_1 [lemma, in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_1 [lemma, in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_1_3_3 [lemma, in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_1_2_3 [lemma, in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_1_2_2 [lemma, in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_1_1_3 [lemma, in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_1_1_2 [lemma, in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_1_1_1 [lemma, in GeoCoq.Tarski_dev.Coplanar_trans]
Coplanar_trans [section, in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trivial [lemma, in GeoCoq.Tarski_dev.Coplanar_perm]
coplanar_perm_23 [lemma, in GeoCoq.Tarski_dev.Coplanar_perm]
coplanar_perm_22 [lemma, in GeoCoq.Tarski_dev.Coplanar_perm]
coplanar_perm_21 [lemma, in GeoCoq.Tarski_dev.Coplanar_perm]
coplanar_perm_20 [lemma, in GeoCoq.Tarski_dev.Coplanar_perm]
coplanar_perm_19 [lemma, in GeoCoq.Tarski_dev.Coplanar_perm]
coplanar_perm_18 [lemma, in GeoCoq.Tarski_dev.Coplanar_perm]
coplanar_perm_17 [lemma, in GeoCoq.Tarski_dev.Coplanar_perm]
coplanar_perm_16 [lemma, in GeoCoq.Tarski_dev.Coplanar_perm]
coplanar_perm_15 [lemma, in GeoCoq.Tarski_dev.Coplanar_perm]
coplanar_perm_14 [lemma, in GeoCoq.Tarski_dev.Coplanar_perm]
coplanar_perm_13 [lemma, in GeoCoq.Tarski_dev.Coplanar_perm]
coplanar_perm_12 [lemma, in GeoCoq.Tarski_dev.Coplanar_perm]
coplanar_perm_11 [lemma, in GeoCoq.Tarski_dev.Coplanar_perm]
coplanar_perm_10 [lemma, in GeoCoq.Tarski_dev.Coplanar_perm]
coplanar_perm_9 [lemma, in GeoCoq.Tarski_dev.Coplanar_perm]
coplanar_perm_8 [lemma, in GeoCoq.Tarski_dev.Coplanar_perm]
coplanar_perm_7 [lemma, in GeoCoq.Tarski_dev.Coplanar_perm]
coplanar_perm_6 [lemma, in GeoCoq.Tarski_dev.Coplanar_perm]
coplanar_perm_5 [lemma, in GeoCoq.Tarski_dev.Coplanar_perm]
coplanar_perm_4 [lemma, in GeoCoq.Tarski_dev.Coplanar_perm]
coplanar_perm_3 [lemma, in GeoCoq.Tarski_dev.Coplanar_perm]
coplanar_perm_2 [lemma, in GeoCoq.Tarski_dev.Coplanar_perm]
coplanar_perm_1 [lemma, in GeoCoq.Tarski_dev.Coplanar_perm]
Coplanar_perm [section, in GeoCoq.Tarski_dev.Coplanar_perm]
Coplanar_perm [library]
Coplanar_trans [library]
cop_per_per_col [lemma, in GeoCoq.Meta_theory.Dimension_axioms.upper_dim]
cop_3 [lemma, in GeoCoq.Tactics.Coinc.tarski_to_coinc_theory_for_cop]
cop_bd [lemma, in GeoCoq.Tactics.Coinc.tarski_to_coinc_theory_for_cop]
cop_perm_2 [lemma, in GeoCoq.Tactics.Coinc.tarski_to_coinc_theory_for_cop]
cop_perm_1 [lemma, in GeoCoq.Tactics.Coinc.tarski_to_coinc_theory_for_cop]
Cosinus [section, in GeoCoq.Tarski_dev.Ch13_4_cos]
Cosinus2 [section, in GeoCoq.Tarski_dev.Ch13_4_cos]
counter_model_segment_construction [library]
counter_model_bet_identity [library]
Couple [record, in GeoCoq.Utils.aux]
co_side [lemma, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
CPCPL [lemma, in GeoCoq.Utils.arity]
CPLCP [lemma, in GeoCoq.Utils.arity]
CPLHd [lemma, in GeoCoq.Utils.arity]
CPLHdTlOK [lemma, in GeoCoq.Utils.arity]
CPLOCPTlOK [lemma, in GeoCoq.Utils.sets]
CPLOK [lemma, in GeoCoq.Utils.arity]
CPLRec [lemma, in GeoCoq.Utils.arity]
CPPair [definition, in GeoCoq.Utils.arity]
CPToList [definition, in GeoCoq.Utils.arity]
CPToListOK [lemma, in GeoCoq.Utils.arity]
CPToListTl1 [lemma, in GeoCoq.Utils.arity]
CPToListTl2 [lemma, in GeoCoq.Utils.arity]
CPToSS [definition, in GeoCoq.Tactics.Coinc.CoincR]
CPToSSHdTl [lemma, in GeoCoq.Tactics.Coinc.CoincR]
CPToSSOK [lemma, in GeoCoq.Tactics.Coinc.CoincR]
CPToSSOKAux [lemma, in GeoCoq.Tactics.Coinc.CoincR]
CP_ind [lemma, in GeoCoq.Utils.arity]
cross_product [definition, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
Cs [definition, in GeoCoq.Tarski_dev.Ch16_coordinates]
Cs_not_Col [lemma, in GeoCoq.Tarski_dev.Ch16_coordinates]
CTcol_trivial_2 [lemma, in GeoCoq.Tactics.Coinc.ColR]
CTcol_trivial_1 [lemma, in GeoCoq.Tactics.Coinc.ColR]
CTcol_permutation_4 [lemma, in GeoCoq.Tactics.Coinc.ColR]
CTcol_permutation_3 [lemma, in GeoCoq.Tactics.Coinc.ColR]
CTcol_permutation_2 [lemma, in GeoCoq.Tactics.Coinc.ColR]
CTcol_permutation_5 [lemma, in GeoCoq.Tactics.Coinc.ColR]
CTcol_permutation_2 [projection, in GeoCoq.Tactics.Coinc.tactics_axioms]
CTcol_permutation_1 [projection, in GeoCoq.Tactics.Coinc.tactics_axioms]
CTcol_trivial [projection, in GeoCoq.Tactics.Coinc.tactics_axioms]
CTcol3 [projection, in GeoCoq.Tactics.Coinc.tactics_axioms]
cut [definition, in GeoCoq.Meta_theory.Models.tarski_to_hilbert]
cut_two_sides [lemma, in GeoCoq.Meta_theory.Models.tarski_to_hilbert]
cut_morphism [instance, in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
cut_same_side_cut [lemma, in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
cut_distinct [lemma, in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
cut_exists [lemma, in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
cut_comm [lemma, in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
cut' [definition, in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
cut'_comm [lemma, in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
cut2_not_cut [lemma, in GeoCoq.Meta_theory.Models.hilbert_to_tarski]


D

decidability_of_intersection [definition, in GeoCoq.Meta_theory.Parallel_postulates.Euclid_def]
decidability_of_not_intersection [definition, in GeoCoq.Meta_theory.Parallel_postulates.Euclid_def]
decidability_of_parallelism [definition, in GeoCoq.Meta_theory.Parallel_postulates.Euclid_def]
decidability_of_betweenness_of_points [definition, in GeoCoq.Meta_theory.Decidability.equivalence_between_decidability_properties_of_basic_relations]
decidability_of_congruence_of_points [definition, in GeoCoq.Meta_theory.Decidability.equivalence_between_decidability_properties_of_basic_relations]
decidability_of_equality_of_points [definition, in GeoCoq.Meta_theory.Decidability.equivalence_between_decidability_properties_of_basic_relations]
Defect [definition, in GeoCoq.Meta_theory.Parallel_postulates.legendre]
defect_ncol_out__rah [lemma, in GeoCoq.Meta_theory.Parallel_postulates.legendre]
defect_perm_132 [lemma, in GeoCoq.Meta_theory.Parallel_postulates.legendre]
defect_perm_213 [lemma, in GeoCoq.Meta_theory.Parallel_postulates.legendre]
defect_perm_321 [lemma, in GeoCoq.Meta_theory.Parallel_postulates.legendre]
defect_perm_312 [lemma, in GeoCoq.Meta_theory.Parallel_postulates.legendre]
defect_perm_231 [lemma, in GeoCoq.Meta_theory.Parallel_postulates.legendre]
defect_distincts [lemma, in GeoCoq.Meta_theory.Parallel_postulates.legendre]
defect2__conga [lemma, in GeoCoq.Meta_theory.Parallel_postulates.legendre]
degenerated_rect_eq [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals_inter_dec]
Desargues_Hessenberg [section, in GeoCoq.Tarski_dev.Ch13_6_Desargues_Hessenberg]
diff [definition, in GeoCoq.Tactics.Coinc.tarski_to_coinc_theory_for_col]
Diff [definition, in GeoCoq.Tarski_dev.Ch14_sum]
Diff_Col_ColB [lemma, in GeoCoq.Meta_theory.Models.tarski_to_beeson]
diff_perm_2 [lemma, in GeoCoq.Tactics.Coinc.tarski_to_coinc_theory_for_col]
diff_perm_1 [lemma, in GeoCoq.Tactics.Coinc.tarski_to_coinc_theory_for_col]
diff_f [lemma, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
diff_col [lemma, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
diff_not_col_col_par4_mid [lemma, in GeoCoq.Highschool.orthocenter]
diff_2_le_le [lemma, in GeoCoq.Tarski_dev.Ch14_order]
diff_pos_diff_neg [lemma, in GeoCoq.Tarski_dev.Ch14_order]
diff_per_diff [lemma, in GeoCoq.Tarski_dev.Ch08_orthogonality]
diff_2_prod [lemma, in GeoCoq.Tarski_dev.Ch14_prod]
diff_of_squares [lemma, in GeoCoq.Tarski_dev.Ch14_prod]
Diff_perm [lemma, in GeoCoq.Tarski_dev.Annexes.Tagged_predicates]
Diff_tagged_Diff [lemma, in GeoCoq.Tarski_dev.Annexes.Tagged_predicates]
Diff_Diff_tagged [lemma, in GeoCoq.Tarski_dev.Annexes.Tagged_predicates]
Diff_tagged [definition, in GeoCoq.Tarski_dev.Annexes.Tagged_predicates]
diff_col_ex3 [lemma, in GeoCoq.Tarski_dev.Ch09_plane]
diff_bet_ex3 [lemma, in GeoCoq.Tarski_dev.Ch09_plane]
diff_col_ex [lemma, in GeoCoq.Tarski_dev.Ch09_plane]
diff_to_plg [lemma, in GeoCoq.Tarski_dev.Ch14_sum]
diff_stable [lemma, in GeoCoq.Tarski_dev.Ch14_sum]
diff_opp [lemma, in GeoCoq.Tarski_dev.Ch14_sum]
diff_sum [lemma, in GeoCoq.Tarski_dev.Ch14_sum]
diff_null_eq [lemma, in GeoCoq.Tarski_dev.Ch14_sum]
diff_uniquenessB [lemma, in GeoCoq.Tarski_dev.Ch14_sum]
diff_uniquenessA [lemma, in GeoCoq.Tarski_dev.Ch14_sum]
diff_O_A_opp [lemma, in GeoCoq.Tarski_dev.Ch14_sum]
diff_O_A [lemma, in GeoCoq.Tarski_dev.Ch14_sum]
diff_A_O [lemma, in GeoCoq.Tarski_dev.Ch14_sum]
diff_uniqueness [lemma, in GeoCoq.Tarski_dev.Ch14_sum]
diff_exists [lemma, in GeoCoq.Tarski_dev.Ch14_sum]
diff_null [lemma, in GeoCoq.Tarski_dev.Ch14_sum]
diff_ar2 [lemma, in GeoCoq.Tarski_dev.Ch14_sum]
disjoint [definition, in GeoCoq.Meta_theory.Models.tarski_to_hilbert]
distinct [lemma, in GeoCoq.Tarski_dev.Ch08_orthogonality]
distinct [lemma, in GeoCoq.Tarski_dev.Ch09_plane]
DistLn [definition, in GeoCoq.Tarski_dev.Ch08_orthogonality]
distr_l_diff [lemma, in GeoCoq.Tarski_dev.Ch14_prod]
distr_r [lemma, in GeoCoq.Tarski_dev.Ch14_prod]
distr_l [lemma, in GeoCoq.Tarski_dev.Ch14_prod]
div [definition, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
DivF [definition, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
divF_morphism [instance, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
div_f [lemma, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
div_col [lemma, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
div_uniqueness [lemma, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
div_exists [lemma, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
double_not_null_not_nul [lemma, in GeoCoq.Tarski_dev.Ch14_sum]
double_null_null [lemma, in GeoCoq.Tarski_dev.Ch14_sum]


E

Eq [definition, in GeoCoq.Meta_theory.Models.tarski_to_hilbert]
EqA [definition, in GeoCoq.Tarski_dev.Ch13_3_angles]
eqA_preserves_anga [lemma, in GeoCoq.Tarski_dev.Ch13_3_angles]
eqA_preserves_ang [lemma, in GeoCoq.Tarski_dev.Ch13_3_angles]
eqA_equivalence [instance, in GeoCoq.Tarski_dev.Ch13_3_angles]
eqbList [definition, in GeoCoq.Utils.sets]
eqbListEqList [lemma, in GeoCoq.Utils.sets]
eqbST [definition, in GeoCoq.Utils.sets]
eqbST_eqST [lemma, in GeoCoq.Utils.sets]
EqF [definition, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
eqF_Equivalence [instance, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
eqF_Transitive [instance, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
eqF_Symmetric [instance, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
eqF_Reflexive [instance, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
EqL [projection, in GeoCoq.Axioms.hilbert_axioms]
EqL [definition, in GeoCoq.Tarski_dev.Ch13_2_length]
eqList [definition, in GeoCoq.Utils.sets]
eqListOK [lemma, in GeoCoq.Utils.sets]
eqListRefl [lemma, in GeoCoq.Utils.sets]
eqListSortOCP [lemma, in GeoCoq.Utils.sets]
eqListSym [lemma, in GeoCoq.Utils.sets]
eqListTrans [lemma, in GeoCoq.Utils.sets]
EqL_Equiv [projection, in GeoCoq.Axioms.hilbert_axioms]
eql_lcos_null [lemma, in GeoCoq.Tarski_dev.Ch13_4_cos]
eqL_equivalence [instance, in GeoCoq.Tarski_dev.Ch13_2_length]
eqo [definition, in GeoCoq.Highschool.orientation]
eqop [definition, in GeoCoq.Tactics.Coinc.ColR]
eqop [definition, in GeoCoq.Tactics.Coinc.CoincR]
eqopp [definition, in GeoCoq.Tactics.Coinc.ColR]
eqopp [definition, in GeoCoq.Tactics.Coinc.CoincR]
eqo_refl [lemma, in GeoCoq.Highschool.orientation]
eqo_one_side [lemma, in GeoCoq.Highschool.orientation]
eqo_eq_o [lemma, in GeoCoq.Highschool.orientation]
eqST [definition, in GeoCoq.Utils.sets]
eqST_dec [lemma, in GeoCoq.Utils.sets]
equality_foot_out_out [lemma, in GeoCoq.Highschool.bisector]
equilateral [definition, in GeoCoq.Highschool.triangles]
equilateral_strict_conga_3 [lemma, in GeoCoq.Highschool.triangles]
equilateral_strict_conga_2 [lemma, in GeoCoq.Highschool.triangles]
equilateral_strict_conga_1 [lemma, in GeoCoq.Highschool.triangles]
equilateral_strict__not_col [lemma, in GeoCoq.Highschool.triangles]
equilateral_strict_swap_5 [lemma, in GeoCoq.Highschool.triangles]
equilateral_strict_swap_4 [lemma, in GeoCoq.Highschool.triangles]
equilateral_strict_swap_3 [lemma, in GeoCoq.Highschool.triangles]
equilateral_strict_swap_2 [lemma, in GeoCoq.Highschool.triangles]
equilateral_strict_swap_1 [lemma, in GeoCoq.Highschool.triangles]
equilateral_strict_neq [lemma, in GeoCoq.Highschool.triangles]
equilateral_isosceles_3 [lemma, in GeoCoq.Highschool.triangles]
equilateral_isosceles_2 [lemma, in GeoCoq.Highschool.triangles]
equilateral_isosceles_1 [lemma, in GeoCoq.Highschool.triangles]
equilateral_swap_rot [lemma, in GeoCoq.Highschool.triangles]
equilateral_swap_2 [lemma, in GeoCoq.Highschool.triangles]
equilateral_rot_2 [lemma, in GeoCoq.Highschool.triangles]
equilateral_swap [lemma, in GeoCoq.Highschool.triangles]
equilateral_rot [lemma, in GeoCoq.Highschool.triangles]
equilateral_cong [lemma, in GeoCoq.Highschool.triangles]
equilateral_strict_equilateral [lemma, in GeoCoq.Highschool.triangles]
equilateral_strict [definition, in GeoCoq.Highschool.triangles]
equivalence_of_aristotle_greenberg_and_decidability_of_intersection [lemma, in GeoCoq.Meta_theory.Parallel_postulates.Euclid]
equivalence_between_decidability_properties_of_basic_relations [lemma, in GeoCoq.Meta_theory.Decidability.equivalence_between_decidability_properties_of_basic_relations]
Equivalence_between_decidability_properties_of_basic_relations [section, in GeoCoq.Meta_theory.Decidability.equivalence_between_decidability_properties_of_basic_relations]
equivalence_between_decidability_properties_of_basic_relations [library]
equivalent_parallel_postulates_without_any_continuity_bis [lemma, in GeoCoq.Meta_theory.Parallel_postulates.Euclid]
equivalent_parallel_postulates_assuming_greenberg_s_postulate [lemma, in GeoCoq.Meta_theory.Parallel_postulates.Euclid]
equivalent_parallel_postulates_without_decidability_of_intersection_of_lines_bis [lemma, in GeoCoq.Meta_theory.Parallel_postulates.Euclid]
equivalent_parallel_postulates_with_decidability_of_intersection_of_lines [lemma, in GeoCoq.Meta_theory.Parallel_postulates.Euclid]
equivalent_parallel_postulates_without_any_continuity [lemma, in GeoCoq.Meta_theory.Parallel_postulates.Euclid]
equivalent_parallel_postulates_without_decidability_of_intersection_of_lines [lemma, in GeoCoq.Meta_theory.Parallel_postulates.Euclid]
EqV [definition, in GeoCoq.Tarski_dev.Annexes.vectors]
eqv_cong [lemma, in GeoCoq.Tarski_dev.Annexes.project]
eqv_eq_project [lemma, in GeoCoq.Tarski_dev.Annexes.project]
eqv_project_eq_eq [lemma, in GeoCoq.Tarski_dev.Annexes.project]
eqv_mid [lemma, in GeoCoq.Tarski_dev.Annexes.vectors]
eqv_sum [lemma, in GeoCoq.Tarski_dev.Annexes.vectors]
eqv_opp_null [lemma, in GeoCoq.Tarski_dev.Annexes.vectors]
eqv_par [lemma, in GeoCoq.Tarski_dev.Annexes.vectors]
eqv_permut [lemma, in GeoCoq.Tarski_dev.Annexes.vectors]
eqv_trivial [lemma, in GeoCoq.Tarski_dev.Annexes.vectors]
eqv_comm [lemma, in GeoCoq.Tarski_dev.Annexes.vectors]
eqv_trans [lemma, in GeoCoq.Tarski_dev.Annexes.vectors]
eqv_sym [lemma, in GeoCoq.Tarski_dev.Annexes.vectors]
eqv_refl [lemma, in GeoCoq.Tarski_dev.Annexes.vectors]
eq_eq_tagged [lemma, in GeoCoq.Tactics.Coinc.ColR]
eq_tagged [definition, in GeoCoq.Tactics.Coinc.ColR]
eq_dec_points_from_classic [lemma, in GeoCoq.Meta_theory.Models.tarski_to_beeson]
eq_dec [lemma, in GeoCoq.Meta_theory.Models.tarski_to_beeson]
eq_o_refl [lemma, in GeoCoq.Highschool.orientation]
eq_o_one_side [lemma, in GeoCoq.Highschool.orientation]
eq_o_eqo [lemma, in GeoCoq.Highschool.orientation]
eq_o [definition, in GeoCoq.Highschool.orientation]
eq_dec_pointsH [projection, in GeoCoq.Axioms.hilbert_axioms]
Eq_Lcos3 [definition, in GeoCoq.Tarski_dev.Ch13_4_cos]
Eq_Lcos2 [definition, in GeoCoq.Tarski_dev.Ch13_4_cos]
Eq_Lcos [definition, in GeoCoq.Tarski_dev.Ch13_4_cos]
eq_dec_F [lemma, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
eq_dec_points [lemma, in GeoCoq.Tarski_dev.Ch02_cong]
eq_conga_out [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
eq_incident [lemma, in GeoCoq.Meta_theory.Models.tarski_to_hilbert]
Eq_Equiv [instance, in GeoCoq.Meta_theory.Models.tarski_to_hilbert]
eq_symmetry [lemma, in GeoCoq.Meta_theory.Models.tarski_to_hilbert]
eq_reflexivity [lemma, in GeoCoq.Meta_theory.Models.tarski_to_hilbert]
eq_transitivity [lemma, in GeoCoq.Meta_theory.Models.tarski_to_hilbert]
eq_points_coordinates [lemma, in GeoCoq.Tarski_dev.Ch16_coordinates]
eq_squares_eq_or_opp [lemma, in GeoCoq.Tarski_dev.Ch14_prod]
eq_dec_bet_dec [lemma, in GeoCoq.Meta_theory.Decidability.equivalence_between_decidability_properties_of_basic_relations]
eq_dec_implies_between_cong_3 [lemma, in GeoCoq.Meta_theory.Decidability.equivalence_between_decidability_properties_of_basic_relations]
eq_dec_cong_dec [lemma, in GeoCoq.Meta_theory.Decidability.equivalence_between_decidability_properties_of_basic_relations]
eq_dec_implies_between_cong [lemma, in GeoCoq.Meta_theory.Decidability.equivalence_between_decidability_properties_of_basic_relations]
eq_dec_implies_segment_construction_2 [lemma, in GeoCoq.Meta_theory.Decidability.equivalence_between_decidability_properties_of_basic_relations]
eq_dec_implies_l5_2 [lemma, in GeoCoq.Meta_theory.Decidability.equivalence_between_decidability_properties_of_basic_relations]
eq_dec_implies_l5_1 [lemma, in GeoCoq.Meta_theory.Decidability.equivalence_between_decidability_properties_of_basic_relations]
eq_dec_implies_l4_17 [lemma, in GeoCoq.Meta_theory.Decidability.equivalence_between_decidability_properties_of_basic_relations]
eq_dec_implies_l4_16 [lemma, in GeoCoq.Meta_theory.Decidability.equivalence_between_decidability_properties_of_basic_relations]
eq_dec_implies_l4_6 [lemma, in GeoCoq.Meta_theory.Decidability.equivalence_between_decidability_properties_of_basic_relations]
eq_dec_implies_l4_5 [lemma, in GeoCoq.Meta_theory.Decidability.equivalence_between_decidability_properties_of_basic_relations]
eq_dec_implies_l4_2 [lemma, in GeoCoq.Meta_theory.Decidability.equivalence_between_decidability_properties_of_basic_relations]
eq_dec_implies_point_construction_different [lemma, in GeoCoq.Meta_theory.Decidability.equivalence_between_decidability_properties_of_basic_relations]
eq_dec_implies_two_distinct_points [lemma, in GeoCoq.Meta_theory.Decidability.equivalence_between_decidability_properties_of_basic_relations]
eq_dec_implies_between_exchange4 [lemma, in GeoCoq.Meta_theory.Decidability.equivalence_between_decidability_properties_of_basic_relations]
eq_dec_implies_outer_transitivity_between2 [lemma, in GeoCoq.Meta_theory.Decidability.equivalence_between_decidability_properties_of_basic_relations]
eq_dec_implies_construction_uniqueness [lemma, in GeoCoq.Meta_theory.Decidability.equivalence_between_decidability_properties_of_basic_relations]
eq_dec_implies_l2_11 [lemma, in GeoCoq.Meta_theory.Decidability.equivalence_between_decidability_properties_of_basic_relations]
euclid [projection, in GeoCoq.Axioms.tarski_axioms]
Euclid [section, in GeoCoq.Meta_theory.Parallel_postulates.Euclid]
euclid [lemma, in GeoCoq.Meta_theory.Counter_models.counter_model_segment_construction]
euclid [lemma, in GeoCoq.Meta_theory.Counter_models.counter_model_bet_identity]
Euclid [library]
euclidG [projection, in GeoCoq.Axioms.independent_tarski_axioms]
euclid_uniqueness [projection, in GeoCoq.Axioms.hilbert_axioms]
euclid_5__original_euclid [lemma, in GeoCoq.Meta_theory.Parallel_postulates.euclid_5_original_euclid]
euclid_5_original_euclid [section, in GeoCoq.Meta_theory.Parallel_postulates.euclid_5_original_euclid]
euclid_s_parallel_postulate [definition, in GeoCoq.Meta_theory.Parallel_postulates.Euclid_def]
euclid_5 [definition, in GeoCoq.Meta_theory.Parallel_postulates.Euclid_def]
Euclid_def [section, in GeoCoq.Meta_theory.Parallel_postulates.Euclid_def]
Euclid_def [library]
euclid_5_original_euclid [library]
Euler_line [lemma, in GeoCoq.Highschool.Euler_line]
Euler_line_special_case [lemma, in GeoCoq.Highschool.Euler_line]
Euler_line [section, in GeoCoq.Highschool.Euler_line]
Euler_line [library]
Exercises [section, in GeoCoq.Highschool.exercises]
exercises [library]
existential_triangle__rah [lemma, in GeoCoq.Meta_theory.Parallel_postulates.existential_triangle_rah]
existential_triangle_rah [section, in GeoCoq.Meta_theory.Parallel_postulates.existential_triangle_rah]
existential_saccheri__rah [lemma, in GeoCoq.Meta_theory.Parallel_postulates.existential_saccheri_rah]
existential_saccheri_rah [section, in GeoCoq.Meta_theory.Parallel_postulates.existential_saccheri_rah]
existential_inverse_projection_postulate__legendre_s_postulate [lemma, in GeoCoq.Meta_theory.Parallel_postulates.existential_inverse_projection_postulate_legendre_s_postulate]
existential_inverse_projection_postulate_legendre_s_postulate [section, in GeoCoq.Meta_theory.Parallel_postulates.existential_inverse_projection_postulate_legendre_s_postulate]
existential_inverse_projection_postulate [definition, in GeoCoq.Meta_theory.Parallel_postulates.Euclid_def]
existential_thales_postulate [definition, in GeoCoq.Meta_theory.Parallel_postulates.Euclid_def]
existential_playfair_s_postulate [definition, in GeoCoq.Meta_theory.Parallel_postulates.Euclid_def]
existential_playfair__rah [lemma, in GeoCoq.Meta_theory.Parallel_postulates.existential_playfair_rah]
existential_playfair_rah [section, in GeoCoq.Meta_theory.Parallel_postulates.existential_playfair_rah]
existential_inverse_projection_postulate_legendre_s_postulate [library]
existential_playfair_rah [library]
existential_saccheri_rah [library]
existential_triangle_rah [library]
exists_witness_ok [lemma, in GeoCoq.Tactics.Coinc.ColR]
exists_witness [definition, in GeoCoq.Tactics.Coinc.ColR]
exists_equilateral_triangle [lemma, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
exists_Cong_Per [lemma, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
exists_witness_ok [lemma, in GeoCoq.Tactics.Coinc.CoincR]
exists_witness [definition, in GeoCoq.Tactics.Coinc.CoincR]
exists_not_incident [lemma, in GeoCoq.Meta_theory.Models.tarski_to_hilbert]
exists_coord [lemma, in GeoCoq.Tarski_dev.Ch16_coordinates]
exists_projp [lemma, in GeoCoq.Tarski_dev.Ch16_coordinates]
exists_grid [lemma, in GeoCoq.Tarski_dev.Ch16_coordinates]
exists_circumcenter [lemma, in GeoCoq.Highschool.circumcenter]
ex_anga [lemma, in GeoCoq.Tarski_dev.Ch13_3_angles]
ex_eqaa [lemma, in GeoCoq.Tarski_dev.Ch13_3_angles]
ex_points_anga [lemma, in GeoCoq.Tarski_dev.Ch13_3_angles]
ex_ang [lemma, in GeoCoq.Tarski_dev.Ch13_3_angles]
ex_eqa [lemma, in GeoCoq.Tarski_dev.Ch13_3_angles]
ex_points_ang [lemma, in GeoCoq.Tarski_dev.Ch13_3_angles]
ex_col1 [lemma, in GeoCoq.Highschool.orientation]
ex_col [lemma, in GeoCoq.Highschool.orientation]
ex_sym1 [lemma, in GeoCoq.Tarski_dev.Ch10_line_reflexivity]
ex_sym [lemma, in GeoCoq.Tarski_dev.Ch10_line_reflexivity]
ex_saccheri [lemma, in GeoCoq.Tarski_dev.Annexes.saccheri]
ex_defect [lemma, in GeoCoq.Meta_theory.Parallel_postulates.legendre]
ex_conga_ts [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
ex_per_cong [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
ex_col2 [lemma, in GeoCoq.Tarski_dev.Ch08_orthogonality]
ex_eqL [lemma, in GeoCoq.Tarski_dev.Ch13_2_length]
ex_lg [lemma, in GeoCoq.Tarski_dev.Ch13_2_length]
ex_eql [lemma, in GeoCoq.Tarski_dev.Ch13_2_length]
ex_points_lg_not_col [lemma, in GeoCoq.Tarski_dev.Ch13_2_length]
ex_point_lg_bet [lemma, in GeoCoq.Tarski_dev.Ch13_2_length]
ex_point_lg_out [lemma, in GeoCoq.Tarski_dev.Ch13_2_length]
ex_point_lg [lemma, in GeoCoq.Tarski_dev.Ch13_2_length]
ex_points_lg [lemma, in GeoCoq.Tarski_dev.Ch13_2_length]
ex_col3 [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals]
ex_trisuma [lemma, in GeoCoq.Tarski_dev.Annexes.suma]
ex_suma [lemma, in GeoCoq.Tarski_dev.Annexes.suma]


F

F [definition, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
Fcri [instance, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
fieldF [lemma, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
field_prop_1 [lemma, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
field_prop_zero [lemma, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
field_prop [lemma, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
Fintegral [instance, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
five_segment [projection, in GeoCoq.Axioms.tarski_axioms]
five_segment [lemma, in GeoCoq.Meta_theory.Models.tarski_to_beeson]
five_segment_B [lemma, in GeoCoq.Meta_theory.Models.tarski_to_beeson]
five_segmentG [projection, in GeoCoq.Axioms.independent_tarski_axioms]
five_segment [lemma, in GeoCoq.Meta_theory.Counter_models.counter_model_segment_construction]
five_segment [lemma, in GeoCoq.Meta_theory.Models.tarski_to_makarios]
five_segment' [lemma, in GeoCoq.Meta_theory.Models.tarski_to_makarios]
five_segment_with_def [lemma, in GeoCoq.Tarski_dev.Ch02_cong]
five_segment [lemma, in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
five_segment [lemma, in GeoCoq.Meta_theory.Counter_models.counter_model_bet_identity]
fixLastCP [definition, in GeoCoq.Utils.arity]
fixLastCPOK [lemma, in GeoCoq.Utils.arity]
flat_ang [lemma, in GeoCoq.Tarski_dev.Ch13_3_angles]
flat_not_acute [lemma, in GeoCoq.Tarski_dev.Ch13_4_cos]
flat_all_lea [lemma, in GeoCoq.Tarski_dev.Ch13_1]
Fmult_integral [lemma, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
Fops [instance, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
fourth_point [lemma, in GeoCoq.Tarski_dev.Ch05_bet_le]
FRing [instance, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
FSC [definition, in GeoCoq.Tarski_dev.Ch04_col]
fstpp [definition, in GeoCoq.Utils.sets]
fst_sp [definition, in GeoCoq.Tactics.Coinc.ColR]
fst_ss [definition, in GeoCoq.Tactics.Coinc.ColR]


G

Ge [definition, in GeoCoq.Tarski_dev.Ch05_bet_le]
GeA [definition, in GeoCoq.Tarski_dev.Ch11_angles]
gea_total [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
gea_dec [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
gea_distincts [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
general_tactics [library]
ge_comm [lemma, in GeoCoq.Tarski_dev.Ch05_bet_le]
ge_right_comm [lemma, in GeoCoq.Tarski_dev.Ch05_bet_le]
ge_left_comm [lemma, in GeoCoq.Tarski_dev.Ch05_bet_le]
GPA [projection, in GeoCoq.Axioms.independent_tarski_axioms]
GPB [projection, in GeoCoq.Axioms.independent_tarski_axioms]
GPC [projection, in GeoCoq.Axioms.independent_tarski_axioms]
Grad [inductive, in GeoCoq.Meta_theory.Parallel_postulates.archimedes]
GradA [inductive, in GeoCoq.Meta_theory.Parallel_postulates.angle_archimedes]
GradAExp [inductive, in GeoCoq.Meta_theory.Parallel_postulates.angle_archimedes]
gradaexp_destruction_aux [lemma, in GeoCoq.Meta_theory.Parallel_postulates.angle_archimedes]
gradaexp__grada [lemma, in GeoCoq.Meta_theory.Parallel_postulates.angle_archimedes]
gradaexp_stab [constructor, in GeoCoq.Meta_theory.Parallel_postulates.angle_archimedes]
gradaexp_init [constructor, in GeoCoq.Meta_theory.Parallel_postulates.angle_archimedes]
grada_out__out [lemma, in GeoCoq.Meta_theory.Parallel_postulates.angle_archimedes]
grada__lea [lemma, in GeoCoq.Meta_theory.Parallel_postulates.angle_archimedes]
grada_distincts [lemma, in GeoCoq.Meta_theory.Parallel_postulates.angle_archimedes]
grada_stab [constructor, in GeoCoq.Meta_theory.Parallel_postulates.angle_archimedes]
grada_init [constructor, in GeoCoq.Meta_theory.Parallel_postulates.angle_archimedes]
grada2_isi_suma__grada [lemma, in GeoCoq.Meta_theory.Parallel_postulates.angle_archimedes]
GradExp [inductive, in GeoCoq.Meta_theory.Parallel_postulates.archimedes]
gradexp_le__reach [lemma, in GeoCoq.Meta_theory.Parallel_postulates.archimedes]
gradexp__grad [lemma, in GeoCoq.Meta_theory.Parallel_postulates.archimedes]
gradexp_stab [constructor, in GeoCoq.Meta_theory.Parallel_postulates.archimedes]
gradexp_init [constructor, in GeoCoq.Meta_theory.Parallel_postulates.archimedes]
GradExp2 [inductive, in GeoCoq.Meta_theory.Parallel_postulates.archimedes]
gradexp2__gradexp456 [lemma, in GeoCoq.Meta_theory.Parallel_postulates.archimedes]
gradexp2__gradexp123 [lemma, in GeoCoq.Meta_theory.Parallel_postulates.archimedes]
gradexp2_stab [constructor, in GeoCoq.Meta_theory.Parallel_postulates.archimedes]
gradexp2_init [constructor, in GeoCoq.Meta_theory.Parallel_postulates.archimedes]
grad__ex_gradexp_le [lemma, in GeoCoq.Meta_theory.Parallel_postulates.archimedes]
grad_sum [lemma, in GeoCoq.Meta_theory.Parallel_postulates.archimedes]
grad__le [lemma, in GeoCoq.Meta_theory.Parallel_postulates.archimedes]
grad_neq__neq12 [lemma, in GeoCoq.Meta_theory.Parallel_postulates.archimedes]
grad_neq__neq13 [lemma, in GeoCoq.Meta_theory.Parallel_postulates.archimedes]
grad__bet [lemma, in GeoCoq.Meta_theory.Parallel_postulates.archimedes]
grad_stab [constructor, in GeoCoq.Meta_theory.Parallel_postulates.archimedes]
grad_init [constructor, in GeoCoq.Meta_theory.Parallel_postulates.archimedes]
grad112__eq [lemma, in GeoCoq.Meta_theory.Parallel_postulates.archimedes]
grad121__eq [lemma, in GeoCoq.Meta_theory.Parallel_postulates.archimedes]
Grad2 [inductive, in GeoCoq.Meta_theory.Parallel_postulates.archimedes]
grad2__grad456 [lemma, in GeoCoq.Meta_theory.Parallel_postulates.archimedes]
grad2__grad123 [lemma, in GeoCoq.Meta_theory.Parallel_postulates.archimedes]
grad2_stab [constructor, in GeoCoq.Meta_theory.Parallel_postulates.archimedes]
grad2_init [constructor, in GeoCoq.Meta_theory.Parallel_postulates.archimedes]
GravityCenter [section, in GeoCoq.Highschool.gravityCenter]
gravityCenter [library]
gravity_center_change_triangle [lemma, in GeoCoq.Highschool.Euler_line]
greenberg_s_postulate [definition, in GeoCoq.Meta_theory.Parallel_postulates.Euclid_def]
grid_exchange_axes [lemma, in GeoCoq.Tarski_dev.Ch16_coordinates]
grid_not_par [lemma, in GeoCoq.Tarski_dev.Ch14_sum]
Gt [definition, in GeoCoq.Tarski_dev.Ch05_bet_le]
GtA [definition, in GeoCoq.Tarski_dev.Ch11_angles]
gta_dec [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
gta_distincts [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
gta_trans [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
gta_to_lta [lemma, in GeoCoq.Tarski_dev.Ch13_1]
gt_comm [lemma, in GeoCoq.Tarski_dev.Ch05_bet_le]
gt_right_comm [lemma, in GeoCoq.Tarski_dev.Ch05_bet_le]
gt_left_comm [lemma, in GeoCoq.Tarski_dev.Ch05_bet_le]
g2_16 [lemma, in GeoCoq.Meta_theory.Models.independent_tarski_to_tarski]
g2_15 [lemma, in GeoCoq.Meta_theory.Models.independent_tarski_to_tarski]
g2_14 [lemma, in GeoCoq.Meta_theory.Models.independent_tarski_to_tarski]
g2_13 [lemma, in GeoCoq.Meta_theory.Models.independent_tarski_to_tarski]
g2_12 [lemma, in GeoCoq.Meta_theory.Models.independent_tarski_to_tarski]
g2_11 [lemma, in GeoCoq.Meta_theory.Models.independent_tarski_to_tarski]
g2_10 [lemma, in GeoCoq.Meta_theory.Models.independent_tarski_to_tarski]
g2_9 [lemma, in GeoCoq.Meta_theory.Models.independent_tarski_to_tarski]
g2_8 [lemma, in GeoCoq.Meta_theory.Models.independent_tarski_to_tarski]
g2_7 [lemma, in GeoCoq.Meta_theory.Models.independent_tarski_to_tarski]
g2_6 [lemma, in GeoCoq.Meta_theory.Models.independent_tarski_to_tarski]
g2_5 [lemma, in GeoCoq.Meta_theory.Models.independent_tarski_to_tarski]
g2_4 [lemma, in GeoCoq.Meta_theory.Models.independent_tarski_to_tarski]
g2_3 [lemma, in GeoCoq.Meta_theory.Models.independent_tarski_to_tarski]
g2_2 [lemma, in GeoCoq.Meta_theory.Models.independent_tarski_to_tarski]
g2_1 [lemma, in GeoCoq.Meta_theory.Models.independent_tarski_to_tarski]


H

half_plgs [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals_inter_dec]
Hcong [definition, in GeoCoq.Meta_theory.Models.tarski_to_hilbert]
hcong_4_uniqueness [projection, in GeoCoq.Axioms.hilbert_axioms]
hcong_4_existence [projection, in GeoCoq.Axioms.hilbert_axioms]
headCP [definition, in GeoCoq.Utils.arity]
headCPbis [definition, in GeoCoq.Utils.arity]
HilbertContext [section, in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
Hilbert_euclidean_2D [record, in GeoCoq.Axioms.hilbert_axioms]
Hilbert_neutral_2D [record, in GeoCoq.Axioms.hilbert_axioms]
hilbert_s_version_of_pasch_aux [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
Hilbert_euclidean_follows_from_Tarski_euclidean [instance, in GeoCoq.Meta_theory.Models.tarski_to_hilbert]
Hilbert_Euclidean_to_Tarski_Euclidean [section, in GeoCoq.Meta_theory.Models.tarski_to_hilbert]
Hilbert_neutral_follows_from_Tarski_neutral [instance, in GeoCoq.Meta_theory.Models.tarski_to_hilbert]
Hilbert_neutral_to_Tarski_neutral [section, in GeoCoq.Meta_theory.Models.tarski_to_hilbert]
Hilbert_is_a_Col_theory [instance, in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
hilbert_s_version_of_pasch [lemma, in GeoCoq.Meta_theory.Parallel_postulates.midpoint_playfair]
hilbert_axioms [library]
hilbert_to_tarski [library]
hyperbolic_plane_postulate [definition, in GeoCoq.Meta_theory.Parallel_postulates.szmielew]
hypothesis_of_obtuse_saccheri_quadrilaterals [definition, in GeoCoq.Tarski_dev.Annexes.saccheri]
hypothesis_of_acute_saccheri_quadrilaterals [definition, in GeoCoq.Tarski_dev.Annexes.saccheri]
hypothesis_of_right_saccheri_quadrilaterals [definition, in GeoCoq.Tarski_dev.Annexes.saccheri]


I

IBet [projection, in GeoCoq.Axioms.beeson_s_axioms]
Ibetween_inner_transitivity [projection, in GeoCoq.Axioms.beeson_s_axioms]
Ibetween_symmetry [projection, in GeoCoq.Axioms.beeson_s_axioms]
Ibetween_identity [projection, in GeoCoq.Axioms.beeson_s_axioms]
ICong [projection, in GeoCoq.Axioms.beeson_s_axioms]
Icong_pseudo_reflexivity [projection, in GeoCoq.Axioms.beeson_s_axioms]
Icong_inner_transitivity [projection, in GeoCoq.Axioms.beeson_s_axioms]
Icong_identity [projection, in GeoCoq.Axioms.beeson_s_axioms]
identify_lines_ok [lemma, in GeoCoq.Tactics.Coinc.ColR]
identify_varieties_ok [lemma, in GeoCoq.Tactics.Coinc.CoincR]
Ifive_segment [projection, in GeoCoq.Axioms.beeson_s_axioms]
IFSC [definition, in GeoCoq.Tarski_dev.Ch04_cong_bet]
Iinner_pasch [projection, in GeoCoq.Axioms.beeson_s_axioms]
Ilower_dim [projection, in GeoCoq.Axioms.beeson_s_axioms]
image_col [lemma, in GeoCoq.Tarski_dev.Ch10_line_reflexivity]
image_in_col0 [lemma, in GeoCoq.Tarski_dev.Ch10_line_reflexivity]
image_image_in [lemma, in GeoCoq.Tarski_dev.Ch10_line_reflexivity]
image_in_gen_is_image [lemma, in GeoCoq.Tarski_dev.Ch10_line_reflexivity]
image_in_is_image_spec [lemma, in GeoCoq.Tarski_dev.Ch10_line_reflexivity]
image_id [lemma, in GeoCoq.Tarski_dev.Ch10_line_reflexivity]
image_preserves_out [lemma, in GeoCoq.Tarski_dev.Ch15_lengths]
image_preserves_col [lemma, in GeoCoq.Tarski_dev.Ch15_lengths]
image_preserves_bet1 [lemma, in GeoCoq.Tarski_dev.Ch15_lengths]
image_cong_col [lemma, in GeoCoq.Tarski_dev.Ch10_line_reflexivity_2D]
image_preserves_per [lemma, in GeoCoq.Tarski_dev.Ch10_line_reflexivity_2D]
image_preserves_midpoint [lemma, in GeoCoq.Tarski_dev.Ch10_line_reflexivity_2D]
image_gen_preserves_bet [lemma, in GeoCoq.Tarski_dev.Ch10_line_reflexivity_2D]
image_preserves_bet [lemma, in GeoCoq.Tarski_dev.Ch10_line_reflexivity_2D]
image_in_col [lemma, in GeoCoq.Tarski_dev.Ch10_line_reflexivity_2D]
impossible_case_8 [lemma, in GeoCoq.Meta_theory.Parallel_postulates.SPP_tarski]
impossible_case_7 [lemma, in GeoCoq.Meta_theory.Parallel_postulates.SPP_tarski]
impossible_case_6 [lemma, in GeoCoq.Meta_theory.Parallel_postulates.SPP_tarski]
impossible_case_5 [lemma, in GeoCoq.Meta_theory.Parallel_postulates.SPP_tarski]
impossible_two_sides_not_col [lemma, in GeoCoq.Meta_theory.Parallel_postulates.TCP_tarski]
impossible_case_4 [lemma, in GeoCoq.Meta_theory.Parallel_postulates.TCP_tarski]
impossible_case_4_2 [lemma, in GeoCoq.Meta_theory.Parallel_postulates.TCP_tarski]
impossible_case_4_1 [lemma, in GeoCoq.Meta_theory.Parallel_postulates.TCP_tarski]
impossible_case_3 [lemma, in GeoCoq.Meta_theory.Parallel_postulates.TCP_tarski]
impossible_case_2 [lemma, in GeoCoq.Meta_theory.Parallel_postulates.TCP_tarski]
impossible_case_1 [lemma, in GeoCoq.Meta_theory.Parallel_postulates.TCP_tarski]
InAngle [definition, in GeoCoq.Tarski_dev.Ch11_angles]
inangle_dec [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
inangle_one_side2 [lemma, in GeoCoq.Tarski_dev.Ch13_1]
inangle_one_side [lemma, in GeoCoq.Tarski_dev.Ch13_1]
inangle__isi [lemma, in GeoCoq.Tarski_dev.Annexes.suma]
inangle__suma [lemma, in GeoCoq.Tarski_dev.Annexes.suma]
InCenter [section, in GeoCoq.Highschool.incenter]
incenter [library]
incenter_dec [lemma, in GeoCoq.Highschool.incenter]
incenter_permut321 [lemma, in GeoCoq.Highschool.incenter]
incenter_permut312 [lemma, in GeoCoq.Highschool.incenter]
incenter_permut231 [lemma, in GeoCoq.Highschool.incenter]
incenter_permut213 [lemma, in GeoCoq.Highschool.incenter]
incenter_permut132 [lemma, in GeoCoq.Highschool.incenter]
incenter_exists [lemma, in GeoCoq.Highschool.incenter]
Incid [projection, in GeoCoq.Axioms.hilbert_axioms]
Incident [definition, in GeoCoq.Meta_theory.Models.tarski_to_hilbert]
incident_col [lemma, in GeoCoq.Meta_theory.Models.tarski_to_hilbert]
incident_Proper [instance, in GeoCoq.Meta_theory.Models.tarski_to_hilbert]
incident_eq [lemma, in GeoCoq.Meta_theory.Models.tarski_to_hilbert]
Incid_dec [projection, in GeoCoq.Axioms.hilbert_axioms]
Incid_morphism [projection, in GeoCoq.Axioms.hilbert_axioms]
Incid_line [lemma, in GeoCoq.Meta_theory.Models.tarski_to_hilbert]
Incid_not_Incid__not_colH [lemma, in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
Incid_morphism [instance, in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
InCP [definition, in GeoCoq.Utils.arity]
InCPOCP [lemma, in GeoCoq.Utils.sets]
InCPOK [lemma, in GeoCoq.Utils.arity]
independent_Tarski_2D_euclidean [record, in GeoCoq.Axioms.independent_tarski_axioms]
independent_Tarski_2D [record, in GeoCoq.Axioms.independent_tarski_axioms]
independent_Tarski_neutral_dimensionless_with_decidable_point_equality [record, in GeoCoq.Axioms.independent_tarski_axioms]
Independent_Tarski_2D_euclidean_to_Tarski_2D_euclidean [section, in GeoCoq.Meta_theory.Models.independent_tarski_to_tarski]
Independent_Tarski_2D_to_Tarski_2D [section, in GeoCoq.Meta_theory.Models.independent_tarski_to_tarski]
Independent_Tarski_neutral_dimensionless_to_Tarski_neutral_dimensionless [section, in GeoCoq.Meta_theory.Models.independent_tarski_to_tarski]
independent_Tarski_neutral_dimensionless_follows_from_Hilbert2D [instance, in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
independent_tarski_to_tarski [library]
independent_tarski_axioms [library]
inner_pasch [projection, in GeoCoq.Axioms.tarski_axioms]
inner_pasch_B [lemma, in GeoCoq.Meta_theory.Models.tarski_to_beeson]
inner_paschG [projection, in GeoCoq.Axioms.independent_tarski_axioms]
inner_paschT [lemma, in GeoCoq.Meta_theory.Models.independent_tarski_to_tarski]
inner_pasch [lemma, in GeoCoq.Meta_theory.Counter_models.counter_model_segment_construction]
inner_pasch_aux [lemma, in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
inner_pasch [lemma, in GeoCoq.Meta_theory.Counter_models.counter_model_bet_identity]
InNth [lemma, in GeoCoq.Utils.arity]
Inter [definition, in GeoCoq.Tarski_dev.Ch12_parallel]
interp [definition, in GeoCoq.Tactics.Coinc.ColR]
interp [definition, in GeoCoq.Tactics.Coinc.CoincR]
interp_CPOK [lemma, in GeoCoq.Tactics.Coinc.CoincR]
interp_CPTlOK [lemma, in GeoCoq.Tactics.Coinc.CoincR]
interp_CPHdOK [lemma, in GeoCoq.Tactics.Coinc.CoincR]
interp_CP [definition, in GeoCoq.Tactics.Coinc.CoincR]
interp_CP_for_col [definition, in GeoCoq.Tactics.Coinc.CoincR_for_col]
intersection_two_medians_exist_unique [lemma, in GeoCoq.Highschool.gravityCenter]
intersection_two_medians_exist [lemma, in GeoCoq.Highschool.gravityCenter]
inter_comm [lemma, in GeoCoq.Tarski_dev.Ch12_parallel]
inter_right_comm [lemma, in GeoCoq.Tarski_dev.Ch12_parallel]
inter_left_comm [lemma, in GeoCoq.Tarski_dev.Ch12_parallel]
inter_sym [lemma, in GeoCoq.Tarski_dev.Ch12_parallel]
inter_trivial [lemma, in GeoCoq.Tarski_dev.Ch12_parallel]
inter_uniqueness_not_par [lemma, in GeoCoq.Tarski_dev.Ch12_parallel]
inter_dec_plus_par_perp_perp_imply_triangle_circumscription [lemma, in GeoCoq.Meta_theory.Parallel_postulates.par_perp_perp_TCP]
inter_incid_uniquenessH [lemma, in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
inter_uniquenessH [lemma, in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
inter_dec [lemma, in GeoCoq.Tarski_dev.Ch12_parallel_inter_dec]
Intuitionistic_Tarski_to_Tarski [section, in GeoCoq.Meta_theory.Models.tarski_to_beeson]
intuitionistic_Tarski_neutral_dimensionless [record, in GeoCoq.Axioms.beeson_s_axioms]
inv [definition, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
inverse_projection_postulate__proclus_bis [lemma, in GeoCoq.Meta_theory.Parallel_postulates.inverse_projection_postulate_proclus_bis]
inverse_projection_postulate_proclus_bis [section, in GeoCoq.Meta_theory.Parallel_postulates.inverse_projection_postulate_proclus_bis]
inverse_projection_postulate [definition, in GeoCoq.Meta_theory.Parallel_postulates.Euclid_def]
inverse_projection_postulate_proclus_bis [library]
invert_one_side [lemma, in GeoCoq.Tarski_dev.Ch09_plane]
invert_two_sides [lemma, in GeoCoq.Tarski_dev.Ch09_plane]
InvF [definition, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
invF_morphism [instance, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
inv_f [lemma, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
inv_uniqueness [lemma, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
inv_col [lemma, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
inv_exists_with_notation [lemma, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
inv_exists [lemma, in GeoCoq.Tarski_dev.Ch14_prod]
in_angle_reverse [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
in_angle_asym [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
in_angle_trans [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
in_angle_line [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
in_angle_trivial_2 [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
in_angle_trivial_1 [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
in_angle_one_side [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
in_angle_out [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
in_angle_two_sides [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
Isegment_construction [projection, in GeoCoq.Axioms.beeson_s_axioms]
ise_to_is [lemma, in GeoCoq.Tarski_dev.Annexes.vectors]
Isi [definition, in GeoCoq.Tarski_dev.Annexes.suma]
isi_dec [lemma, in GeoCoq.Tarski_dev.Annexes.suma]
isi_lta2_suma2__lta456 [lemma, in GeoCoq.Tarski_dev.Annexes.suma]
isi_lta2_suma2__lta123 [lemma, in GeoCoq.Tarski_dev.Annexes.suma]
isi_lea_lta789_suma2__lta456 [lemma, in GeoCoq.Tarski_dev.Annexes.suma]
isi_lea_lta789_suma2__lta123 [lemma, in GeoCoq.Tarski_dev.Annexes.suma]
isi_lea_lta123_suma2__lta456 [lemma, in GeoCoq.Tarski_dev.Annexes.suma]
isi_lea_lta456_suma2__lta123 [lemma, in GeoCoq.Tarski_dev.Annexes.suma]
isi_lea2_suma2__lea456 [lemma, in GeoCoq.Tarski_dev.Annexes.suma]
isi_lea2_suma2__lea123 [lemma, in GeoCoq.Tarski_dev.Annexes.suma]
isi_lta2_suma2__lta [lemma, in GeoCoq.Tarski_dev.Annexes.suma]
isi_lea_lta456_suma2__lta [lemma, in GeoCoq.Tarski_dev.Annexes.suma]
isi_lea_lta123_suma2__lta [lemma, in GeoCoq.Tarski_dev.Annexes.suma]
isi_suma__out546 [lemma, in GeoCoq.Tarski_dev.Annexes.suma]
isi_suma__out213 [lemma, in GeoCoq.Tarski_dev.Annexes.suma]
isi_lea2_suma2__conga456 [lemma, in GeoCoq.Tarski_dev.Annexes.suma]
isi_lea2_suma2__conga123 [lemma, in GeoCoq.Tarski_dev.Annexes.suma]
isi_assoc [lemma, in GeoCoq.Tarski_dev.Annexes.suma]
isi_assoc_2 [lemma, in GeoCoq.Tarski_dev.Annexes.suma]
isi_assoc_1 [lemma, in GeoCoq.Tarski_dev.Annexes.suma]
isi_lea2_suma2__lea [lemma, in GeoCoq.Tarski_dev.Annexes.suma]
isi_lea123_suma2__lea [lemma, in GeoCoq.Tarski_dev.Annexes.suma]
isi_lea456_suma2__lea [lemma, in GeoCoq.Tarski_dev.Annexes.suma]
isi_lea2__isi [lemma, in GeoCoq.Tarski_dev.Annexes.suma]
isi_suma__lea456789 [lemma, in GeoCoq.Tarski_dev.Annexes.suma]
isi_suma__lea123789 [lemma, in GeoCoq.Tarski_dev.Annexes.suma]
isi_comm [lemma, in GeoCoq.Tarski_dev.Annexes.suma]
isi_left_comm [lemma, in GeoCoq.Tarski_dev.Annexes.suma]
isi_right_comm [lemma, in GeoCoq.Tarski_dev.Annexes.suma]
isi_sym [lemma, in GeoCoq.Tarski_dev.Annexes.suma]
isi_distincts [lemma, in GeoCoq.Tarski_dev.Annexes.suma]
isi_chara [lemma, in GeoCoq.Tarski_dev.Annexes.suma]
isi123231 [lemma, in GeoCoq.Tarski_dev.Annexes.suma]
isi2_suma2__conga123 [lemma, in GeoCoq.Tarski_dev.Annexes.suma]
isi2_suma2__conga456 [lemma, in GeoCoq.Tarski_dev.Annexes.suma]
isosceles [definition, in GeoCoq.Highschool.triangles]
isosceles_congaH [lemma, in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
isosceles_conga [lemma, in GeoCoq.Highschool.triangles]
isosceles_sym [lemma, in GeoCoq.Highschool.triangles]
is_null_all [lemma, in GeoCoq.Tarski_dev.Ch13_3_angles]
is_null_ang_out [lemma, in GeoCoq.Tarski_dev.Ch13_3_angles]
is_null_anga_out [lemma, in GeoCoq.Tarski_dev.Ch13_3_angles]
is_null_anga' [definition, in GeoCoq.Tarski_dev.Ch13_3_angles]
is_anga_distinct [lemma, in GeoCoq.Tarski_dev.Ch13_3_angles]
is_anga_conga_is_anga [lemma, in GeoCoq.Tarski_dev.Ch13_3_angles]
is_anga_conga [lemma, in GeoCoq.Tarski_dev.Ch13_3_angles]
is_anga_to_is_ang [lemma, in GeoCoq.Tarski_dev.Ch13_3_angles]
is_ang_distinct [lemma, in GeoCoq.Tarski_dev.Ch13_3_angles]
is_ang_conga_is_ang [lemma, in GeoCoq.Tarski_dev.Ch13_3_angles]
is_ang_conga [lemma, in GeoCoq.Tarski_dev.Ch13_3_angles]
is_image_spec_dec [lemma, in GeoCoq.Tarski_dev.Ch10_line_reflexivity]
is_image_spec_triv [lemma, in GeoCoq.Tarski_dev.Ch10_line_reflexivity]
is_image_rev [lemma, in GeoCoq.Tarski_dev.Ch10_line_reflexivity]
is_image_spec_rev [lemma, in GeoCoq.Tarski_dev.Ch10_line_reflexivity]
is_image_spec_col_cong [lemma, in GeoCoq.Tarski_dev.Ch10_line_reflexivity]
is_image_col_cong [lemma, in GeoCoq.Tarski_dev.Ch10_line_reflexivity]
is_image_is_image_spec [lemma, in GeoCoq.Tarski_dev.Ch10_line_reflexivity]
is_null_anga_dec [lemma, in GeoCoq.Tarski_dev.Ch13_4_cos]
is_length_exists [lemma, in GeoCoq.Tarski_dev.Ch15_lengths]
Is_length [definition, in GeoCoq.Tarski_dev.Ch15_lengths]
is_orthocenter_perm_5 [lemma, in GeoCoq.Highschool.orthocenter]
is_orthocenter_perm_4 [lemma, in GeoCoq.Highschool.orthocenter]
is_orthocenter_perm_3 [lemma, in GeoCoq.Highschool.orthocenter]
is_orthocenter_perm_2 [lemma, in GeoCoq.Highschool.orthocenter]
is_orthocenter_perm_1 [lemma, in GeoCoq.Highschool.orthocenter]
is_orthocenter_perm [lemma, in GeoCoq.Highschool.orthocenter]
is_orthocenter_cases [lemma, in GeoCoq.Highschool.orthocenter]
is_orthocenter [definition, in GeoCoq.Highschool.orthocenter]
is_midpoint_id_2 [lemma, in GeoCoq.Tarski_dev.Ch07_midpoint]
is_midpoint_id [lemma, in GeoCoq.Tarski_dev.Ch07_midpoint]
is_midpoint_dec [lemma, in GeoCoq.Tarski_dev.Ch07_midpoint]
is_image_perp_in [lemma, in GeoCoq.Tarski_dev.Ch13_1]
is_line [definition, in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
is_incenter [definition, in GeoCoq.Highschool.incenter]
is_to_ise [lemma, in GeoCoq.Tarski_dev.Annexes.vectors]
is_gravity_center_cases [lemma, in GeoCoq.Highschool.gravityCenter]
is_gravity_center_perm_5 [lemma, in GeoCoq.Highschool.gravityCenter]
is_gravity_center_perm_4 [lemma, in GeoCoq.Highschool.gravityCenter]
is_gravity_center_perm_3 [lemma, in GeoCoq.Highschool.gravityCenter]
is_gravity_center_perm_2 [lemma, in GeoCoq.Highschool.gravityCenter]
is_gravity_center_perm_1 [lemma, in GeoCoq.Highschool.gravityCenter]
is_gravity_center_perm [lemma, in GeoCoq.Highschool.gravityCenter]
is_gravity_center_third_reci [lemma, in GeoCoq.Highschool.gravityCenter]
is_gravity_center_third [lemma, in GeoCoq.Highschool.gravityCenter]
is_gravity_center_diff_3 [lemma, in GeoCoq.Highschool.gravityCenter]
is_gravity_center_diff_2 [lemma, in GeoCoq.Highschool.gravityCenter]
is_gravity_center_diff_1 [lemma, in GeoCoq.Highschool.gravityCenter]
is_gravity_center_col [lemma, in GeoCoq.Highschool.gravityCenter]
is_gravity_center_exist_unique [lemma, in GeoCoq.Highschool.gravityCenter]
is_gravity_center [definition, in GeoCoq.Highschool.gravityCenter]
Is_on_perp_bisect [definition, in GeoCoq.Tarski_dev.Annexes.perp_bisect]
is_len_cong_is_len [lemma, in GeoCoq.Tarski_dev.Ch13_2_length]
is_len_cong [lemma, in GeoCoq.Tarski_dev.Ch13_2_length]
is_circumcenter_uniqueness [lemma, in GeoCoq.Highschool.circumcenter]
is_circumcenter_perm_5 [lemma, in GeoCoq.Highschool.circumcenter]
is_circumcenter_perm_4 [lemma, in GeoCoq.Highschool.circumcenter]
is_circumcenter_perm_3 [lemma, in GeoCoq.Highschool.circumcenter]
is_circumcenter_perm_2 [lemma, in GeoCoq.Highschool.circumcenter]
is_circumcenter_perm_1 [lemma, in GeoCoq.Highschool.circumcenter]
is_circumcenter_perm [lemma, in GeoCoq.Highschool.circumcenter]
is_circumcenter_cases [lemma, in GeoCoq.Highschool.circumcenter]
is_circumcenter [definition, in GeoCoq.Highschool.circumcenter]
ITpoint [projection, in GeoCoq.Axioms.beeson_s_axioms]
IT_to_TID [instance, in GeoCoq.Meta_theory.Models.tarski_to_beeson]
IT_to_T [instance, in GeoCoq.Meta_theory.Models.tarski_to_beeson]
IT_trivial2 [lemma, in GeoCoq.Meta_theory.Models.tarski_to_beeson]
IT_trivial [lemma, in GeoCoq.Meta_theory.Models.tarski_to_beeson]
IT_chara [lemma, in GeoCoq.Meta_theory.Models.tarski_to_beeson]


K

ker_par [lemma, in GeoCoq.Tarski_dev.Annexes.project]
ker_col [lemma, in GeoCoq.Tarski_dev.Annexes.project]
Kite [definition, in GeoCoq.Tarski_dev.Annexes.quadrilaterals]
Kite_comm [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals]
KnuthAx1 [lemma, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]


L

Lambert [definition, in GeoCoq.Tarski_dev.Annexes.saccheri]
lam_obtuse__oah [lemma, in GeoCoq.Tarski_dev.Annexes.saccheri]
lam_acute__aah [lemma, in GeoCoq.Tarski_dev.Annexes.saccheri]
lam_per__rah [lemma, in GeoCoq.Tarski_dev.Annexes.saccheri]
lam__os [lemma, in GeoCoq.Tarski_dev.Annexes.saccheri]
lam_perm [lemma, in GeoCoq.Tarski_dev.Annexes.saccheri]
lam6521_mid2__sac [lemma, in GeoCoq.Tarski_dev.Annexes.saccheri]
lam6534_mid2__sac [lemma, in GeoCoq.Tarski_dev.Annexes.saccheri]
lastCP [definition, in GeoCoq.Utils.arity]
lastCPIn [lemma, in GeoCoq.Utils.arity]
lastCPTl [lemma, in GeoCoq.Utils.arity]
lastTailOK [lemma, in GeoCoq.Utils.arity]
Lcos [definition, in GeoCoq.Tarski_dev.Ch13_4_cos]
lcos_lcos_col [lemma, in GeoCoq.Tarski_dev.Ch13_5_Pappus_Pascal]
lcos_per_anga [lemma, in GeoCoq.Tarski_dev.Ch13_5_Pappus_Pascal]
lcos_eq_lcos3_eq [lemma, in GeoCoq.Tarski_dev.Ch13_4_cos]
lcos_eq_lcos2_eq [lemma, in GeoCoq.Tarski_dev.Ch13_4_cos]
lcos_eq_trans [lemma, in GeoCoq.Tarski_dev.Ch13_4_cos]
lcos_eq_sym [lemma, in GeoCoq.Tarski_dev.Ch13_4_cos]
lcos_eq_refl [lemma, in GeoCoq.Tarski_dev.Ch13_4_cos]
lcos_eqa_lcos [lemma, in GeoCoq.Tarski_dev.Ch13_4_cos]
lcos_uniqueness [lemma, in GeoCoq.Tarski_dev.Ch13_4_cos]
lcos_exists [lemma, in GeoCoq.Tarski_dev.Ch13_4_cos]
lcos_lg [lemma, in GeoCoq.Tarski_dev.Ch13_4_cos]
lcos_per [lemma, in GeoCoq.Tarski_dev.Ch13_4_cos]
lcos_const_o [lemma, in GeoCoq.Tarski_dev.Ch13_4_cos]
lcos_not_lg_null [lemma, in GeoCoq.Tarski_dev.Ch13_4_cos]
lcos_morphism [instance, in GeoCoq.Tarski_dev.Ch13_4_cos]
lcos_eql_lcos [lemma, in GeoCoq.Tarski_dev.Ch13_4_cos]
lcos_lg_anga [lemma, in GeoCoq.Tarski_dev.Ch13_4_cos]
lcos_const_cb [lemma, in GeoCoq.Tarski_dev.Ch13_4_cos]
lcos_const_ab [lemma, in GeoCoq.Tarski_dev.Ch13_4_cos]
lcos_const_a [lemma, in GeoCoq.Tarski_dev.Ch13_4_cos]
lcos_lg_distincts [lemma, in GeoCoq.Tarski_dev.Ch13_4_cos]
lcos_const [lemma, in GeoCoq.Tarski_dev.Ch13_4_cos]
lcos_const1 [lemma, in GeoCoq.Tarski_dev.Ch13_4_cos]
lcos_const0 [lemma, in GeoCoq.Tarski_dev.Ch13_4_cos]
lcos_lg_not_null [lemma, in GeoCoq.Tarski_dev.Ch13_4_cos]
lcos2 [definition, in GeoCoq.Tarski_dev.Ch13_4_cos]
lcos2_lcos [lemma, in GeoCoq.Tarski_dev.Ch13_5_Pappus_Pascal]
lcos2_eq_lcos3_eq [lemma, in GeoCoq.Tarski_dev.Ch13_4_cos]
lcos2_lg_not_null [lemma, in GeoCoq.Tarski_dev.Ch13_4_cos]
lcos2_eq_trans [lemma, in GeoCoq.Tarski_dev.Ch13_4_cos]
lcos2_lg_anga [lemma, in GeoCoq.Tarski_dev.Ch13_4_cos]
lcos2_eql_lcos2 [lemma, in GeoCoq.Tarski_dev.Ch13_4_cos]
lcos2_uniqueness [lemma, in GeoCoq.Tarski_dev.Ch13_4_cos]
lcos2_eq_sym [lemma, in GeoCoq.Tarski_dev.Ch13_4_cos]
lcos2_eq_refl [lemma, in GeoCoq.Tarski_dev.Ch13_4_cos]
lcos2_exists' [lemma, in GeoCoq.Tarski_dev.Ch13_4_cos]
lcos2_exists [lemma, in GeoCoq.Tarski_dev.Ch13_4_cos]
lcos2_comm [lemma, in GeoCoq.Tarski_dev.Ch13_4_cos]
Lcos3 [definition, in GeoCoq.Tarski_dev.Ch13_4_cos]
lcos3_lcos2 [lemma, in GeoCoq.Tarski_dev.Ch13_5_Pappus_Pascal]
lcos3_eq_trans [lemma, in GeoCoq.Tarski_dev.Ch13_4_cos]
lcos3_lg_not_null [lemma, in GeoCoq.Tarski_dev.Ch13_4_cos]
lcos3_lg_anga [lemma, in GeoCoq.Tarski_dev.Ch13_4_cos]
lcos3_eql_lcos3 [lemma, in GeoCoq.Tarski_dev.Ch13_4_cos]
lcos3_uniqueness [lemma, in GeoCoq.Tarski_dev.Ch13_4_cos]
lcos3_eq_sym [lemma, in GeoCoq.Tarski_dev.Ch13_4_cos]
lcos3_eq_refl [lemma, in GeoCoq.Tarski_dev.Ch13_4_cos]
lcos3_exists [lemma, in GeoCoq.Tarski_dev.Ch13_4_cos]
lcos3_permut2 [lemma, in GeoCoq.Tarski_dev.Ch13_4_cos]
lcos3_permut1 [lemma, in GeoCoq.Tarski_dev.Ch13_4_cos]
lcos3_permut3 [lemma, in GeoCoq.Tarski_dev.Ch13_4_cos]
lcos3_lcos_2_1 [lemma, in GeoCoq.Tarski_dev.Ch13_4_cos]
lcos3_lcos_1_2 [lemma, in GeoCoq.Tarski_dev.Ch13_4_cos]
Le [definition, in GeoCoq.Tarski_dev.Ch05_bet_le]
LeA [definition, in GeoCoq.Tarski_dev.Ch11_angles]
lea__nlta [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
lea_total [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
lea_dec [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
lea_in_angle [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
lea_distincts [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
lea_acute_obtuse [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
lea_comm [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
lea_right_comm [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
lea_left_comm [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
lea_asym [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
lea_trans [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
lea_refl [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
lea_line [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
lea_cases [lemma, in GeoCoq.Tarski_dev.Ch12_parallel_inter_dec]
lea121345 [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
lea123456_lta__lta [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
lea456789_lta__lta [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
LeF [definition, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
leF_Transitive [instance, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
leF_Antisymmetric [instance, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
Legendre [section, in GeoCoq.Meta_theory.Parallel_postulates.legendre]
legendre [library]
legendre_s_theorem [lemma, in GeoCoq.Meta_theory.Parallel_postulates.legendre]
legendre_aux2 [lemma, in GeoCoq.Meta_theory.Parallel_postulates.legendre]
legendre_aux1 [lemma, in GeoCoq.Meta_theory.Parallel_postulates.legendre]
legendre_aux [lemma, in GeoCoq.Meta_theory.Parallel_postulates.legendre]
legendre_aux2 [lemma, in GeoCoq.Meta_theory.Parallel_postulates.triangle_playfair_bis]
legendre_aux1 [lemma, in GeoCoq.Meta_theory.Parallel_postulates.triangle_playfair_bis]
legendre_s_postulate [definition, in GeoCoq.Meta_theory.Parallel_postulates.Euclid_def]
Len [definition, in GeoCoq.Tarski_dev.Ch13_2_length]
Length [definition, in GeoCoq.Tarski_dev.Ch15_lengths]
lengthAtLeastOne [lemma, in GeoCoq.Utils.sets]
lengthNilOK [lemma, in GeoCoq.Utils.arity]
lengthOfCPToList [lemma, in GeoCoq.Utils.arity]
lengthOne [lemma, in GeoCoq.Utils.sets]
length_sym [lemma, in GeoCoq.Tarski_dev.Ch15_lengths]
length_existence [lemma, in GeoCoq.Tarski_dev.Ch15_lengths]
length_out [lemma, in GeoCoq.Tarski_dev.Ch15_lengths]
length_O [lemma, in GeoCoq.Tarski_dev.Ch15_lengths]
length_not_col_null [lemma, in GeoCoq.Tarski_dev.Ch15_lengths]
length_Ps [lemma, in GeoCoq.Tarski_dev.Ch15_lengths]
length_cong [lemma, in GeoCoq.Tarski_dev.Ch15_lengths]
length_uniqueness [lemma, in GeoCoq.Tarski_dev.Ch15_lengths]
length_leP_le_2 [lemma, in GeoCoq.Tarski_dev.Ch15_lengths]
length_leP_le_1 [lemma, in GeoCoq.Tarski_dev.Ch15_lengths]
length_Ar2 [lemma, in GeoCoq.Tarski_dev.Ch15_lengths]
length_eq_cong_2 [lemma, in GeoCoq.Tarski_dev.Ch15_lengths]
length_eq_cong_1 [lemma, in GeoCoq.Tarski_dev.Ch15_lengths]
length_id [lemma, in GeoCoq.Tarski_dev.Ch15_lengths]
length_id_2 [lemma, in GeoCoq.Tarski_dev.Ch15_lengths]
length_id_1 [lemma, in GeoCoq.Tarski_dev.Ch15_lengths]
length_pos [lemma, in GeoCoq.Tarski_dev.Ch15_lengths]
length_eq_or_opp [lemma, in GeoCoq.Tarski_dev.Ch16_coordinates]
_ =l= _ [notation, in GeoCoq.Tarski_dev.Ch13_2_length]
Length_4 [section, in GeoCoq.Tarski_dev.Ch13_2_length]
Length_3 [section, in GeoCoq.Tarski_dev.Ch13_2_length]
Length_2 [section, in GeoCoq.Tarski_dev.Ch13_2_length]
Length_1 [section, in GeoCoq.Tarski_dev.Ch13_2_length]
LeP [definition, in GeoCoq.Tarski_dev.Ch14_order]
leP_bet [lemma, in GeoCoq.Tarski_dev.Ch15_lengths]
leP_sum_leP [lemma, in GeoCoq.Tarski_dev.Ch14_order]
leP_trans [lemma, in GeoCoq.Tarski_dev.Ch14_order]
leP_asym [lemma, in GeoCoq.Tarski_dev.Ch14_order]
leP_refl [lemma, in GeoCoq.Tarski_dev.Ch14_order]
le_cong_le [lemma, in GeoCoq.Highschool.orientation]
le_comm [lemma, in GeoCoq.Highschool.orientation]
le_right_comm [lemma, in GeoCoq.Highschool.orientation]
le_left_comm [lemma, in GeoCoq.Highschool.orientation]
le__nlt [lemma, in GeoCoq.Tarski_dev.Ch05_bet_le]
le_comm [lemma, in GeoCoq.Tarski_dev.Ch05_bet_le]
le_right_comm [lemma, in GeoCoq.Tarski_dev.Ch05_bet_le]
le_left_comm [lemma, in GeoCoq.Tarski_dev.Ch05_bet_le]
le_zero [lemma, in GeoCoq.Tarski_dev.Ch05_bet_le]
le_cases [lemma, in GeoCoq.Tarski_dev.Ch05_bet_le]
le_trivial [lemma, in GeoCoq.Tarski_dev.Ch05_bet_le]
le_anti_symmetry [lemma, in GeoCoq.Tarski_dev.Ch05_bet_le]
le_transitivity [lemma, in GeoCoq.Tarski_dev.Ch05_bet_le]
le_reflexivity [lemma, in GeoCoq.Tarski_dev.Ch05_bet_le]
le_bet [lemma, in GeoCoq.Tarski_dev.Ch05_bet_le]
le_pos_prod_le [lemma, in GeoCoq.Tarski_dev.Ch14_order]
le_mid2__le12 [lemma, in GeoCoq.Tarski_dev.Ch07_midpoint]
le_mid2__le13 [lemma, in GeoCoq.Tarski_dev.Ch07_midpoint]
le_cong_le [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals]
le_comm [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals]
le_right_comm [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals]
le_left_comm [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals]
le1221 [lemma, in GeoCoq.Tarski_dev.Ch05_bet_le]
le1234_lt__lt [lemma, in GeoCoq.Tarski_dev.Ch05_bet_le]
le3456_lt__lt [lemma, in GeoCoq.Tarski_dev.Ch05_bet_le]
lg_eql_lg [lemma, in GeoCoq.Tarski_dev.Ch13_2_length]
lg_null_dec [lemma, in GeoCoq.Tarski_dev.Ch13_2_length]
lg_null_trivial [lemma, in GeoCoq.Tarski_dev.Ch13_2_length]
lg_null_instance [lemma, in GeoCoq.Tarski_dev.Ch13_2_length]
lg_sym [lemma, in GeoCoq.Tarski_dev.Ch13_2_length]
lg_cong_lg [lemma, in GeoCoq.Tarski_dev.Ch13_2_length]
lg_cong [lemma, in GeoCoq.Tarski_dev.Ch13_2_length]
lg_exists [lemma, in GeoCoq.Tarski_dev.Ch13_2_length]
Lin [definition, in GeoCoq.Meta_theory.Models.tarski_to_hilbert]
Line [projection, in GeoCoq.Axioms.hilbert_axioms]
Line [definition, in GeoCoq.Meta_theory.Models.tarski_to_hilbert]
line_uniqueness [projection, in GeoCoq.Axioms.hilbert_axioms]
line_existence [projection, in GeoCoq.Axioms.hilbert_axioms]
line_dec [lemma, in GeoCoq.Tarski_dev.Ch12_parallel]
listInd [lemma, in GeoCoq.Utils.arity]
ListToCP [definition, in GeoCoq.Utils.arity]
ListToCPTl [lemma, in GeoCoq.Utils.arity]
list_assoc_inv [definition, in GeoCoq.Tactics.Coinc.ColR]
list_assoc_inv [definition, in GeoCoq.Tactics.Coinc.CoincR]
lower_dim [projection, in GeoCoq.Axioms.tarski_axioms]
lower_dim [lemma, in GeoCoq.Meta_theory.Models.tarski_to_beeson]
lower_dim_B [lemma, in GeoCoq.Meta_theory.Models.tarski_to_beeson]
lower_dim_ex [lemma, in GeoCoq.Tarski_dev.Ch03_bet]
lower_dimG [projection, in GeoCoq.Axioms.independent_tarski_axioms]
lower_dim [lemma, in GeoCoq.Meta_theory.Counter_models.counter_model_segment_construction]
lower_dim_ex [lemma, in GeoCoq.Meta_theory.Models.tarski_to_makarios]
lower_dim_l [lemma, in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
lower_dim [lemma, in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
lower_dim [lemma, in GeoCoq.Meta_theory.Counter_models.counter_model_bet_identity]
Lt [definition, in GeoCoq.Tarski_dev.Ch05_bet_le]
LtA [definition, in GeoCoq.Tarski_dev.Ch11_angles]
ltac_something_show [lemma, in GeoCoq.Utils.general_tactics]
ltac_something_hide [lemma, in GeoCoq.Utils.general_tactics]
ltac_something_eq [lemma, in GeoCoq.Utils.general_tactics]
ltac_something [definition, in GeoCoq.Utils.general_tactics]
lta_per2_os__lt [lemma, in GeoCoq.Tarski_dev.Annexes.saccheri]
lta__nlea [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
lta_dec [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
lta__lea [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
lta_distincts [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
lta_diff [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
lta_not_conga [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
lta_comm [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
lta_right_comm [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
lta_left_comm [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
lta_trans [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
lta_to_gta [lemma, in GeoCoq.Tarski_dev.Ch13_1]
lta123234_per2_os__lt [lemma, in GeoCoq.Tarski_dev.Annexes.saccheri]
ltList [definition, in GeoCoq.Utils.sets]
ltListIrrefl [lemma, in GeoCoq.Utils.sets]
ltListTrans [lemma, in GeoCoq.Utils.sets]
LtP [definition, in GeoCoq.Tarski_dev.Ch14_order]
ltP_pos [lemma, in GeoCoq.Tarski_dev.Ch15_lengths]
ltP_neg [lemma, in GeoCoq.Tarski_dev.Ch14_order]
ltP_sum_pos [lemma, in GeoCoq.Tarski_dev.Ch14_order]
ltP_neq [lemma, in GeoCoq.Tarski_dev.Ch14_order]
ltP_ar2 [lemma, in GeoCoq.Tarski_dev.Ch14_order]
ltST [definition, in GeoCoq.Utils.sets]
ltTrans [lemma, in GeoCoq.Utils.sets]
lt__le [lemma, in GeoCoq.Tarski_dev.Ch05_bet_le]
lt_comm [lemma, in GeoCoq.Tarski_dev.Ch05_bet_le]
lt_left_comm [lemma, in GeoCoq.Tarski_dev.Ch05_bet_le]
lt_right_comm [lemma, in GeoCoq.Tarski_dev.Ch05_bet_le]
lt_sac__obtuse [lemma, in GeoCoq.Tarski_dev.Annexes.saccheri]
lt_sac__acute [lemma, in GeoCoq.Tarski_dev.Annexes.saccheri]
lt_per2_os__lta [lemma, in GeoCoq.Tarski_dev.Annexes.saccheri]
lt_diff_ps [lemma, in GeoCoq.Tarski_dev.Ch14_order]
lt4321_per2_os__lta [lemma, in GeoCoq.Tarski_dev.Annexes.saccheri]
l_3_9_4 [lemma, in GeoCoq.Tarski_dev.Ch03_bet]
l0 [projection, in GeoCoq.Axioms.hilbert_axioms]
l0 [definition, in GeoCoq.Meta_theory.Models.tarski_to_hilbert]
l10_15 [lemma, in GeoCoq.Tarski_dev.Ch10_line_reflexivity]
l10_14 [lemma, in GeoCoq.Tarski_dev.Ch10_line_reflexivity]
l10_8 [lemma, in GeoCoq.Tarski_dev.Ch10_line_reflexivity]
l10_7 [lemma, in GeoCoq.Tarski_dev.Ch10_line_reflexivity]
l10_6_existence [lemma, in GeoCoq.Tarski_dev.Ch10_line_reflexivity]
l10_6_existence_spec [lemma, in GeoCoq.Tarski_dev.Ch10_line_reflexivity]
l10_6_uniqueness [lemma, in GeoCoq.Tarski_dev.Ch10_line_reflexivity]
l10_5 [lemma, in GeoCoq.Tarski_dev.Ch10_line_reflexivity]
l10_4 [lemma, in GeoCoq.Tarski_dev.Ch10_line_reflexivity]
l10_4_spec [lemma, in GeoCoq.Tarski_dev.Ch10_line_reflexivity]
l10_2_existence [lemma, in GeoCoq.Tarski_dev.Ch10_line_reflexivity]
l10_2_existence_spec [lemma, in GeoCoq.Tarski_dev.Ch10_line_reflexivity]
l10_2_uniqueness [lemma, in GeoCoq.Tarski_dev.Ch10_line_reflexivity]
l10_16 [lemma, in GeoCoq.Tarski_dev.Ch10_line_reflexivity_2D]
l10_12 [lemma, in GeoCoq.Tarski_dev.Ch10_line_reflexivity_2D]
l10_10 [lemma, in GeoCoq.Tarski_dev.Ch10_line_reflexivity_2D]
l10_10_spec [lemma, in GeoCoq.Tarski_dev.Ch10_line_reflexivity_2D]
l11_53 [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
l11_52 [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
l11_51 [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
l11_50_2 [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
l11_50_1 [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
l11_49 [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
l11_47 [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
l11_46 [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
l11_44_2 [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
l11_44_1 [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
l11_44_2_b [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
l11_44_1_b [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
l11_44_2_a [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
l11_44_1_a [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
l11_43 [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
l11_43_aux [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
l11_41 [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
l11_41_aux [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
l11_36 [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
l11_31_2 [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
l11_31_1 [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
l11_30 [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
l11_29_b [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
l11_29_a [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
l11_28 [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
l11_25 [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
l11_25_aux [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
l11_24 [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
l11_22 [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
l11_22b [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
l11_22a [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
l11_22_bet [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
l11_19 [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
l11_15 [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
l11_22_aux [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
l11_21_b [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
l11_21_a [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
l11_18_2 [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
l11_18_1 [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
l11_17 [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
l11_16 [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
l11_14 [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
l11_13 [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
l11_10 [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
l11_4_2 [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
l11_4_1 [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
l11_3_bis [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
l11_aux [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
l11_3 [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
l12_22_b [lemma, in GeoCoq.Tarski_dev.Ch12_parallel]
l12_22_aux [lemma, in GeoCoq.Tarski_dev.Ch12_parallel]
l12_21_b [lemma, in GeoCoq.Tarski_dev.Ch12_parallel]
l12_18 [lemma, in GeoCoq.Tarski_dev.Ch12_parallel]
l12_18_d [lemma, in GeoCoq.Tarski_dev.Ch12_parallel]
l12_18_c [lemma, in GeoCoq.Tarski_dev.Ch12_parallel]
l12_18_b [lemma, in GeoCoq.Tarski_dev.Ch12_parallel]
l12_18_a [lemma, in GeoCoq.Tarski_dev.Ch12_parallel]
l12_17 [lemma, in GeoCoq.Tarski_dev.Ch12_parallel]
l12_9 [lemma, in GeoCoq.Tarski_dev.Ch12_parallel]
l12_6 [lemma, in GeoCoq.Tarski_dev.Ch12_parallel]
l12_23 [lemma, in GeoCoq.Tarski_dev.Ch12_parallel_inter_dec]
l12_22 [lemma, in GeoCoq.Tarski_dev.Ch12_parallel_inter_dec]
l12_22_a [lemma, in GeoCoq.Tarski_dev.Ch12_parallel_inter_dec]
l12_21 [lemma, in GeoCoq.Tarski_dev.Ch12_parallel_inter_dec]
l12_21_a [lemma, in GeoCoq.Tarski_dev.Ch12_parallel_inter_dec]
l12_20 [lemma, in GeoCoq.Tarski_dev.Ch12_parallel_inter_dec]
l12_20_bis [lemma, in GeoCoq.Tarski_dev.Ch12_parallel_inter_dec]
l12_19 [lemma, in GeoCoq.Tarski_dev.Ch12_parallel_inter_dec]
l12_16 [lemma, in GeoCoq.Tarski_dev.Ch12_parallel_inter_dec]
l13_14 [lemma, in GeoCoq.Tarski_dev.Ch13_5_Pappus_Pascal]
l13_11 [lemma, in GeoCoq.Tarski_dev.Ch13_5_Pappus_Pascal]
l13_10 [lemma, in GeoCoq.Tarski_dev.Ch13_5_Pappus_Pascal]
l13_10_aux5 [lemma, in GeoCoq.Tarski_dev.Ch13_5_Pappus_Pascal]
l13_10_aux4 [lemma, in GeoCoq.Tarski_dev.Ch13_5_Pappus_Pascal]
l13_10_aux3 [lemma, in GeoCoq.Tarski_dev.Ch13_5_Pappus_Pascal]
l13_6_bis [lemma, in GeoCoq.Tarski_dev.Ch13_5_Pappus_Pascal]
l13_10_aux2 [lemma, in GeoCoq.Tarski_dev.Ch13_5_Pappus_Pascal]
l13_10_aux1 [lemma, in GeoCoq.Tarski_dev.Ch13_5_Pappus_Pascal]
l13_19_par [lemma, in GeoCoq.Tarski_dev.Ch13_6_Desargues_Hessenberg]
l13_19_par_aux [lemma, in GeoCoq.Tarski_dev.Ch13_6_Desargues_Hessenberg]
l13_19 [lemma, in GeoCoq.Tarski_dev.Ch13_6_Desargues_Hessenberg]
l13_19_aux [lemma, in GeoCoq.Tarski_dev.Ch13_6_Desargues_Hessenberg]
l13_18 [lemma, in GeoCoq.Tarski_dev.Ch13_6_Desargues_Hessenberg]
l13_18_3 [lemma, in GeoCoq.Tarski_dev.Ch13_6_Desargues_Hessenberg]
l13_18_2 [lemma, in GeoCoq.Tarski_dev.Ch13_6_Desargues_Hessenberg]
l13_15_par [lemma, in GeoCoq.Tarski_dev.Ch13_6_Desargues_Hessenberg]
l13_15 [lemma, in GeoCoq.Tarski_dev.Ch13_6_Desargues_Hessenberg]
l13_15_2 [lemma, in GeoCoq.Tarski_dev.Ch13_6_Desargues_Hessenberg]
l13_15_2_aux [lemma, in GeoCoq.Tarski_dev.Ch13_6_Desargues_Hessenberg]
l13_15_1 [lemma, in GeoCoq.Tarski_dev.Ch13_6_Desargues_Hessenberg]
l13_7 [lemma, in GeoCoq.Tarski_dev.Ch13_4_cos]
l13_6 [lemma, in GeoCoq.Tarski_dev.Ch13_4_cos]
l13_8 [lemma, in GeoCoq.Tarski_dev.Ch13_1]
l13_2 [lemma, in GeoCoq.Tarski_dev.Ch13_1]
l13_2_1 [lemma, in GeoCoq.Tarski_dev.Ch13_1]
l13_1 [lemma, in GeoCoq.Tarski_dev.Ch13_1]
L13_1 [section, in GeoCoq.Tarski_dev.Ch13_1]
l14_36_b [lemma, in GeoCoq.Tarski_dev.Ch14_order]
l14_36_a [lemma, in GeoCoq.Tarski_dev.Ch14_order]
l14_31_2 [lemma, in GeoCoq.Tarski_dev.Ch14_prod]
l14_31_1 [lemma, in GeoCoq.Tarski_dev.Ch14_prod]
l15_7_2 [lemma, in GeoCoq.Tarski_dev.Ch15_lengths]
l15_7_1 [lemma, in GeoCoq.Tarski_dev.Ch15_lengths]
l15_7 [lemma, in GeoCoq.Tarski_dev.Ch15_lengths]
l15_3 [lemma, in GeoCoq.Tarski_dev.Ch15_lengths]
l16_9_2 [lemma, in GeoCoq.Tarski_dev.Ch16_coordinates]
l16_9_1 [lemma, in GeoCoq.Tarski_dev.Ch16_coordinates]
l2_11_b [lemma, in GeoCoq.Tarski_dev.Ch03_bet]
l2_11T [lemma, in GeoCoq.Meta_theory.Models.independent_tarski_to_tarski]
l2_11 [lemma, in GeoCoq.Tarski_dev.Ch02_cong]
l3_17 [lemma, in GeoCoq.Tarski_dev.Ch03_bet]
l4_6 [lemma, in GeoCoq.Tarski_dev.Ch04_cong_bet]
l4_5 [lemma, in GeoCoq.Tarski_dev.Ch04_cong_bet]
l4_3_1 [lemma, in GeoCoq.Tarski_dev.Ch04_cong_bet]
l4_3 [lemma, in GeoCoq.Tarski_dev.Ch04_cong_bet]
l4_2 [lemma, in GeoCoq.Tarski_dev.Ch04_cong_bet]
l4_19 [lemma, in GeoCoq.Tarski_dev.Ch04_col]
l4_18 [lemma, in GeoCoq.Tarski_dev.Ch04_col]
l4_17 [lemma, in GeoCoq.Tarski_dev.Ch04_col]
l4_16 [lemma, in GeoCoq.Tarski_dev.Ch04_col]
l4_14 [lemma, in GeoCoq.Tarski_dev.Ch04_col]
l4_13 [lemma, in GeoCoq.Tarski_dev.Ch04_col]
l5_12_b [lemma, in GeoCoq.Tarski_dev.Ch05_bet_le]
l5_12_a [lemma, in GeoCoq.Tarski_dev.Ch05_bet_le]
l5_6 [lemma, in GeoCoq.Tarski_dev.Ch05_bet_le]
l5_5_2 [lemma, in GeoCoq.Tarski_dev.Ch05_bet_le]
l5_5_1 [lemma, in GeoCoq.Tarski_dev.Ch05_bet_le]
l5_3 [lemma, in GeoCoq.Tarski_dev.Ch05_bet_le]
l5_2 [lemma, in GeoCoq.Tarski_dev.Ch05_bet_le]
l5_1 [lemma, in GeoCoq.Tarski_dev.Ch05_bet_le]
l6_25 [lemma, in GeoCoq.Tarski_dev.Ch06_out_lines]
l6_21 [lemma, in GeoCoq.Tarski_dev.Ch06_out_lines]
l6_16_1 [lemma, in GeoCoq.Tarski_dev.Ch06_out_lines]
l6_13_2 [lemma, in GeoCoq.Tarski_dev.Ch06_out_lines]
l6_13_1 [lemma, in GeoCoq.Tarski_dev.Ch06_out_lines]
l6_11_existence [lemma, in GeoCoq.Tarski_dev.Ch06_out_lines]
l6_11_uniqueness [lemma, in GeoCoq.Tarski_dev.Ch06_out_lines]
l6_7 [lemma, in GeoCoq.Tarski_dev.Ch06_out_lines]
l6_6 [lemma, in GeoCoq.Tarski_dev.Ch06_out_lines]
l6_4_2 [lemma, in GeoCoq.Tarski_dev.Ch06_out_lines]
l6_4_1 [lemma, in GeoCoq.Tarski_dev.Ch06_out_lines]
l6_3_2 [lemma, in GeoCoq.Tarski_dev.Ch06_out_lines]
l6_3_1 [lemma, in GeoCoq.Tarski_dev.Ch06_out_lines]
l6_2 [lemma, in GeoCoq.Tarski_dev.Ch06_out_lines]
l7_25 [lemma, in GeoCoq.Tarski_dev.Ch07_midpoint]
l7_22 [lemma, in GeoCoq.Tarski_dev.Ch07_midpoint]
l7_22_aux [lemma, in GeoCoq.Tarski_dev.Ch07_midpoint]
l7_21 [lemma, in GeoCoq.Tarski_dev.Ch07_midpoint]
l7_20_bis [lemma, in GeoCoq.Tarski_dev.Ch07_midpoint]
l7_20 [lemma, in GeoCoq.Tarski_dev.Ch07_midpoint]
l7_17_bis [lemma, in GeoCoq.Tarski_dev.Ch07_midpoint]
l7_17 [lemma, in GeoCoq.Tarski_dev.Ch07_midpoint]
l7_16 [lemma, in GeoCoq.Tarski_dev.Ch07_midpoint]
l7_15 [lemma, in GeoCoq.Tarski_dev.Ch07_midpoint]
l7_13 [lemma, in GeoCoq.Tarski_dev.Ch07_midpoint]
l7_9_bis [lemma, in GeoCoq.Tarski_dev.Ch07_midpoint]
l7_9 [lemma, in GeoCoq.Tarski_dev.Ch07_midpoint]
l7_3_2 [lemma, in GeoCoq.Tarski_dev.Ch07_midpoint]
l7_3 [lemma, in GeoCoq.Tarski_dev.Ch07_midpoint]
l7_2 [lemma, in GeoCoq.Tarski_dev.Ch07_midpoint]
l8_21_bis [lemma, in GeoCoq.Meta_theory.Dimension_axioms.upper_dim]
l8_24 [lemma, in GeoCoq.Tarski_dev.Ch08_orthogonality]
l8_22_bis [lemma, in GeoCoq.Tarski_dev.Ch08_orthogonality]
l8_22 [lemma, in GeoCoq.Tarski_dev.Ch08_orthogonality]
l8_21 [lemma, in GeoCoq.Tarski_dev.Ch08_orthogonality]
l8_21_aux [lemma, in GeoCoq.Tarski_dev.Ch08_orthogonality]
l8_18_existence [lemma, in GeoCoq.Tarski_dev.Ch08_orthogonality]
l8_20_2 [lemma, in GeoCoq.Tarski_dev.Ch08_orthogonality]
l8_20_1 [lemma, in GeoCoq.Tarski_dev.Ch08_orthogonality]
l8_18_uniqueness [lemma, in GeoCoq.Tarski_dev.Ch08_orthogonality]
l8_16_2 [lemma, in GeoCoq.Tarski_dev.Ch08_orthogonality]
l8_16_1 [lemma, in GeoCoq.Tarski_dev.Ch08_orthogonality]
l8_15_2 [lemma, in GeoCoq.Tarski_dev.Ch08_orthogonality]
l8_15_1 [lemma, in GeoCoq.Tarski_dev.Ch08_orthogonality]
l8_14_3 [lemma, in GeoCoq.Tarski_dev.Ch08_orthogonality]
l8_14_2_2 [lemma, in GeoCoq.Tarski_dev.Ch08_orthogonality]
l8_14_2_1b_bis [lemma, in GeoCoq.Tarski_dev.Ch08_orthogonality]
l8_14_2_1b [lemma, in GeoCoq.Tarski_dev.Ch08_orthogonality]
l8_14_2_1a [lemma, in GeoCoq.Tarski_dev.Ch08_orthogonality]
l8_14_1 [lemma, in GeoCoq.Tarski_dev.Ch08_orthogonality]
l8_13_2 [lemma, in GeoCoq.Tarski_dev.Ch08_orthogonality]
l8_12 [lemma, in GeoCoq.Tarski_dev.Ch08_orthogonality]
l8_10 [lemma, in GeoCoq.Tarski_dev.Ch08_orthogonality]
l8_9 [lemma, in GeoCoq.Tarski_dev.Ch08_orthogonality]
l8_8 [lemma, in GeoCoq.Tarski_dev.Ch08_orthogonality]
l8_7 [lemma, in GeoCoq.Tarski_dev.Ch08_orthogonality]
l8_6 [lemma, in GeoCoq.Tarski_dev.Ch08_orthogonality]
l8_5 [lemma, in GeoCoq.Tarski_dev.Ch08_orthogonality]
l8_4 [lemma, in GeoCoq.Tarski_dev.Ch08_orthogonality]
l8_3 [lemma, in GeoCoq.Tarski_dev.Ch08_orthogonality]
l8_2 [lemma, in GeoCoq.Tarski_dev.Ch08_orthogonality]
l9_31 [lemma, in GeoCoq.Tarski_dev.Ch09_plane]
l9_19 [lemma, in GeoCoq.Tarski_dev.Ch09_plane]
l9_18 [lemma, in GeoCoq.Tarski_dev.Ch09_plane]
l9_17 [lemma, in GeoCoq.Tarski_dev.Ch09_plane]
l9_10 [lemma, in GeoCoq.Tarski_dev.Ch09_plane]
l9_9_bis [lemma, in GeoCoq.Tarski_dev.Ch09_plane]
l9_9 [lemma, in GeoCoq.Tarski_dev.Ch09_plane]
l9_8_2 [lemma, in GeoCoq.Tarski_dev.Ch09_plane]
l9_8_1 [lemma, in GeoCoq.Tarski_dev.Ch09_plane]
l9_5 [lemma, in GeoCoq.Tarski_dev.Ch09_plane]
l9_4_2 [lemma, in GeoCoq.Tarski_dev.Ch09_plane]
l9_4_2_aux [lemma, in GeoCoq.Tarski_dev.Ch09_plane]
l9_4_1 [lemma, in GeoCoq.Tarski_dev.Ch09_plane]
l9_4_1_aux [lemma, in GeoCoq.Tarski_dev.Ch09_plane]
l9_3 [lemma, in GeoCoq.Tarski_dev.Ch09_plane]
l9_2 [lemma, in GeoCoq.Tarski_dev.Ch09_plane]


M

Makarios_variant_to_Tarski83 [section, in GeoCoq.Meta_theory.Models.tarski_to_makarios]
Makarios_Variant_follows_from_Tarski [instance, in GeoCoq.Meta_theory.Models.tarski_to_makarios]
makarios_variant_axioms [library]
Mbetween_identity [projection, in GeoCoq.Axioms.makarios_variant_axioms]
mca_pick_variety_aux_pca [lemma, in GeoCoq.Tactics.Coinc.CoincR]
Mcong_left_commutativity [lemma, in GeoCoq.Meta_theory.Models.tarski_to_makarios]
Mcong_symmetry [lemma, in GeoCoq.Meta_theory.Models.tarski_to_makarios]
Mcong_reflexivity [lemma, in GeoCoq.Meta_theory.Models.tarski_to_makarios]
Mcong_inner_transitivity [projection, in GeoCoq.Axioms.makarios_variant_axioms]
Mcong_identity [projection, in GeoCoq.Axioms.makarios_variant_axioms]
memCP [definition, in GeoCoq.Tactics.Coinc.CoincR]
memCPAux [definition, in GeoCoq.Tactics.Coinc.CoincR]
memCPAuxHdTl [lemma, in GeoCoq.Tactics.Coinc.CoincR]
memCPAuxOK [lemma, in GeoCoq.Tactics.Coinc.CoincR]
memCPAuxProperOK [lemma, in GeoCoq.Tactics.Coinc.CoincR]
memCPAuxTlOK [lemma, in GeoCoq.Tactics.Coinc.CoincR]
memCPConsHd [lemma, in GeoCoq.Tactics.Coinc.CoincR]
memCPProper [lemma, in GeoCoq.Tactics.Coinc.CoincR]
memCPToSSOK [lemma, in GeoCoq.Tactics.Coinc.CoincR]
memMemCPAuxOK [lemma, in GeoCoq.Tactics.Coinc.CoincR]
memMemCPOK [lemma, in GeoCoq.Tactics.Coinc.CoincR]
Mfive_segment [projection, in GeoCoq.Axioms.makarios_variant_axioms]
Midpoint [definition, in GeoCoq.Tarski_dev.Ch07_midpoint]
midpoint_preserves_bet [lemma, in GeoCoq.Highschool.orientation]
midpoint_par_strict [lemma, in GeoCoq.Highschool.orientation]
midpoint_par [lemma, in GeoCoq.Highschool.orientation]
midpoint_col [lemma, in GeoCoq.Highschool.orientation]
midpoint_preserves_out [lemma, in GeoCoq.Tarski_dev.Ch12_parallel]
midpoint_preserves_per [lemma, in GeoCoq.Tarski_dev.Ch10_line_reflexivity]
midpoint_preserves_image [lemma, in GeoCoq.Tarski_dev.Ch10_line_reflexivity]
midpoint_not_midpoint [lemma, in GeoCoq.Tarski_dev.Ch07_midpoint]
midpoint_cong [lemma, in GeoCoq.Tarski_dev.Ch07_midpoint]
midpoint_col [lemma, in GeoCoq.Tarski_dev.Ch07_midpoint]
midpoint_bet [lemma, in GeoCoq.Tarski_dev.Ch07_midpoint]
midpoint_def [lemma, in GeoCoq.Tarski_dev.Ch07_midpoint]
midpoint_distinct_3 [lemma, in GeoCoq.Tarski_dev.Ch07_midpoint]
midpoint_distinct_2 [lemma, in GeoCoq.Tarski_dev.Ch07_midpoint]
midpoint_distinct_1 [lemma, in GeoCoq.Tarski_dev.Ch07_midpoint]
midpoint_existence [lemma, in GeoCoq.Tarski_dev.Ch08_orthogonality]
midpoint_existence_aux [lemma, in GeoCoq.Tarski_dev.Ch08_orthogonality]
midpoint_converse_postulate_implies_playfair [lemma, in GeoCoq.Meta_theory.Parallel_postulates.midpoint_playfair]
midpoint_playfair [section, in GeoCoq.Meta_theory.Parallel_postulates.midpoint_playfair]
midpoint_converse_postulate [definition, in GeoCoq.Meta_theory.Parallel_postulates.Euclid_def]
midpoint_cong_uniqueness [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals]
midpoint_preserves_bet [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals]
midpoint_par_strict [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals]
midpoint_par [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals]
midpoint_midpoint_col [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals]
midpoint_thales_reci [lemma, in GeoCoq.Highschool.midpoint_thales]
midpoint_thales [lemma, in GeoCoq.Highschool.midpoint_thales]
midpoint_opp [lemma, in GeoCoq.Tarski_dev.Ch14_sum]
midpoint_thales_reci_circum [lemma, in GeoCoq.Highschool.circumcenter]
midpoint_thales [library]
midpoint_playfair [library]
midpoint_theorems [library]
Mid_perm [lemma, in GeoCoq.Tarski_dev.Ch07_midpoint]
Mid_cases [lemma, in GeoCoq.Tarski_dev.Ch07_midpoint]
mid_eqv [lemma, in GeoCoq.Tarski_dev.Annexes.vectors]
Mid_tagged_Mid [lemma, in GeoCoq.Tarski_dev.Annexes.Tagged_predicates]
Mid_Mid_tagged [lemma, in GeoCoq.Tarski_dev.Annexes.Tagged_predicates]
Mid_tagged [definition, in GeoCoq.Tarski_dev.Annexes.Tagged_predicates]
mid_two_sides [lemma, in GeoCoq.Tarski_dev.Ch09_plane]
mid_preserves_col [lemma, in GeoCoq.Tarski_dev.Ch09_plane]
mid_plg_2 [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals]
mid_plg_1 [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals]
mid_plg [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals]
mid_plgf [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals]
mid_plgf_aux [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals]
mid_plgs [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals]
mid_par_cong [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals]
mid_par_cong2 [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals]
mid_par_cong1 [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals]
mid2_sac__lam6534 [lemma, in GeoCoq.Tarski_dev.Annexes.saccheri]
mid2_sac__lam6521 [lemma, in GeoCoq.Tarski_dev.Annexes.saccheri]
mid2_sac__perp_upper [lemma, in GeoCoq.Tarski_dev.Annexes.saccheri]
mid2_sac__perp_lower [lemma, in GeoCoq.Tarski_dev.Annexes.saccheri]
Minner_pasch [projection, in GeoCoq.Axioms.makarios_variant_axioms]
minus_n1_n2_0 [lemma, in GeoCoq.Utils.arity]
minus_n_0 [lemma, in GeoCoq.Utils.arity]
Mlower_dim [projection, in GeoCoq.Axioms.makarios_variant_axioms]
morph [lemma, in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
MPA [projection, in GeoCoq.Axioms.makarios_variant_axioms]
MPB [projection, in GeoCoq.Axioms.makarios_variant_axioms]
MPC [projection, in GeoCoq.Axioms.makarios_variant_axioms]
Mpoint_equality_decidability [projection, in GeoCoq.Axioms.makarios_variant_axioms]
Msegment_construction [projection, in GeoCoq.Axioms.makarios_variant_axioms]
MTpoint [projection, in GeoCoq.Axioms.makarios_variant_axioms]
MulF [definition, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
mulF__eq0 [lemma, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
mulF_morphism [instance, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]


N

n [projection, in GeoCoq.Tactics.Coinc.tactics_axioms]
nbet_isi_suma__acute [lemma, in GeoCoq.Tarski_dev.Annexes.suma]
NColB_NColOrEq [lemma, in GeoCoq.Meta_theory.Models.tarski_to_beeson]
NColB_NDiffCol [lemma, in GeoCoq.Meta_theory.Models.tarski_to_beeson]
ncolH_expand [lemma, in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
ncolH_exists [lemma, in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
ncolH_distincts [lemma, in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
ncol_conga_ncol [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
NCol_tagged_NCol [lemma, in GeoCoq.Tarski_dev.Annexes.Tagged_predicates]
NCol_NCol_tagged [lemma, in GeoCoq.Tarski_dev.Annexes.Tagged_predicates]
NCol_tagged [definition, in GeoCoq.Tarski_dev.Annexes.Tagged_predicates]
ncol_suma__ncol [lemma, in GeoCoq.Tarski_dev.Annexes.suma]
NCol_perm [lemma, in GeoCoq.Tarski_dev.Ch04_col]
NCol_cases [lemma, in GeoCoq.Tarski_dev.Ch04_col]
ncol123_plg__pars1423 [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals_inter_dec]
ncol123_plg__pars1234 [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals_inter_dec]
ncol123_plg__plgs [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals_inter_dec]
ncol124_plg__pars1423 [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals_inter_dec]
ncol124_plg__pars1234 [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals_inter_dec]
ncol124_plg__plgs [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals_inter_dec]
ncol134_plg__pars1423 [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals_inter_dec]
ncol134_plg__pars1234 [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals_inter_dec]
ncol134_plg__plgs [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals_inter_dec]
ncol234_plg__pars1423 [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals_inter_dec]
ncol234_plg__pars1234 [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals_inter_dec]
ncol234_plg__plgs [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals_inter_dec]
neg_and_eqF [lemma, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
neg_not_pos [lemma, in GeoCoq.Tarski_dev.Ch14_order]
neqO_mul_neqO [lemma, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
neq20 [lemma, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
new_pair_2 [definition, in GeoCoq.Tactics.Coinc.ColR]
new_pair_1 [definition, in GeoCoq.Tactics.Coinc.ColR]
Ng [definition, in GeoCoq.Tarski_dev.Ch14_order]
nisi__obtuse [lemma, in GeoCoq.Tarski_dev.Annexes.suma]
nlea__lta [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
nlt [lemma, in GeoCoq.Tarski_dev.Ch05_bet_le]
nlta [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
nlta__lea [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
noah_suma__isi [lemma, in GeoCoq.Meta_theory.Parallel_postulates.legendre]
NoDupOK [lemma, in GeoCoq.Utils.arity]
NoDup_dec [lemma, in GeoCoq.Utils.arity]
NotNoDupDup [lemma, in GeoCoq.Utils.arity]
not_ex_forall_not_7 [lemma, in GeoCoq.Meta_theory.Parallel_postulates.par_trans_NID]
not_null_not_col [lemma, in GeoCoq.Tarski_dev.Ch13_3_angles]
not_flat_ang_def_equiv [lemma, in GeoCoq.Tarski_dev.Ch13_3_angles]
not_null_ang_def_equiv [lemma, in GeoCoq.Tarski_dev.Ch13_3_angles]
not_null_ang_ang [lemma, in GeoCoq.Tarski_dev.Ch13_3_angles]
not_cong_is_anga1 [lemma, in GeoCoq.Tarski_dev.Ch13_3_angles]
not_conga_is_anga [lemma, in GeoCoq.Tarski_dev.Ch13_3_angles]
not_cong_is_ang1 [lemma, in GeoCoq.Tarski_dev.Ch13_3_angles]
not_conga_is_ang [lemma, in GeoCoq.Tarski_dev.Ch13_3_angles]
not_conga_not_ang [lemma, in GeoCoq.Tarski_dev.Ch13_3_angles]
not_and_lt [lemma, in GeoCoq.Tarski_dev.Ch05_bet_le]
not_bet_distincts [lemma, in GeoCoq.Tarski_dev.Ch03_bet]
not_par_inter_uniqueness [lemma, in GeoCoq.Tarski_dev.Ch12_parallel]
not_par_not_col [lemma, in GeoCoq.Tarski_dev.Ch12_parallel]
not_strict_par [lemma, in GeoCoq.Tarski_dev.Ch12_parallel]
not_strict_par2 [lemma, in GeoCoq.Tarski_dev.Ch12_parallel]
not_strict_par1 [lemma, in GeoCoq.Tarski_dev.Ch12_parallel]
not_par_strict_id [lemma, in GeoCoq.Tarski_dev.Ch12_parallel]
not_col_exists [lemma, in GeoCoq.Tarski_dev.Ch10_line_reflexivity]
not_segment_construction [lemma, in GeoCoq.Meta_theory.Counter_models.counter_model_segment_construction]
not_oah [lemma, in GeoCoq.Tarski_dev.Annexes.saccheri]
not_rah [lemma, in GeoCoq.Tarski_dev.Annexes.saccheri]
not_aah [lemma, in GeoCoq.Tarski_dev.Annexes.saccheri]
not_bet_out [lemma, in GeoCoq.Meta_theory.Dimension_axioms.upper_dim]
not_triangular_equality1 [lemma, in GeoCoq.Tarski_dev.Ch15_lengths]
not_col_par_col2_diff [lemma, in GeoCoq.Highschool.orthocenter]
not_pos_and_neg [lemma, in GeoCoq.Tarski_dev.Ch14_order]
not_cong_4321 [lemma, in GeoCoq.Tarski_dev.Ch02_cong]
not_cong_3421 [lemma, in GeoCoq.Tarski_dev.Ch02_cong]
not_cong_4312 [lemma, in GeoCoq.Tarski_dev.Ch02_cong]
not_cong_3412 [lemma, in GeoCoq.Tarski_dev.Ch02_cong]
not_cong_2143 [lemma, in GeoCoq.Tarski_dev.Ch02_cong]
not_cong_1243 [lemma, in GeoCoq.Tarski_dev.Ch02_cong]
not_cong_2134 [lemma, in GeoCoq.Tarski_dev.Ch02_cong]
not_par_same_side [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
not_par_other_side [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
not_par_two_sides [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
not_one_side_two_sides [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
not_lta_and_gta [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
not_gta_and_cong [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
not_lta_and_cong [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
not_and_lta [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
not_conga_sym [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
not_conga [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
not_two_sides_one_side [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
not_col_perm_2 [lemma, in GeoCoq.Tactics.Coinc.tarski_to_coinc_theory_for_concyclic]
not_col_perm_1 [lemma, in GeoCoq.Tactics.Coinc.tarski_to_coinc_theory_for_concyclic]
not_col [definition, in GeoCoq.Tactics.Coinc.tarski_to_coinc_theory_for_concyclic]
not_bet_and_out [lemma, in GeoCoq.Tarski_dev.Ch06_out_lines]
not_out_bet [lemma, in GeoCoq.Tarski_dev.Ch06_out_lines]
not_cut3 [lemma, in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
not_betH121 [lemma, in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
not_bet_diff [lemma, in GeoCoq.Meta_theory.Counter_models.counter_model_bet_identity]
not_between_identity [lemma, in GeoCoq.Meta_theory.Counter_models.counter_model_bet_identity]
not_col_perm_2 [lemma, in GeoCoq.Tactics.Coinc.tarski_to_coinc_theory_for_cop]
not_col_perm_1 [lemma, in GeoCoq.Tactics.Coinc.tarski_to_coinc_theory_for_cop]
not_col [definition, in GeoCoq.Tactics.Coinc.tarski_to_coinc_theory_for_cop]
not_cong_is_len1 [lemma, in GeoCoq.Tarski_dev.Ch13_2_length]
not_cong_is_len [lemma, in GeoCoq.Tarski_dev.Ch13_2_length]
not_two_sides_id [lemma, in GeoCoq.Tarski_dev.Ch09_plane]
not_par_pars_not_cong [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals_inter_dec]
not_col_exists [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals]
not_col_sym_not_col [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals]
not_par_one_not_par [lemma, in GeoCoq.Tarski_dev.Ch12_parallel_inter_dec]
not_par_inter [lemma, in GeoCoq.Tarski_dev.Ch12_parallel_inter_dec]
not_par_strict_inter_exists [lemma, in GeoCoq.Tarski_dev.Ch12_parallel_inter_dec]
not_lta_gea [lemma, in GeoCoq.Tarski_dev.Ch12_parallel_inter_dec]
not_par_inter_exists [lemma, in GeoCoq.Tarski_dev.Ch12_parallel_inter_dec]
not_null_double_not_null [lemma, in GeoCoq.Tarski_dev.Ch14_sum]
not_col_efoot_not_equality [lemma, in GeoCoq.Highschool.bisector]
not_col_bfoot_not_equality [lemma, in GeoCoq.Highschool.bisector]
not_col_distincts [lemma, in GeoCoq.Tarski_dev.Ch04_col]
not_col_permutation_5 [lemma, in GeoCoq.Tarski_dev.Ch04_col]
not_col_permutation_4 [lemma, in GeoCoq.Tarski_dev.Ch04_col]
not_col_permutation_3 [lemma, in GeoCoq.Tarski_dev.Ch04_col]
not_col_permutation_2 [lemma, in GeoCoq.Tarski_dev.Ch04_col]
not_col_permutation_1 [lemma, in GeoCoq.Tarski_dev.Ch04_col]
nthCircPermNAny [lemma, in GeoCoq.Utils.arity]
nthCircPerm1 [lemma, in GeoCoq.Utils.arity]
nthCircPerm1Eq [lemma, in GeoCoq.Utils.arity]
nthCircPerm2 [lemma, in GeoCoq.Utils.arity]
nthCircPerm2Eq [lemma, in GeoCoq.Utils.arity]
nthCP [definition, in GeoCoq.Utils.arity]
nthCPTlOK [lemma, in GeoCoq.Utils.arity]
nthCP01 [lemma, in GeoCoq.Utils.arity]
nthEqOK [lemma, in GeoCoq.Utils.arity]
nthFirst [lemma, in GeoCoq.Utils.arity]
nthLast [lemma, in GeoCoq.Utils.arity]
NT_NBet [lemma, in GeoCoq.Meta_theory.Models.tarski_to_beeson]
null_anga_null_anga' [lemma, in GeoCoq.Tarski_dev.Ch13_3_angles]
null_anga [lemma, in GeoCoq.Tarski_dev.Ch13_3_angles]
null_ang [lemma, in GeoCoq.Tarski_dev.Ch13_3_angles]
null_lcos [lemma, in GeoCoq.Tarski_dev.Ch13_4_cos]
null_lcos_eql [lemma, in GeoCoq.Tarski_dev.Ch13_4_cos]
null_sum_eq [lemma, in GeoCoq.Tarski_dev.Annexes.vectors]
null_sum [lemma, in GeoCoq.Tarski_dev.Annexes.vectors]
null_vector [lemma, in GeoCoq.Tarski_dev.Annexes.vectors]
null_len [lemma, in GeoCoq.Tarski_dev.Ch13_2_length]


O

Obtuse [definition, in GeoCoq.Tarski_dev.Ch11_angles]
obtuse_sac__oah [lemma, in GeoCoq.Tarski_dev.Annexes.saccheri]
obtuse_sac__lt [lemma, in GeoCoq.Tarski_dev.Annexes.saccheri]
obtuse_not_acute [lemma, in GeoCoq.Tarski_dev.Ch13_4_cos]
obtuse_chara [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
obtuse_per__lta [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
obtuse_conga__obtuse [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
obtuse_distincts [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
obtuse_gea_obtuse [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
obtuse_sym [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
obtuse__nisi [lemma, in GeoCoq.Tarski_dev.Annexes.suma]
OCP [definition, in GeoCoq.Utils.sets]
OCPALengthOK [lemma, in GeoCoq.Utils.sets]
OCPAux [definition, in GeoCoq.Utils.sets]
OCPPerm [lemma, in GeoCoq.Utils.sets]
OCPSortedAux [lemma, in GeoCoq.Utils.sets]
OCPSortedTl [lemma, in GeoCoq.Utils.sets]
OCPTlOK [lemma, in GeoCoq.Utils.sets]
OF [definition, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
OFSC [definition, in GeoCoq.Tarski_dev.Ch02_cong]
OneF [definition, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
one_side_eqo [lemma, in GeoCoq.Highschool.orientation]
one_side_eq_o [lemma, in GeoCoq.Highschool.orientation]
one_or_two_sides [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
one_side_same_side [lemma, in GeoCoq.Meta_theory.Models.tarski_to_hilbert]
one_side_col_out [lemma, in GeoCoq.Tarski_dev.Annexes.vectors]
one_side_not_col [lemma, in GeoCoq.Tarski_dev.Ch09_plane]
one_side_transitivity [lemma, in GeoCoq.Tarski_dev.Ch09_plane]
one_side_symmetry [lemma, in GeoCoq.Tarski_dev.Ch09_plane]
one_side_reflexivity [lemma, in GeoCoq.Tarski_dev.Ch09_plane]
one_side_chara [lemma, in GeoCoq.Tarski_dev.Ch09_plane]
one_side_dec [lemma, in GeoCoq.Tarski_dev.Ch10_line_reflexivity_2D]
Opp [definition, in GeoCoq.Tarski_dev.Ch14_sum]
OppF [definition, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
oppF_neq0 [lemma, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
oppF_morphism [instance, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
opposite_sum [lemma, in GeoCoq.Tarski_dev.Annexes.vectors]
opp_same_square [lemma, in GeoCoq.Tarski_dev.Ch15_pyth_rel]
opp_pythrel [lemma, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
opp_f [lemma, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
opp_col [lemma, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
opp_2_le_le [lemma, in GeoCoq.Tarski_dev.Ch14_order]
opp_neg_pos [lemma, in GeoCoq.Tarski_dev.Ch14_order]
opp_pos_neg [lemma, in GeoCoq.Tarski_dev.Ch14_order]
opp_not_same_dir [lemma, in GeoCoq.Tarski_dev.Annexes.vectors]
opp_dir_to_null [lemma, in GeoCoq.Tarski_dev.Annexes.vectors]
opp_dir_id [lemma, in GeoCoq.Tarski_dev.Annexes.vectors]
Opp_dir [definition, in GeoCoq.Tarski_dev.Annexes.vectors]
opp_prod [lemma, in GeoCoq.Tarski_dev.Ch14_prod]
opp_midpoint [lemma, in GeoCoq.Tarski_dev.Ch14_sum]
opp_uniqueness [lemma, in GeoCoq.Tarski_dev.Ch14_sum]
opp_comm [lemma, in GeoCoq.Tarski_dev.Ch14_sum]
opp_exists [lemma, in GeoCoq.Tarski_dev.Ch14_sum]
opp0 [lemma, in GeoCoq.Tarski_dev.Ch14_sum]
opp0_uniqueness [lemma, in GeoCoq.Tarski_dev.Ch14_sum]
Order [section, in GeoCoq.Tarski_dev.Ch14_order]
Orientation [section, in GeoCoq.Highschool.orientation]
orientation [library]
original_spp__inverse_projection_postulate [lemma, in GeoCoq.Meta_theory.Parallel_postulates.original_spp_inverse_projection_postulate]
original_spp_inverse_projection_postulate [section, in GeoCoq.Meta_theory.Parallel_postulates.original_spp_inverse_projection_postulate]
original_euclid__original_spp [lemma, in GeoCoq.Meta_theory.Parallel_postulates.original_euclid_original_spp]
original_euclid_original_spp [section, in GeoCoq.Meta_theory.Parallel_postulates.original_euclid_original_spp]
original_spp_inverse_projection_postulate [library]
original_euclid_original_spp [library]
Orthocenter [section, in GeoCoq.Highschool.orthocenter]
orthocenter [library]
orthocenter_col [lemma, in GeoCoq.Highschool.orthocenter]
orthocenter_per [lemma, in GeoCoq.Highschool.orthocenter]
or_lt_cong_gt [lemma, in GeoCoq.Tarski_dev.Ch05_bet_le]
or_bet_out [lemma, in GeoCoq.Meta_theory.Dimension_axioms.upper_dim]
or_lta_conga_gta [lemma, in GeoCoq.Tarski_dev.Ch12_parallel_inter_dec]
OS [definition, in GeoCoq.Tarski_dev.Ch09_plane]
osym_not_col [lemma, in GeoCoq.Tarski_dev.Ch10_line_reflexivity]
os_ts__inangle [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
OS_same_side' [lemma, in GeoCoq.Meta_theory.Models.tarski_to_hilbert]
OS_distinct [lemma, in GeoCoq.Meta_theory.Models.tarski_to_hilbert]
os_ts1324__os [lemma, in GeoCoq.Tarski_dev.Ch09_plane]
os_out_os [lemma, in GeoCoq.Tarski_dev.Ch09_plane]
os_cong_par_cong_par [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals_inter_dec]
os2__inangle [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
OS2__TS [lemma, in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
os3__lta [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
other_point_exists [lemma, in GeoCoq.Tarski_dev.Ch12_parallel]
other_point_on_line [lemma, in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
other_point_exists [lemma, in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
Out [definition, in GeoCoq.Tarski_dev.Ch06_out_lines]
outer_transitivity_between [lemma, in GeoCoq.Tarski_dev.Ch03_bet]
outer_transitivity_between2 [lemma, in GeoCoq.Tarski_dev.Ch03_bet]
outer_pasch [lemma, in GeoCoq.Tarski_dev.Ch09_plane]
outH [definition, in GeoCoq.Meta_theory.Models.tarski_to_hilbert]
outH_out [lemma, in GeoCoq.Meta_theory.Models.tarski_to_hilbert]
outH_sym [lemma, in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
outH_col [lemma, in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
outH_dec [lemma, in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
outH_expand [lemma, in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
outH_trivial [lemma, in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
out_out_anga [lemma, in GeoCoq.Tarski_dev.Ch13_3_angles]
out_null_anga [lemma, in GeoCoq.Tarski_dev.Ch13_3_angles]
out_null_ang [lemma, in GeoCoq.Tarski_dev.Ch13_3_angles]
out_len_eq [lemma, in GeoCoq.Tarski_dev.Ch13_3_angles]
out_is_len_eq [lemma, in GeoCoq.Tarski_dev.Ch13_3_angles]
out_preserves_eqo [lemma, in GeoCoq.Highschool.orientation]
out_preserves_eqo1 [lemma, in GeoCoq.Highschool.orientation]
out_preserves_eq_o [lemma, in GeoCoq.Highschool.orientation]
out_one_side_1 [lemma, in GeoCoq.Tarski_dev.Ch12_parallel]
out_two_sides_two_sides [lemma, in GeoCoq.Meta_theory.Dimension_axioms.upper_dim]
out_acute [lemma, in GeoCoq.Tarski_dev.Ch13_4_cos]
out__acute [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
out_lea__out [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
out_conga_out [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
out_in_angle_out [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
out_in_angle [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
out_conga [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
out_bet__out [lemma, in GeoCoq.Tarski_dev.Ch06_out_lines]
out_bet_out_2 [lemma, in GeoCoq.Tarski_dev.Ch06_out_lines]
out_bet_out_1 [lemma, in GeoCoq.Tarski_dev.Ch06_out_lines]
out_to_bet [lemma, in GeoCoq.Tarski_dev.Ch06_out_lines]
out_cong_cong [lemma, in GeoCoq.Tarski_dev.Ch06_out_lines]
out_trivial [lemma, in GeoCoq.Tarski_dev.Ch06_out_lines]
out_col [lemma, in GeoCoq.Tarski_dev.Ch06_out_lines]
out_distinct [lemma, in GeoCoq.Tarski_dev.Ch06_out_lines]
out_diff2 [lemma, in GeoCoq.Tarski_dev.Ch06_out_lines]
out_diff1 [lemma, in GeoCoq.Tarski_dev.Ch06_out_lines]
out_dec [lemma, in GeoCoq.Tarski_dev.Ch06_out_lines]
out_outH [lemma, in GeoCoq.Meta_theory.Models.tarski_to_hilbert]
out_same_side' [lemma, in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
out_construction [lemma, in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
out_same_side [lemma, in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
out_distinct [lemma, in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
out_one_side [lemma, in GeoCoq.Tarski_dev.Ch09_plane]
out_out_one_side [lemma, in GeoCoq.Tarski_dev.Ch09_plane]
out_out_two_sides [lemma, in GeoCoq.Tarski_dev.Ch09_plane]
out2_out_2 [lemma, in GeoCoq.Tarski_dev.Ch06_out_lines]
out2_out_1 [lemma, in GeoCoq.Tarski_dev.Ch06_out_lines]
out2__bet [lemma, in GeoCoq.Tarski_dev.Ch06_out_lines]
out2_bet_out [lemma, in GeoCoq.Tarski_dev.Ch06_out_lines]
out2_out1 [lemma, in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
out2_out [lemma, in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
out213__isi [lemma, in GeoCoq.Tarski_dev.Annexes.suma]
out213__suma [lemma, in GeoCoq.Tarski_dev.Annexes.suma]
out213_suma__conga [lemma, in GeoCoq.Tarski_dev.Annexes.suma]
out546__isi [lemma, in GeoCoq.Tarski_dev.Annexes.suma]
out546__suma [lemma, in GeoCoq.Tarski_dev.Annexes.suma]
out546_suma__conga [lemma, in GeoCoq.Tarski_dev.Annexes.suma]
out6_suma__suma [lemma, in GeoCoq.Tarski_dev.Annexes.suma]
O_not_positive [lemma, in GeoCoq.Tarski_dev.Ch14_order]


P

PA [projection, in GeoCoq.Axioms.tarski_axioms]
PA [projection, in GeoCoq.Axioms.beeson_s_axioms]
PAneqPB [lemma, in GeoCoq.Meta_theory.Models.tarski_to_hilbert]
Pappus_Pascal_2 [section, in GeoCoq.Tarski_dev.Ch13_5_Pappus_Pascal]
Pappus_Pascal [section, in GeoCoq.Tarski_dev.Ch13_5_Pappus_Pascal]
Par [definition, in GeoCoq.Tarski_dev.Ch12_parallel]
Para [definition, in GeoCoq.Meta_theory.Models.tarski_to_hilbert]
Para [definition, in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
Parallelogram [definition, in GeoCoq.Tarski_dev.Annexes.quadrilaterals]
parallelogram_strict_midpoint [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals_inter_dec]
parallelogram_strict_not_col_4 [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals_inter_dec]
parallelogram_strict_not_col_3 [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals_inter_dec]
parallelogram_strict_not_col_2 [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals_inter_dec]
parallelogram_equiv_plg [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals_inter_dec]
parallelogram_to_plg [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals_inter_dec]
parallelogram_strict_not_col [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals]
Parallelogram_strict_Parallelogram [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals]
Parallelogram_flat [definition, in GeoCoq.Tarski_dev.Annexes.quadrilaterals]
Parallelogram_strict [definition, in GeoCoq.Tarski_dev.Annexes.quadrilaterals]
parallel_existence_spec [lemma, in GeoCoq.Tarski_dev.Ch12_parallel]
parallel_existence [lemma, in GeoCoq.Tarski_dev.Ch12_parallel]
parallel_2_plg [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals_inter_dec]
parallel_existence1 [lemma, in GeoCoq.Tarski_dev.Ch12_parallel_inter_dec]
parallel_uniqueness [lemma, in GeoCoq.Tarski_dev.Ch12_parallel_inter_dec]
ParaP [definition, in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
Para_Par [lemma, in GeoCoq.Meta_theory.Models.tarski_to_hilbert]
pars__os3412 [lemma, in GeoCoq.Tarski_dev.Ch12_parallel]
pars_par_plg [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals_inter_dec]
pars_par_pars [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals_inter_dec]
partition_sp_2 [definition, in GeoCoq.Tactics.Coinc.ColR]
partition_sp_1 [definition, in GeoCoq.Tactics.Coinc.ColR]
partition_ss [definition, in GeoCoq.Tactics.Coinc.ColR]
par_trans_implies_playfair [lemma, in GeoCoq.Meta_theory.Parallel_postulates.par_trans_playfair]
par_trans_playfair [section, in GeoCoq.Meta_theory.Parallel_postulates.par_trans_playfair]
par_trans__NID [lemma, in GeoCoq.Meta_theory.Parallel_postulates.par_trans_NID]
par_trans__par_dec [lemma, in GeoCoq.Meta_theory.Parallel_postulates.par_trans_NID]
par_trans_NID [section, in GeoCoq.Meta_theory.Parallel_postulates.par_trans_NID]
par_perp2 [lemma, in GeoCoq.Tarski_dev.Ch13_5_Pappus_Pascal]
par_col [lemma, in GeoCoq.Highschool.orientation]
par_cong_mid [lemma, in GeoCoq.Highschool.orientation]
par_strict_distinct [lemma, in GeoCoq.Tarski_dev.Ch12_parallel]
par_strict_par [lemma, in GeoCoq.Tarski_dev.Ch12_parallel]
par_two_sides_two_sides [lemma, in GeoCoq.Tarski_dev.Ch12_parallel]
par_strict_col4__par_strict [lemma, in GeoCoq.Tarski_dev.Ch12_parallel]
par_col4__par [lemma, in GeoCoq.Tarski_dev.Ch12_parallel]
par_distinct [lemma, in GeoCoq.Tarski_dev.Ch12_parallel]
par_strict_col2_par_strict [lemma, in GeoCoq.Tarski_dev.Ch12_parallel]
par_strict_col_par_strict [lemma, in GeoCoq.Tarski_dev.Ch12_parallel]
par_col2_par_bis [lemma, in GeoCoq.Tarski_dev.Ch12_parallel]
par_col2_par [lemma, in GeoCoq.Tarski_dev.Ch12_parallel]
par_col_par_2 [lemma, in GeoCoq.Tarski_dev.Ch12_parallel]
par_not_col_strict [lemma, in GeoCoq.Tarski_dev.Ch12_parallel]
par_distincts [lemma, in GeoCoq.Tarski_dev.Ch12_parallel]
par_not_col [lemma, in GeoCoq.Tarski_dev.Ch12_parallel]
par_col_par [lemma, in GeoCoq.Tarski_dev.Ch12_parallel]
Par_strict_perm [lemma, in GeoCoq.Tarski_dev.Ch12_parallel]
Par_strict_cases [lemma, in GeoCoq.Tarski_dev.Ch12_parallel]
Par_perm [lemma, in GeoCoq.Tarski_dev.Ch12_parallel]
Par_cases [lemma, in GeoCoq.Tarski_dev.Ch12_parallel]
par_neq2 [lemma, in GeoCoq.Tarski_dev.Ch12_parallel]
par_neq1 [lemma, in GeoCoq.Tarski_dev.Ch12_parallel]
par_strict_neq2 [lemma, in GeoCoq.Tarski_dev.Ch12_parallel]
par_strict_neq1 [lemma, in GeoCoq.Tarski_dev.Ch12_parallel]
par_strict_comm [lemma, in GeoCoq.Tarski_dev.Ch12_parallel]
par_strict_right_comm [lemma, in GeoCoq.Tarski_dev.Ch12_parallel]
par_strict_left_comm [lemma, in GeoCoq.Tarski_dev.Ch12_parallel]
par_comm [lemma, in GeoCoq.Tarski_dev.Ch12_parallel]
par_right_comm [lemma, in GeoCoq.Tarski_dev.Ch12_parallel]
par_left_comm [lemma, in GeoCoq.Tarski_dev.Ch12_parallel]
par_symmetry [lemma, in GeoCoq.Tarski_dev.Ch12_parallel]
par_strict_symmetry [lemma, in GeoCoq.Tarski_dev.Ch12_parallel]
par_id_5 [lemma, in GeoCoq.Tarski_dev.Ch12_parallel]
par_id_4 [lemma, in GeoCoq.Tarski_dev.Ch12_parallel]
par_id_3 [lemma, in GeoCoq.Tarski_dev.Ch12_parallel]
par_id_2 [lemma, in GeoCoq.Tarski_dev.Ch12_parallel]
par_id_1 [lemma, in GeoCoq.Tarski_dev.Ch12_parallel]
par_strict_not_col_4 [lemma, in GeoCoq.Tarski_dev.Ch12_parallel]
par_strict_not_col_3 [lemma, in GeoCoq.Tarski_dev.Ch12_parallel]
par_strict_not_col_2 [lemma, in GeoCoq.Tarski_dev.Ch12_parallel]
par_strict_not_col_1 [lemma, in GeoCoq.Tarski_dev.Ch12_parallel]
par_id [lemma, in GeoCoq.Tarski_dev.Ch12_parallel]
par_strict_irreflexivity [lemma, in GeoCoq.Tarski_dev.Ch12_parallel]
par_reflexivity [lemma, in GeoCoq.Tarski_dev.Ch12_parallel]
Par_strict [definition, in GeoCoq.Tarski_dev.Ch12_parallel]
par_perp_perp_implies_par_perp_2_par [lemma, in GeoCoq.Meta_theory.Parallel_postulates.par_perp_perp_par_perp_2_par]
par_perp_perp_par_perp_2_par [section, in GeoCoq.Meta_theory.Parallel_postulates.par_perp_perp_par_perp_2_par]
par_perp_perp_implies_playfair [lemma, in GeoCoq.Meta_theory.Parallel_postulates.par_perp_perp_playfair]
par_perp_perp_playfair [section, in GeoCoq.Meta_theory.Parallel_postulates.par_perp_perp_playfair]
Par_AM_Par [lemma, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
par_perp_perp_implies_perp_bisect_existence [lemma, in GeoCoq.Meta_theory.Parallel_postulates.par_perp_perp_TCP]
par_perp_perp_TCP [section, in GeoCoq.Meta_theory.Parallel_postulates.par_perp_perp_TCP]
par_col_project [lemma, in GeoCoq.Tarski_dev.Annexes.project]
par_perp_2_par_implies_par_perp_perp [lemma, in GeoCoq.Meta_theory.Parallel_postulates.par_perp_2_par_par_perp_perp]
par_perp_2_par_par_perp_perp [section, in GeoCoq.Meta_theory.Parallel_postulates.par_perp_2_par_par_perp_perp]
par_ts_same_dir [lemma, in GeoCoq.Tarski_dev.Annexes.vectors]
Par_tagged_Par [lemma, in GeoCoq.Tarski_dev.Annexes.Tagged_predicates]
Par_Par_tagged [lemma, in GeoCoq.Tarski_dev.Annexes.Tagged_predicates]
Par_tagged [definition, in GeoCoq.Tarski_dev.Annexes.Tagged_predicates]
Par_strict_tagged_Par_strict [lemma, in GeoCoq.Tarski_dev.Annexes.Tagged_predicates]
Par_strict_Par_strict_tagged [lemma, in GeoCoq.Tarski_dev.Annexes.Tagged_predicates]
Par_strict_tagged [definition, in GeoCoq.Tarski_dev.Annexes.Tagged_predicates]
par_par_cong_cong_parallelogram [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals_inter_dec]
par_strict_trans [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals_inter_dec]
par_cong3_rect [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals_inter_dec]
par_cong_plg_2 [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals_inter_dec]
par_cong_plg [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals_inter_dec]
par_cong_cong [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals_inter_dec]
par_perp_2_par [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals_inter_dec]
par_perp_perp [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals_inter_dec]
par_2_plg [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals_inter_dec]
par_preserves_conga_os [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals_inter_dec]
par_preserves_conga_ts [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals_inter_dec]
par_cong_mid [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals_inter_dec]
par_strict_cong_mid1 [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals_inter_dec]
par_strict_cong_mid [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals_inter_dec]
par_cong_mid_os [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals_inter_dec]
par_cong_mid_ts [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals_inter_dec]
par_strict_not_col [lemma, in GeoCoq.Tarski_dev.Ch12_parallel_inter_dec]
par_one_or_two_sides [lemma, in GeoCoq.Tarski_dev.Ch12_parallel_inter_dec]
par_inter [lemma, in GeoCoq.Tarski_dev.Ch12_parallel_inter_dec]
par_not_par [lemma, in GeoCoq.Tarski_dev.Ch12_parallel_inter_dec]
Par_dec [lemma, in GeoCoq.Tarski_dev.Ch12_parallel_inter_dec]
par_strict_all_one_side [lemma, in GeoCoq.Tarski_dev.Ch12_parallel_inter_dec]
par_strict_one_side [lemma, in GeoCoq.Tarski_dev.Ch12_parallel_inter_dec]
par_trans [lemma, in GeoCoq.Tarski_dev.Ch12_parallel_inter_dec]
par_perp_2_par_par_perp_perp [library]
par_perp_perp_playfair [library]
par_perp_perp_par_perp_2_par [library]
par_perp_perp_TCP [library]
par_trans_playfair [library]
par_trans_NID [library]
par3_conga3 [lemma, in GeoCoq.Tarski_dev.Annexes.project]
pasch [lemma, in GeoCoq.Meta_theory.Models.tarski_to_beeson]
pasch [projection, in GeoCoq.Axioms.hilbert_axioms]
pasch_col_case [lemma, in GeoCoq.Meta_theory.Models.tarski_to_beeson]
pasch_general_case [lemma, in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
PB [projection, in GeoCoq.Axioms.tarski_axioms]
PB [projection, in GeoCoq.Axioms.beeson_s_axioms]
PC [projection, in GeoCoq.Axioms.tarski_axioms]
PC [projection, in GeoCoq.Axioms.beeson_s_axioms]
pcaHdTl [lemma, in GeoCoq.Utils.arity]
Per [definition, in GeoCoq.Tarski_dev.Ch08_orthogonality]
perBAB [lemma, in GeoCoq.Tarski_dev.Ch08_orthogonality]
PermCoincOK [lemma, in GeoCoq.Tactics.Coinc.Permutations]
PermOK [lemma, in GeoCoq.Utils.arity]
PermOKAux [lemma, in GeoCoq.Utils.arity]
PermSorted [lemma, in GeoCoq.Utils.sets]
Permutations [section, in GeoCoq.Tactics.Coinc.Permutations]
Permutations [library]
PermWdOK [lemma, in GeoCoq.Tactics.Coinc.Permutations]
Perp [definition, in GeoCoq.Tarski_dev.Ch08_orthogonality]
PerpBisect_3 [section, in GeoCoq.Tarski_dev.Annexes.perp_bisect]
PerpBisect_2 [section, in GeoCoq.Tarski_dev.Annexes.perp_bisect]
PerpBisect_1 [section, in GeoCoq.Tarski_dev.Annexes.perp_bisect]
perpendicular_transversal_postulate [definition, in GeoCoq.Meta_theory.Parallel_postulates.Euclid_def]
perp_not_eq_3 [lemma, in GeoCoq.Highschool.orientation]
perp_not_par [lemma, in GeoCoq.Tarski_dev.Ch12_parallel]
perp_perp_col_col [lemma, in GeoCoq.Tarski_dev.Ch12_parallel]
Perp_dec [lemma, in GeoCoq.Tarski_dev.Ch12_parallel]
perp_exists [lemma, in GeoCoq.Tarski_dev.Ch10_line_reflexivity]
perp_acute [lemma, in GeoCoq.Tarski_dev.Ch13_4_cos]
perp_obtuse_bet [lemma, in GeoCoq.Tarski_dev.Ch13_4_cos]
perp_out__acute [lemma, in GeoCoq.Tarski_dev.Ch13_4_cos]
perp_acute_out [lemma, in GeoCoq.Tarski_dev.Ch13_4_cos]
perp_triangle_area [lemma, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
Perp_AM_Perp [lemma, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
perp_bet_obtuse [lemma, in GeoCoq.Tarski_dev.Ch13_1]
perp_out_acute [lemma, in GeoCoq.Tarski_dev.Ch13_1]
perp_in_rewrite [lemma, in GeoCoq.Tarski_dev.Ch13_1]
perp_inter_perp_in_n [lemma, in GeoCoq.Tarski_dev.Ch13_1]
perp_in_perp_in_col [lemma, in GeoCoq.Tarski_dev.Ch13_1]
perp_per_bet [lemma, in GeoCoq.Tarski_dev.Ch13_1]
perp_in_perp_bis [lemma, in GeoCoq.Tarski_dev.Ch08_orthogonality]
perp_col2_bis [lemma, in GeoCoq.Tarski_dev.Ch08_orthogonality]
perp_in_col_perp_in [lemma, in GeoCoq.Tarski_dev.Ch08_orthogonality]
perp_not_col [lemma, in GeoCoq.Tarski_dev.Ch08_orthogonality]
perp_not_col2 [lemma, in GeoCoq.Tarski_dev.Ch08_orthogonality]
perp_proj [lemma, in GeoCoq.Tarski_dev.Ch08_orthogonality]
perp_in_perp [lemma, in GeoCoq.Tarski_dev.Ch08_orthogonality]
perp_in_id [lemma, in GeoCoq.Tarski_dev.Ch08_orthogonality]
perp_cong [lemma, in GeoCoq.Tarski_dev.Ch08_orthogonality]
perp_not_eq_2 [lemma, in GeoCoq.Tarski_dev.Ch08_orthogonality]
perp_not_eq_1 [lemma, in GeoCoq.Tarski_dev.Ch08_orthogonality]
perp_col2 [lemma, in GeoCoq.Tarski_dev.Ch08_orthogonality]
perp_col [lemma, in GeoCoq.Tarski_dev.Ch08_orthogonality]
perp_per_2 [lemma, in GeoCoq.Tarski_dev.Ch08_orthogonality]
perp_per_1 [lemma, in GeoCoq.Tarski_dev.Ch08_orthogonality]
perp_perp_in [lemma, in GeoCoq.Tarski_dev.Ch08_orthogonality]
perp_in_col [lemma, in GeoCoq.Tarski_dev.Ch08_orthogonality]
perp_col1 [lemma, in GeoCoq.Tarski_dev.Ch08_orthogonality]
Perp_in_perm [lemma, in GeoCoq.Tarski_dev.Ch08_orthogonality]
Perp_in_cases [lemma, in GeoCoq.Tarski_dev.Ch08_orthogonality]
Perp_perm [lemma, in GeoCoq.Tarski_dev.Ch08_orthogonality]
Perp_cases [lemma, in GeoCoq.Tarski_dev.Ch08_orthogonality]
perp_in_comm [lemma, in GeoCoq.Tarski_dev.Ch08_orthogonality]
perp_in_right_comm [lemma, in GeoCoq.Tarski_dev.Ch08_orthogonality]
perp_in_left_comm [lemma, in GeoCoq.Tarski_dev.Ch08_orthogonality]
perp_in_sym [lemma, in GeoCoq.Tarski_dev.Ch08_orthogonality]
perp_comm [lemma, in GeoCoq.Tarski_dev.Ch08_orthogonality]
perp_right_comm [lemma, in GeoCoq.Tarski_dev.Ch08_orthogonality]
perp_left_comm [lemma, in GeoCoq.Tarski_dev.Ch08_orthogonality]
perp_col0 [lemma, in GeoCoq.Tarski_dev.Ch08_orthogonality]
perp_sym [lemma, in GeoCoq.Tarski_dev.Ch08_orthogonality]
perp_in_per [lemma, in GeoCoq.Tarski_dev.Ch08_orthogonality]
perp_in_distinct [lemma, in GeoCoq.Tarski_dev.Ch08_orthogonality]
perp_distinct [lemma, in GeoCoq.Tarski_dev.Ch08_orthogonality]
Perp_in_dec [lemma, in GeoCoq.Tarski_dev.Ch08_orthogonality]
Perp_at [definition, in GeoCoq.Tarski_dev.Ch08_orthogonality]
perp_projp2_eq [lemma, in GeoCoq.Tarski_dev.Annexes.project]
perp_projp [lemma, in GeoCoq.Tarski_dev.Annexes.project]
perp_mid_perp_bisect [lemma, in GeoCoq.Tarski_dev.Annexes.perp_bisect]
perp_bisect_is_on_perp_bisect [lemma, in GeoCoq.Tarski_dev.Annexes.perp_bisect]
perp_bisect_conc [lemma, in GeoCoq.Tarski_dev.Annexes.perp_bisect]
perp_bisect_cong [lemma, in GeoCoq.Tarski_dev.Annexes.perp_bisect]
perp_bisect_cong_2 [lemma, in GeoCoq.Tarski_dev.Annexes.perp_bisect]
perp_bisect_cong_1 [lemma, in GeoCoq.Tarski_dev.Annexes.perp_bisect]
perp_bisect_perp [lemma, in GeoCoq.Tarski_dev.Annexes.perp_bisect]
perp_in_per_4 [lemma, in GeoCoq.Tarski_dev.Annexes.perp_bisect]
perp_in_per_3 [lemma, in GeoCoq.Tarski_dev.Annexes.perp_bisect]
perp_in_per_2 [lemma, in GeoCoq.Tarski_dev.Annexes.perp_bisect]
perp_in_per_1 [lemma, in GeoCoq.Tarski_dev.Annexes.perp_bisect]
perp_bisect_sym_3 [lemma, in GeoCoq.Tarski_dev.Annexes.perp_bisect]
perp_bisect_sym_2 [lemma, in GeoCoq.Tarski_dev.Annexes.perp_bisect]
perp_bisect_sym_1 [lemma, in GeoCoq.Tarski_dev.Annexes.perp_bisect]
perp_bisect_equiv_def [lemma, in GeoCoq.Tarski_dev.Annexes.perp_bisect]
Perp_bisect_bis [definition, in GeoCoq.Tarski_dev.Annexes.perp_bisect]
Perp_bisect [definition, in GeoCoq.Tarski_dev.Annexes.perp_bisect]
Perp_tagged_Perp [lemma, in GeoCoq.Tarski_dev.Annexes.Tagged_predicates]
Perp_Perp_tagged [lemma, in GeoCoq.Tarski_dev.Annexes.Tagged_predicates]
Perp_tagged [definition, in GeoCoq.Tarski_dev.Annexes.Tagged_predicates]
Perp_in_tagged_Perp_in [lemma, in GeoCoq.Tarski_dev.Annexes.Tagged_predicates]
Perp_in_Perp_in_tagged [lemma, in GeoCoq.Tarski_dev.Annexes.Tagged_predicates]
Perp_in_tagged [definition, in GeoCoq.Tarski_dev.Annexes.Tagged_predicates]
perp_3_rect [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals_inter_dec]
perp_3_perp [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals_inter_dec]
perp_rmb [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals_inter_dec]
perp_perp_col [lemma, in GeoCoq.Tarski_dev.Ch10_line_reflexivity_2D]
perp_inter_perp_in [lemma, in GeoCoq.Tarski_dev.Ch12_parallel_inter_dec]
perp_inter_exists [lemma, in GeoCoq.Tarski_dev.Ch12_parallel_inter_dec]
perp_vector [lemma, in GeoCoq.Tarski_dev.Ch12_parallel_inter_dec]
perp_equality_bisector [lemma, in GeoCoq.Highschool.bisector]
perp_bisect [library]
Perp2 [definition, in GeoCoq.Tarski_dev.Ch13_1]
perp2_perp_in [lemma, in GeoCoq.Tarski_dev.Ch13_1]
perp2_preserves_bet13 [lemma, in GeoCoq.Tarski_dev.Ch13_1]
perp2_preserves_bet23 [lemma, in GeoCoq.Tarski_dev.Ch13_1]
perp2_par [lemma, in GeoCoq.Tarski_dev.Ch13_1]
perp2_trans [lemma, in GeoCoq.Tarski_dev.Ch13_1]
perp2_comm [lemma, in GeoCoq.Tarski_dev.Ch13_1]
perp2_right_comm [lemma, in GeoCoq.Tarski_dev.Ch13_1]
perp2_left_comm [lemma, in GeoCoq.Tarski_dev.Ch13_1]
perp2_sym [lemma, in GeoCoq.Tarski_dev.Ch13_1]
perp2_refl [lemma, in GeoCoq.Tarski_dev.Ch13_1]
Per_mid_rectangle [lemma, in GeoCoq.Highschool.exercises]
per_per_perp [lemma, in GeoCoq.Tarski_dev.Ch13_5_Pappus_Pascal]
per_one_side [lemma, in GeoCoq.Highschool.orientation]
per_preserves_bet [lemma, in GeoCoq.Highschool.orientation]
per_diff [lemma, in GeoCoq.Highschool.orientation]
per_preserves_bet_aux2 [lemma, in GeoCoq.Highschool.orientation]
per_preserves_bet_aux1 [lemma, in GeoCoq.Highschool.orientation]
per_id [lemma, in GeoCoq.Highschool.orientation]
per_proj [lemma, in GeoCoq.Highschool.orientation]
per__ex_saccheri [lemma, in GeoCoq.Tarski_dev.Annexes.saccheri]
per_sac__rah [lemma, in GeoCoq.Tarski_dev.Annexes.saccheri]
per_sac__cong [lemma, in GeoCoq.Tarski_dev.Annexes.saccheri]
Per_AM_Per [lemma, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
per_lt [lemma, in GeoCoq.Tarski_dev.Ch13_1]
per_distinct [lemma, in GeoCoq.Tarski_dev.Ch13_1]
per_double_cong [lemma, in GeoCoq.Tarski_dev.Ch08_orthogonality]
per_cong_mid [lemma, in GeoCoq.Tarski_dev.Ch08_orthogonality]
per_cong [lemma, in GeoCoq.Tarski_dev.Ch08_orthogonality]
per_not_col [lemma, in GeoCoq.Tarski_dev.Ch08_orthogonality]
per_not_colp [lemma, in GeoCoq.Tarski_dev.Ch08_orthogonality]
per_perp [lemma, in GeoCoq.Tarski_dev.Ch08_orthogonality]
per_perp_in [lemma, in GeoCoq.Tarski_dev.Ch08_orthogonality]
per_col [lemma, in GeoCoq.Tarski_dev.Ch08_orthogonality]
Per_perm [lemma, in GeoCoq.Tarski_dev.Ch08_orthogonality]
Per_cases [lemma, in GeoCoq.Tarski_dev.Ch08_orthogonality]
Per_dec [lemma, in GeoCoq.Tarski_dev.Ch08_orthogonality]
Per_tagged_Per [lemma, in GeoCoq.Tarski_dev.Annexes.Tagged_predicates]
Per_Per_tagged [lemma, in GeoCoq.Tarski_dev.Annexes.Tagged_predicates]
Per_tagged [definition, in GeoCoq.Tarski_dev.Annexes.Tagged_predicates]
per_col_eq [lemma, in GeoCoq.Tarski_dev.Ch09_plane]
per_mid_per [lemma, in GeoCoq.Tarski_dev.Ch09_plane]
per_rmb [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals_inter_dec]
per_per_cong_gen [lemma, in GeoCoq.Tarski_dev.Ch10_line_reflexivity_2D]
per_per_cong [lemma, in GeoCoq.Tarski_dev.Ch10_line_reflexivity_2D]
per_per_cong_1 [lemma, in GeoCoq.Tarski_dev.Ch10_line_reflexivity_2D]
per_per_col [lemma, in GeoCoq.Tarski_dev.Ch10_line_reflexivity_2D]
per13_preserves_bet_inv [lemma, in GeoCoq.Tarski_dev.Ch13_5_Pappus_Pascal]
per13_preserves_bet_inv [lemma, in GeoCoq.Tarski_dev.Ch13_1]
per13_preserves_bet [lemma, in GeoCoq.Tarski_dev.Ch13_1]
per2_os__ncol234 [lemma, in GeoCoq.Tarski_dev.Annexes.saccheri]
per2_os__ncol123 [lemma, in GeoCoq.Tarski_dev.Annexes.saccheri]
per2_preserves_diff [lemma, in GeoCoq.Tarski_dev.Ch13_1]
per2_col_eq [lemma, in GeoCoq.Tarski_dev.Ch13_1]
per2_suma__bet [lemma, in GeoCoq.Tarski_dev.Annexes.suma]
per23_preserves_bet_inv [lemma, in GeoCoq.Tarski_dev.Ch13_1]
per23_preserves_bet [lemma, in GeoCoq.Tarski_dev.Ch13_1]
per3_preserves_bet2 [lemma, in GeoCoq.Tarski_dev.Ch13_1]
per3_preserves_bet2_aux [lemma, in GeoCoq.Tarski_dev.Ch13_1]
per3_preserves_bet1 [lemma, in GeoCoq.Tarski_dev.Ch13_1]
pick_lines_ok_2 [lemma, in GeoCoq.Tactics.Coinc.ColR]
pick_lines_ok_1 [lemma, in GeoCoq.Tactics.Coinc.ColR]
pick_lines [definition, in GeoCoq.Tactics.Coinc.ColR]
pick_lines_aux [definition, in GeoCoq.Tactics.Coinc.ColR]
pick_line [definition, in GeoCoq.Tactics.Coinc.ColR]
pick_variety_aux_memCPAux2 [lemma, in GeoCoq.Tactics.Coinc.CoincR]
pick_variety_aux_memCPAux1 [lemma, in GeoCoq.Tactics.Coinc.CoincR]
pick_varieties_ok_2 [lemma, in GeoCoq.Tactics.Coinc.CoincR]
pick_varieties_ok_1 [lemma, in GeoCoq.Tactics.Coinc.CoincR]
pick_varieties [definition, in GeoCoq.Tactics.Coinc.CoincR]
pick_varieties_aux [definition, in GeoCoq.Tactics.Coinc.CoincR]
pick_variety [definition, in GeoCoq.Tactics.Coinc.CoincR]
pick_variety_auxCP_existsF [lemma, in GeoCoq.Tactics.Coinc.CoincR]
pick_variety_auxCP_forallT [lemma, in GeoCoq.Tactics.Coinc.CoincR]
pick_variety_aux [definition, in GeoCoq.Tactics.Coinc.CoincR]
pick_variety_auxCP [definition, in GeoCoq.Tactics.Coinc.CoincR]
Pj [definition, in GeoCoq.Tarski_dev.Ch14_sum]
pj_comm [lemma, in GeoCoq.Tarski_dev.Ch14_sum]
pj_left_comm [lemma, in GeoCoq.Tarski_dev.Ch14_sum]
pj_right_comm [lemma, in GeoCoq.Tarski_dev.Ch14_sum]
pj_uniqueness [lemma, in GeoCoq.Tarski_dev.Ch14_sum]
pj_trivial [lemma, in GeoCoq.Tarski_dev.Ch14_sum]
pj_col_project [lemma, in GeoCoq.Tarski_dev.Ch14_sum]
Pj_exists [lemma, in GeoCoq.Tarski_dev.Ch14_sum]
plan [projection, in GeoCoq.Axioms.hilbert_axioms]
plan [lemma, in GeoCoq.Meta_theory.Models.tarski_to_hilbert]
plane_separation [lemma, in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
plan' [lemma, in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
playfair_quater__playfair [lemma, in GeoCoq.Meta_theory.Parallel_postulates.par_trans_NID]
playfair_ter__playfair [lemma, in GeoCoq.Meta_theory.Parallel_postulates.par_trans_NID]
playfair__playfair_quater [lemma, in GeoCoq.Meta_theory.Parallel_postulates.par_trans_NID]
playfair__playfair_ter [lemma, in GeoCoq.Meta_theory.Parallel_postulates.par_trans_NID]
playfair_quater [definition, in GeoCoq.Meta_theory.Parallel_postulates.par_trans_NID]
playfair_quater_qf [definition, in GeoCoq.Meta_theory.Parallel_postulates.par_trans_NID]
playfair_ter [definition, in GeoCoq.Meta_theory.Parallel_postulates.par_trans_NID]
playfair_implies_par_trans [lemma, in GeoCoq.Meta_theory.Parallel_postulates.playfair_par_trans]
playfair_par_trans [section, in GeoCoq.Meta_theory.Parallel_postulates.playfair_par_trans]
playfair_bis__playfair [lemma, in GeoCoq.Meta_theory.Parallel_postulates.playfair_bis_playfair]
playfair_bis_playfair [section, in GeoCoq.Meta_theory.Parallel_postulates.playfair_bis_playfair]
playfair__existential_playfair [lemma, in GeoCoq.Meta_theory.Parallel_postulates.playfair_existential_playfair]
playfair_existential_playfair [section, in GeoCoq.Meta_theory.Parallel_postulates.playfair_existential_playfair]
playfair_s_postulate_implies_midpoint_converse_postulate [lemma, in GeoCoq.Meta_theory.Parallel_postulates.playfair_midpoint]
playfair_midpoints [section, in GeoCoq.Meta_theory.Parallel_postulates.playfair_midpoint]
playfair__alternate_interior [lemma, in GeoCoq.Meta_theory.Parallel_postulates.playfair_alternate_interior_angles]
playfair_alternate_interior_angles [section, in GeoCoq.Meta_theory.Parallel_postulates.playfair_alternate_interior_angles]
playfair_s_postulate [definition, in GeoCoq.Meta_theory.Parallel_postulates.Euclid_def]
playfair__universal_posidonius_postulate [lemma, in GeoCoq.Meta_theory.Parallel_postulates.playfair_universal_posidonius_postulate]
playfair_universal_posidonius_postulate [section, in GeoCoq.Meta_theory.Parallel_postulates.playfair_universal_posidonius_postulate]
playfair_alternate_interior_angles [library]
playfair_universal_posidonius_postulate [library]
playfair_existential_playfair [library]
playfair_bis_playfair [library]
playfair_par_trans [library]
playfair_midpoint [library]
Plg [definition, in GeoCoq.Tarski_dev.Annexes.quadrilaterals]
plgf_out_plgf [lemma, in GeoCoq.Tarski_dev.Annexes.vectors]
plgf_plgf_bet [lemma, in GeoCoq.Tarski_dev.Annexes.vectors]
plgf_plgf_plgf [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals_inter_dec]
plgf_plgs_trans [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals_inter_dec]
plgf_rect_id [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals_inter_dec]
plgf_comm2 [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals_inter_dec]
plgf_bet [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals]
plgf_trivial [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals]
plgf_trivial_trans [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals]
plgf_trivial_neq [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals]
plgf_not_point [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals]
plgf_trivial2 [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals]
plgf_trivial1 [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals]
plgf_cong [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals]
plgf_not_comm [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals]
plgf_mid [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals]
plgf_irreflexive [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals]
plgf_sym [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals]
plgf_permut [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals]
plgf3_mid [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals]
plgs_plgs_bet [lemma, in GeoCoq.Tarski_dev.Annexes.vectors]
plgs_out_plgs [lemma, in GeoCoq.Tarski_dev.Annexes.vectors]
plgs_in_angle [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals_inter_dec]
plgs_pseudo_trans [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals_inter_dec]
plgs_trans_trivial [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals_inter_dec]
plgs_pars_2 [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals_inter_dec]
plgs_pars_1 [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals_inter_dec]
plgs_cong_2 [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals_inter_dec]
plgs_cong_1 [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals_inter_dec]
plgs_half_plgs [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals_inter_dec]
plgs_comm2 [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals_inter_dec]
plgs_half_plgs_aux [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals_inter_dec]
plgs_par_strict [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals_inter_dec]
plgs_two_sides [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals_inter_dec]
plgs_not_comm [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals_inter_dec]
plgs_mid [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals_inter_dec]
plgs_sym [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals_inter_dec]
plgs_permut [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals_inter_dec]
plgs_cong [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals_inter_dec]
plgs_existence [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals]
plgs_diff [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals]
plgs_not_col [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals]
plgs_one_side [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals]
plgs_irreflexive [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals]
plg_opp_dir [lemma, in GeoCoq.Tarski_dev.Annexes.vectors]
plg_out_plg [lemma, in GeoCoq.Tarski_dev.Annexes.vectors]
plg_plg_bet [lemma, in GeoCoq.Tarski_dev.Annexes.vectors]
Plg_tagged_Plg [lemma, in GeoCoq.Tarski_dev.Annexes.Tagged_predicates]
Plg_Plg_tagged [lemma, in GeoCoq.Tarski_dev.Annexes.Tagged_predicates]
Plg_tagged [definition, in GeoCoq.Tarski_dev.Annexes.Tagged_predicates]
plg_pseudo_trans [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals_inter_dec]
plg_uniqueness [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals_inter_dec]
plg_par_2 [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals_inter_dec]
plg_par_1 [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals_inter_dec]
plg_par [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals_inter_dec]
plg_per_rect [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals_inter_dec]
plg_per_rect4 [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals_inter_dec]
plg_per_rect3 [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals_inter_dec]
plg_per_rect2 [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals_inter_dec]
plg_per_rect1 [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals_inter_dec]
plg_not_comm_2 [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals_inter_dec]
plg_not_comm_1 [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals_inter_dec]
Plg_perm [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals_inter_dec]
plg_cong_2 [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals_inter_dec]
plg_cong_1 [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals_inter_dec]
plg_comm2 [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals_inter_dec]
plg_conga [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals_inter_dec]
plg_not_comm [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals_inter_dec]
plg_mid_2 [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals_inter_dec]
plg_mid [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals_inter_dec]
plg_sym [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals_inter_dec]
plg_permut [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals_inter_dec]
plg_conga1 [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals_inter_dec]
plg_cong [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals_inter_dec]
plg_existence [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals]
plg_bet1 [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals]
plg_col_plgf [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals]
plg_trivial1 [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals]
plg_trivial [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals]
plg_cong_rectangle [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals]
plg_to_parallelogram [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals]
plg_irreflexive [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals]
plg_to_sum [lemma, in GeoCoq.Tarski_dev.Ch14_sum]
plus_n_1 [lemma, in GeoCoq.Utils.arity]
plus_n_0 [lemma, in GeoCoq.Utils.arity]
plus_0_n [lemma, in GeoCoq.Utils.arity]
Point [projection, in GeoCoq.Axioms.hilbert_axioms]
Point [inductive, in GeoCoq.Meta_theory.Counter_models.counter_model_segment_construction]
Point [inductive, in GeoCoq.Meta_theory.Counter_models.counter_model_bet_identity]
point_equality_decidability [projection, in GeoCoq.Axioms.tarski_axioms]
point_construction_different [lemma, in GeoCoq.Tarski_dev.Ch03_bet]
point_equality_decidabilityG [projection, in GeoCoq.Axioms.independent_tarski_axioms]
point_of_coordinates [lemma, in GeoCoq.Tarski_dev.Ch16_coordinates]
point_of_coordinates_on_an_axis [lemma, in GeoCoq.Tarski_dev.Ch16_coordinates]
point_of_coordinates_origin [lemma, in GeoCoq.Tarski_dev.Ch16_coordinates]
point_eq_dec [lemma, in GeoCoq.Meta_theory.Counter_models.counter_model_bet_identity]
point3_online_exists [lemma, in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
posidonius_postulate__rah [lemma, in GeoCoq.Meta_theory.Parallel_postulates.posidonius_postulate_rah]
posidonius_postulate_rah [section, in GeoCoq.Meta_theory.Parallel_postulates.posidonius_postulate_rah]
posidonius_postulate [definition, in GeoCoq.Meta_theory.Parallel_postulates.Euclid_def]
posidonius_postulate_rah [library]
positive_dec [lemma, in GeoCoq.Tactics.Coinc.ColR]
positive_dec [lemma, in GeoCoq.Tactics.Coinc.CoincR]
PosOrder [module, in GeoCoq.Utils.sets]
PosOrder.leb [definition, in GeoCoq.Utils.sets]
PosOrder.leb_dec [lemma, in GeoCoq.Utils.sets]
PosOrder.leb_total [lemma, in GeoCoq.Utils.sets]
PosOrder.t [definition, in GeoCoq.Utils.sets]
PosSort [module, in GeoCoq.Utils.sets]
PosSort [module, in GeoCoq.Tactics.Coinc.CoincR]
postulate_of_existence_of_similar_triangles [definition, in GeoCoq.Meta_theory.Parallel_postulates.Euclid_def]
postulate_of_existence_of_a_right_lambert_quadrilateral [definition, in GeoCoq.Meta_theory.Parallel_postulates.Euclid_def]
postulate_of_right_lambert_quadrilaterals [definition, in GeoCoq.Meta_theory.Parallel_postulates.Euclid_def]
postulate_of_existence_of_a_right_saccheri_quadrilateral [definition, in GeoCoq.Meta_theory.Parallel_postulates.Euclid_def]
postulate_of_right_saccheri_quadrilaterals [definition, in GeoCoq.Meta_theory.Parallel_postulates.Euclid_def]
postulate_of_existence_of_a_triangle_whose_angles_sum_to_two_rights [definition, in GeoCoq.Meta_theory.Parallel_postulates.Euclid_def]
postulate_of_parallelism_of_perpendicular_transversals [definition, in GeoCoq.Meta_theory.Parallel_postulates.Euclid_def]
postulate_of_transitivity_of_parallelism [definition, in GeoCoq.Meta_theory.Parallel_postulates.Euclid_def]
pos_inv_pos [lemma, in GeoCoq.Tarski_dev.Ch14_order]
pos_opp_neg [lemma, in GeoCoq.Tarski_dev.Ch14_order]
pos_not_neg [lemma, in GeoCoq.Tarski_dev.Ch14_order]
pos_null_neg [lemma, in GeoCoq.Tarski_dev.Ch14_order]
Pred [projection, in GeoCoq.Utils.aux]
pred_conj [definition, in GeoCoq.Utils.arity]
pred_conj_aux [definition, in GeoCoq.Utils.arity]
proclus_s_postulate_implies_strong_parallel_postulate [lemma, in GeoCoq.Meta_theory.Parallel_postulates.proclus_SPP]
proclus_SPP [section, in GeoCoq.Meta_theory.Parallel_postulates.proclus_SPP]
proclus_bis__proclus [lemma, in GeoCoq.Meta_theory.Parallel_postulates.proclus_bis_proclus]
proclus_bis_proclus [section, in GeoCoq.Meta_theory.Parallel_postulates.proclus_bis_proclus]
proclus__aristotle [lemma, in GeoCoq.Meta_theory.Parallel_postulates.proclus_aristotle]
proclus_aristotle [section, in GeoCoq.Meta_theory.Parallel_postulates.proclus_aristotle]
proclus_postulate [definition, in GeoCoq.Meta_theory.Parallel_postulates.Euclid_def]
proclus_bis_proclus [library]
proclus_aristotle [library]
proclus_SPP [library]
Prod [definition, in GeoCoq.Tarski_dev.Ch14_prod]
Prodg [definition, in GeoCoq.Tarski_dev.Ch15_lengths]
Prodp [definition, in GeoCoq.Tarski_dev.Ch14_prod]
prodp_to_prod [lemma, in GeoCoq.Tarski_dev.Ch14_prod]
prod_f [lemma, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
prod_col [lemma, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
prod_pos_pos [lemma, in GeoCoq.Tarski_dev.Ch14_order]
prod_x_axis_unit_change [lemma, in GeoCoq.Tarski_dev.Ch14_prod]
prod_sym [lemma, in GeoCoq.Tarski_dev.Ch14_prod]
prod_1_r_eq [lemma, in GeoCoq.Tarski_dev.Ch14_prod]
prod_1_l_eq [lemma, in GeoCoq.Tarski_dev.Ch14_prod]
prod_uniquenessB [lemma, in GeoCoq.Tarski_dev.Ch14_prod]
prod_uniquenessA [lemma, in GeoCoq.Tarski_dev.Ch14_prod]
prod_O_r_eq [lemma, in GeoCoq.Tarski_dev.Ch14_prod]
prod_O_l_eq [lemma, in GeoCoq.Tarski_dev.Ch14_prod]
prod_comm [lemma, in GeoCoq.Tarski_dev.Ch14_prod]
prod_assoc [lemma, in GeoCoq.Tarski_dev.Ch14_prod]
prod_assoc2 [lemma, in GeoCoq.Tarski_dev.Ch14_prod]
prod_assoc1 [lemma, in GeoCoq.Tarski_dev.Ch14_prod]
prod_y_axis_change [lemma, in GeoCoq.Tarski_dev.Ch14_prod]
prod_null [lemma, in GeoCoq.Tarski_dev.Ch14_prod]
prod_1_r [lemma, in GeoCoq.Tarski_dev.Ch14_prod]
prod_1_l [lemma, in GeoCoq.Tarski_dev.Ch14_prod]
prod_0_r [lemma, in GeoCoq.Tarski_dev.Ch14_prod]
prod_0_l [lemma, in GeoCoq.Tarski_dev.Ch14_prod]
prod_uniqueness [lemma, in GeoCoq.Tarski_dev.Ch14_prod]
prod_exists [lemma, in GeoCoq.Tarski_dev.Ch14_prod]
prod_to_prodp [lemma, in GeoCoq.Tarski_dev.Ch14_prod]
proj [definition, in GeoCoq.Highschool.orientation]
Proj [definition, in GeoCoq.Tarski_dev.Annexes.project]
project [library]
Projections [section, in GeoCoq.Tarski_dev.Annexes.project]
project_preserves_out [lemma, in GeoCoq.Tarski_dev.Ch15_lengths]
project_project_par [lemma, in GeoCoq.Tarski_dev.Annexes.project]
project_par_project [lemma, in GeoCoq.Tarski_dev.Annexes.project]
project_to_projp [lemma, in GeoCoq.Tarski_dev.Annexes.project]
project_preserves_eqv [lemma, in GeoCoq.Tarski_dev.Annexes.project]
project_idem [lemma, in GeoCoq.Tarski_dev.Annexes.project]
project_par_dir [lemma, in GeoCoq.Tarski_dev.Annexes.project]
project_par_eqv [lemma, in GeoCoq.Tarski_dev.Annexes.project]
project_preserves_bet [lemma, in GeoCoq.Tarski_dev.Annexes.project]
project_col_eq [lemma, in GeoCoq.Tarski_dev.Annexes.project]
project_existence [lemma, in GeoCoq.Tarski_dev.Annexes.project]
project_uniqueness [lemma, in GeoCoq.Tarski_dev.Annexes.project]
project_par [lemma, in GeoCoq.Tarski_dev.Annexes.project]
project_not_col [lemma, in GeoCoq.Tarski_dev.Annexes.project]
project_col [lemma, in GeoCoq.Tarski_dev.Annexes.project]
project_not_id [lemma, in GeoCoq.Tarski_dev.Annexes.project]
project_id [lemma, in GeoCoq.Tarski_dev.Annexes.project]
project_pj [lemma, in GeoCoq.Tarski_dev.Ch14_prod]
project_trivial [lemma, in GeoCoq.Tarski_dev.Ch14_sum]
project_col_project [lemma, in GeoCoq.Tarski_dev.Ch14_sum]
Projp [definition, in GeoCoq.Tarski_dev.Annexes.project]
projp_col [lemma, in GeoCoq.Tarski_dev.Annexes.project]
projp_projp_perp [lemma, in GeoCoq.Tarski_dev.Annexes.project]
projp_idem [lemma, in GeoCoq.Tarski_dev.Annexes.project]
projp_preserves_eqv [lemma, in GeoCoq.Tarski_dev.Annexes.project]
projp_preserves_bet [lemma, in GeoCoq.Tarski_dev.Annexes.project]
projp_id [lemma, in GeoCoq.Tarski_dev.Annexes.project]
projp_project_to_perp [lemma, in GeoCoq.Tarski_dev.Annexes.project]
projp_to_project [lemma, in GeoCoq.Tarski_dev.Annexes.project]
projp_is_project_perp [lemma, in GeoCoq.Tarski_dev.Annexes.project]
projp_is_project [lemma, in GeoCoq.Tarski_dev.Annexes.project]
projp2_col [lemma, in GeoCoq.Tarski_dev.Annexes.project]
proj_preserves_bet [lemma, in GeoCoq.Highschool.orientation]
proj_preserves_bet1 [lemma, in GeoCoq.Highschool.orientation]
proj_diff_not_col_inv [lemma, in GeoCoq.Highschool.orientation]
proj_diff_not_col [lemma, in GeoCoq.Highschool.orientation]
proj_perp_id [lemma, in GeoCoq.Highschool.orientation]
proj_inv_exists [lemma, in GeoCoq.Highschool.orientation]
proj_diff [lemma, in GeoCoq.Highschool.orientation]
proj_id [lemma, in GeoCoq.Highschool.orientation]
proj_par_strict [lemma, in GeoCoq.Highschool.orientation]
proj_not_eq_not_col [lemma, in GeoCoq.Highschool.orientation]
proj_not_eq [lemma, in GeoCoq.Highschool.orientation]
proj_comm [lemma, in GeoCoq.Highschool.orientation]
proj_not_col [lemma, in GeoCoq.Highschool.orientation]
proj_par [lemma, in GeoCoq.Highschool.orientation]
proj_eq_col [lemma, in GeoCoq.Highschool.orientation]
proj_one_side [lemma, in GeoCoq.Highschool.orientation]
proj_col_proj [lemma, in GeoCoq.Highschool.orientation]
proj_col [lemma, in GeoCoq.Highschool.orientation]
proj_uniqueness [lemma, in GeoCoq.Highschool.orientation]
proj_per [lemma, in GeoCoq.Highschool.orientation]
proj_exists [lemma, in GeoCoq.Highschool.orientation]
proj_distinct [lemma, in GeoCoq.Tarski_dev.Annexes.project]
proj_preserves_prod [lemma, in GeoCoq.Tarski_dev.Ch14_prod]
proj_preserves_sum [lemma, in GeoCoq.Tarski_dev.Ch14_sum]
proj_id [lemma, in GeoCoq.Tarski_dev.Ch14_sum]
proj_col [lemma, in GeoCoq.Tarski_dev.Ch14_sum]
proj_pars [lemma, in GeoCoq.Tarski_dev.Ch14_sum]
proj3_id [lemma, in GeoCoq.Highschool.orientation]
proj3_col [lemma, in GeoCoq.Highschool.orientation]
Proof_of_eq_stability_in_IT [section, in GeoCoq.Meta_theory.Models.tarski_to_beeson]
proper_9 [lemma, in GeoCoq.Tactics.Coinc.ColR]
proper_8 [lemma, in GeoCoq.Tactics.Coinc.ColR]
proper_7 [lemma, in GeoCoq.Tactics.Coinc.ColR]
proper_6 [lemma, in GeoCoq.Tactics.Coinc.ColR]
proper_5 [lemma, in GeoCoq.Tactics.Coinc.ColR]
proper_4 [lemma, in GeoCoq.Tactics.Coinc.ColR]
proper_3 [lemma, in GeoCoq.Tactics.Coinc.ColR]
proper_2 [lemma, in GeoCoq.Tactics.Coinc.ColR]
proper_1 [lemma, in GeoCoq.Tactics.Coinc.ColR]
proper_0 [lemma, in GeoCoq.Tactics.Coinc.ColR]
proper_00 [lemma, in GeoCoq.Tactics.Coinc.ColR]
proper_3 [lemma, in GeoCoq.Tactics.Coinc.CoincR]
proper_2 [lemma, in GeoCoq.Tactics.Coinc.CoincR]
proper_1 [lemma, in GeoCoq.Tactics.Coinc.CoincR]
proper_0 [lemma, in GeoCoq.Tactics.Coinc.CoincR]
proper_00 [lemma, in GeoCoq.Tactics.Coinc.CoincR]
PropToTagged [lemma, in GeoCoq.Tactics.Coinc.ColR]
PropToTagged [lemma, in GeoCoq.Tactics.Coinc.CoincR]
Ps [definition, in GeoCoq.Tarski_dev.Ch14_order]
Ps_Col [lemma, in GeoCoq.Tarski_dev.Ch15_pyth_rel]
Ps_One [lemma, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
ps_le [lemma, in GeoCoq.Tarski_dev.Ch14_order]
put_neg_in_goal [lemma, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
Py [definition, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
pythagoras [lemma, in GeoCoq.Tarski_dev.Ch15_lengths]
PythagoreanFun [section, in GeoCoq.Tarski_dev.Ch15_pyth_rel]
PythF [definition, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
PythFOk [lemma, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
PythOK [lemma, in GeoCoq.Tarski_dev.Ch15_pyth_rel]
PythRel [definition, in GeoCoq.Tarski_dev.Ch15_pyth_rel]
pythrelOO [lemma, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
PythRel_uniqueness [lemma, in GeoCoq.Tarski_dev.Ch15_pyth_rel]
PythRel_exists [lemma, in GeoCoq.Tarski_dev.Ch15_pyth_rel]
pythrel_not_null [lemma, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
pythrel_null [lemma, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
Pyth_f [lemma, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
Py_triv_ABB [lemma, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
Py4 [definition, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
P0 [projection, in GeoCoq.Axioms.hilbert_axioms]
P0 [constructor, in GeoCoq.Meta_theory.Counter_models.counter_model_segment_construction]
P0 [constructor, in GeoCoq.Meta_theory.Counter_models.counter_model_bet_identity]
P1 [projection, in GeoCoq.Utils.aux]
P1 [definition, in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
P1 [constructor, in GeoCoq.Meta_theory.Counter_models.counter_model_bet_identity]
P2 [projection, in GeoCoq.Utils.aux]
P2 [definition, in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
P2 [constructor, in GeoCoq.Meta_theory.Counter_models.counter_model_bet_identity]
P3 [constructor, in GeoCoq.Meta_theory.Counter_models.counter_model_bet_identity]


Q

Quadrilateral [section, in GeoCoq.Tarski_dev.Annexes.quadrilaterals]
quadrilaterals [library]
quadrilaterals_inter_dec [library]
Quadrilateral_inter_dec_3 [section, in GeoCoq.Tarski_dev.Annexes.quadrilaterals_inter_dec]
Quadrilateral_inter_dec_2 [section, in GeoCoq.Tarski_dev.Annexes.quadrilaterals_inter_dec]
Quadrilateral_inter_dec_1 [section, in GeoCoq.Tarski_dev.Annexes.quadrilaterals_inter_dec]
quadrileral_midpoints [lemma, in GeoCoq.Highschool.exercises]
Q_CongA_nNull_Acute [definition, in GeoCoq.Tarski_dev.Ch13_3_angles]
Q_CongA_Null_Acute [definition, in GeoCoq.Tarski_dev.Ch13_3_angles]
Q_CongA_Null [definition, in GeoCoq.Tarski_dev.Ch13_3_angles]
Q_CongA_nFlat [definition, in GeoCoq.Tarski_dev.Ch13_3_angles]
Q_CongA_nNull [definition, in GeoCoq.Tarski_dev.Ch13_3_angles]
Q_CongA_Acute [definition, in GeoCoq.Tarski_dev.Ch13_3_angles]
Q_CongA [definition, in GeoCoq.Tarski_dev.Ch13_3_angles]
Q_Cong_Null [definition, in GeoCoq.Tarski_dev.Ch13_2_length]
Q_Cong [definition, in GeoCoq.Tarski_dev.Ch13_2_length]


R

rah__similar [lemma, in GeoCoq.Meta_theory.Parallel_postulates.rah_similar]
rah_similar [section, in GeoCoq.Meta_theory.Parallel_postulates.rah_similar]
rah__rectangle_principle [lemma, in GeoCoq.Meta_theory.Parallel_postulates.rah_rectangle_principle]
rah_rectangle_principle [section, in GeoCoq.Meta_theory.Parallel_postulates.rah_rectangle_principle]
rah_defect__out [lemma, in GeoCoq.Meta_theory.Parallel_postulates.legendre]
rah__thales_postulate [lemma, in GeoCoq.Meta_theory.Parallel_postulates.rah_thales_postulate]
rah_thales_postulate [section, in GeoCoq.Meta_theory.Parallel_postulates.rah_thales_postulate]
rah__triangle [lemma, in GeoCoq.Meta_theory.Parallel_postulates.rah_triangle]
rah_triangle [section, in GeoCoq.Meta_theory.Parallel_postulates.rah_triangle]
rah__existential_saccheri [lemma, in GeoCoq.Meta_theory.Parallel_postulates.rah_existential_saccheri]
rah_existential_saccheri [section, in GeoCoq.Meta_theory.Parallel_postulates.rah_existential_saccheri]
rah__posidonius [lemma, in GeoCoq.Meta_theory.Parallel_postulates.rah_posidonius_postulate]
rah__posidonius_aux [lemma, in GeoCoq.Meta_theory.Parallel_postulates.rah_posidonius_postulate]
rah_posidonius [section, in GeoCoq.Meta_theory.Parallel_postulates.rah_posidonius_postulate]
rah_existential_saccheri [library]
rah_similar [library]
rah_posidonius_postulate [library]
rah_triangle [library]
rah_rectangle_principle [library]
rah_thales_postulate [library]
ratio [definition, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
ratio_zero [lemma, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
Reach [definition, in GeoCoq.Meta_theory.Parallel_postulates.archimedes]
reach__ex_gradexp_le [lemma, in GeoCoq.Meta_theory.Parallel_postulates.archimedes]
Rectangle [definition, in GeoCoq.Tarski_dev.Annexes.quadrilaterals]
rectangle_principle__rectangle_existence [lemma, in GeoCoq.Meta_theory.Parallel_postulates.rectangle_principle_rectangle_existence]
rectangle_principle_rectangle_existence [section, in GeoCoq.Meta_theory.Parallel_postulates.rectangle_principle_rectangle_existence]
rectangle_existence__rah [lemma, in GeoCoq.Meta_theory.Parallel_postulates.rectangle_existence_rah]
rectangle_existence_rah [section, in GeoCoq.Meta_theory.Parallel_postulates.rectangle_existence_rah]
Rectangle_not_triv_2 [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals]
Rectangle_triv [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals]
Rectangle_not_triv [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals]
Rectangle_Parallelogram [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals]
Rectangle_Plg [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals]
rectangle_principle_rectangle_existence [library]
rectangle_existence_rah [library]
rect_2_rect [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals_inter_dec]
rect_per [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals_inter_dec]
rect_per4 [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals_inter_dec]
rect_per3 [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals_inter_dec]
rect_per2 [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals_inter_dec]
rect_per1 [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals_inter_dec]
rect_comm2 [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals_inter_dec]
rect_permut [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals_inter_dec]
Reflect [definition, in GeoCoq.Tarski_dev.Ch10_line_reflexivity]
ReflectL [definition, in GeoCoq.Tarski_dev.Ch10_line_reflexivity]
ReflectL_at [definition, in GeoCoq.Tarski_dev.Ch10_line_reflexivity]
ReflectP [definition, in GeoCoq.Tarski_dev.Ch09_plane]
Reflect_at [definition, in GeoCoq.Tarski_dev.Ch10_line_reflexivity]
Rhombus [definition, in GeoCoq.Tarski_dev.Annexes.quadrilaterals]
rhombus_cong_square [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals]
Rhombus_Rectangle_Square [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals]
Rhombus_Plg [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals]
ringF [lemma, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
rmb_perp [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals_inter_dec]
rmb_per [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals_inter_dec]
rmb_cong [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals_inter_dec]


S

S [module, in GeoCoq.Utils.sets]
Saccheri [definition, in GeoCoq.Tarski_dev.Annexes.saccheri]
saccheri [library]
saccheri_s_three_hypotheses [lemma, in GeoCoq.Tarski_dev.Annexes.saccheri]
sac__perp3414 [lemma, in GeoCoq.Tarski_dev.Annexes.saccheri]
sac__perp1214 [lemma, in GeoCoq.Tarski_dev.Annexes.saccheri]
sac__par1234 [lemma, in GeoCoq.Tarski_dev.Annexes.saccheri]
sac__par1423 [lemma, in GeoCoq.Tarski_dev.Annexes.saccheri]
sac__par_strict1234 [lemma, in GeoCoq.Tarski_dev.Annexes.saccheri]
sac__par_strict1423 [lemma, in GeoCoq.Tarski_dev.Annexes.saccheri]
sac__ncol234 [lemma, in GeoCoq.Tarski_dev.Annexes.saccheri]
sac__ncol134 [lemma, in GeoCoq.Tarski_dev.Annexes.saccheri]
sac__ncol124 [lemma, in GeoCoq.Tarski_dev.Annexes.saccheri]
sac__ncol123 [lemma, in GeoCoq.Tarski_dev.Annexes.saccheri]
sac__conga [lemma, in GeoCoq.Tarski_dev.Annexes.saccheri]
sac__cong [lemma, in GeoCoq.Tarski_dev.Annexes.saccheri]
sac_distincts [lemma, in GeoCoq.Tarski_dev.Annexes.saccheri]
sac_perm [lemma, in GeoCoq.Tarski_dev.Annexes.saccheri]
sac2__sac [lemma, in GeoCoq.Tarski_dev.Annexes.saccheri]
same_side_sym [lemma, in GeoCoq.Meta_theory.Models.tarski_to_hilbert]
same_side_trans [lemma, in GeoCoq.Meta_theory.Models.tarski_to_hilbert]
same_side_OS [lemma, in GeoCoq.Meta_theory.Models.tarski_to_hilbert]
same_side' [definition, in GeoCoq.Meta_theory.Models.tarski_to_hilbert]
same_side_one_side [lemma, in GeoCoq.Meta_theory.Models.tarski_to_hilbert]
same_side [definition, in GeoCoq.Meta_theory.Models.tarski_to_hilbert]
same_side_scott [definition, in GeoCoq.Meta_theory.Models.tarski_to_hilbert]
same_abscissa_col [lemma, in GeoCoq.Tarski_dev.Ch16_coordinates]
same_side_prime_not_colH [lemma, in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
same_side_trans [lemma, in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
same_side_not_incid [lemma, in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
same_side_comm [lemma, in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
same_side_morphism [instance, in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
same_side_not_cut [lemma, in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
same_side_prime_refl [lemma, in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
same_side_refl [lemma, in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
same_not_opp_dir [lemma, in GeoCoq.Tarski_dev.Annexes.vectors]
same_dir_to_null [lemma, in GeoCoq.Tarski_dev.Annexes.vectors]
same_dir_id [lemma, in GeoCoq.Tarski_dev.Annexes.vectors]
same_or_opp_dir [lemma, in GeoCoq.Tarski_dev.Annexes.vectors]
same_dir_dec [lemma, in GeoCoq.Tarski_dev.Annexes.vectors]
same_dir_comm [lemma, in GeoCoq.Tarski_dev.Annexes.vectors]
same_dir_trans [lemma, in GeoCoq.Tarski_dev.Annexes.vectors]
same_dir_sym [lemma, in GeoCoq.Tarski_dev.Annexes.vectors]
same_dir_null [lemma, in GeoCoq.Tarski_dev.Annexes.vectors]
same_dir_out1 [lemma, in GeoCoq.Tarski_dev.Annexes.vectors]
same_dir_out [lemma, in GeoCoq.Tarski_dev.Annexes.vectors]
same_dir_ts [lemma, in GeoCoq.Tarski_dev.Annexes.vectors]
same_dir_refl [lemma, in GeoCoq.Tarski_dev.Annexes.vectors]
Same_dir [definition, in GeoCoq.Tarski_dev.Annexes.vectors]
scalar_product [definition, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
Sec [section, in GeoCoq.Tarski_dev.Annexes.saccheri]
Sec [section, in GeoCoq.Tarski_dev.Annexes.suma]
Sec2 [section, in GeoCoq.Tarski_dev.Annexes.suma]
segment_construction [projection, in GeoCoq.Axioms.tarski_axioms]
segment_construction [lemma, in GeoCoq.Meta_theory.Models.tarski_to_beeson]
segment_construction_B [lemma, in GeoCoq.Meta_theory.Models.tarski_to_beeson]
segment_construction_2 [lemma, in GeoCoq.Tarski_dev.Ch05_bet_le]
segment_constructionG [projection, in GeoCoq.Axioms.independent_tarski_axioms]
segment_construction_independent [section, in GeoCoq.Meta_theory.Counter_models.counter_model_segment_construction]
segment_construction_0 [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
segment_construction_3 [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
segment_constructionH [lemma, in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
segment_construction [lemma, in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
segment_construction [lemma, in GeoCoq.Meta_theory.Counter_models.counter_model_bet_identity]
SetOfPairsOfPositiveOrderedType [module, in GeoCoq.Utils.sets]
SetOfPairsOfPositiveOrderedType.compare [definition, in GeoCoq.Utils.sets]
SetOfPairsOfPositiveOrderedType.compare_spec [lemma, in GeoCoq.Utils.sets]
SetOfPairsOfPositiveOrderedType.eq [definition, in GeoCoq.Utils.sets]
SetOfPairsOfPositiveOrderedType.eqb [definition, in GeoCoq.Utils.sets]
SetOfPairsOfPositiveOrderedType.eqb_eq [lemma, in GeoCoq.Utils.sets]
SetOfPairsOfPositiveOrderedType.lt [definition, in GeoCoq.Utils.sets]
SetOfPairsOfPositiveOrderedType.lt_strorder [instance, in GeoCoq.Utils.sets]
SetOfPairsOfPositiveOrderedType.lt_compat [instance, in GeoCoq.Utils.sets]
SetOfPairsOfPositiveOrderedType.lt_trans [lemma, in GeoCoq.Utils.sets]
SetOfPairsOfPositiveOrderedType.lt_antiref [lemma, in GeoCoq.Utils.sets]
SetOfPairsOfPositiveOrderedType.lt_irrefl [lemma, in GeoCoq.Utils.sets]
SetOfPairsOfPositiveOrderedType.t [definition, in GeoCoq.Utils.sets]
SetOfSetsOfPositiveOrderedType [module, in GeoCoq.Utils.sets]
SetOfSetsOfPositiveOrderedType.compare [definition, in GeoCoq.Utils.sets]
SetOfSetsOfPositiveOrderedType.compare_spec [definition, in GeoCoq.Utils.sets]
SetOfSetsOfPositiveOrderedType.eq [definition, in GeoCoq.Utils.sets]
SetOfSetsOfPositiveOrderedType.eqb [definition, in GeoCoq.Utils.sets]
SetOfSetsOfPositiveOrderedType.eqb_eq [definition, in GeoCoq.Utils.sets]
SetOfSetsOfPositiveOrderedType.lt [definition, in GeoCoq.Utils.sets]
SetOfSetsOfPositiveOrderedType.lt_strorder [instance, in GeoCoq.Utils.sets]
SetOfSetsOfPositiveOrderedType.lt_compat [instance, in GeoCoq.Utils.sets]
SetOfSetsOfPositiveOrderedType.t [definition, in GeoCoq.Utils.sets]
sets [library]
Set_of_tuple_of_positive [section, in GeoCoq.Utils.sets]
signed_area_ABB [lemma, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
signed_area_ABA [lemma, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
signed_area_AAB [lemma, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
signed_area4 [definition, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
signed_area_sum [lemma, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
signed_area_perm [lemma, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
signed_area_cyclic [lemma, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
signed_area [definition, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
similar__rah [lemma, in GeoCoq.Meta_theory.Parallel_postulates.similar_rah]
similar__rah_aux [lemma, in GeoCoq.Meta_theory.Parallel_postulates.similar_rah]
similar_rah [section, in GeoCoq.Meta_theory.Parallel_postulates.similar_rah]
similar_rah [library]
sndpp [definition, in GeoCoq.Utils.sets]
snd_sp [definition, in GeoCoq.Tactics.Coinc.ColR]
snd_ss [definition, in GeoCoq.Tactics.Coinc.ColR]
sortOK [lemma, in GeoCoq.Utils.sets]
soustraction_betH [lemma, in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
SP [module, in GeoCoq.Utils.sets]
SPP [definition, in GeoCoq.Meta_theory.Parallel_postulates.Euclid_def]
SPP_tarski [section, in GeoCoq.Meta_theory.Parallel_postulates.SPP_tarski]
SPP_ID [section, in GeoCoq.Meta_theory.Parallel_postulates.SPP_ID]
SPP_ID [library]
SPP_tarski [library]
SPWEqP [module, in GeoCoq.Tactics.Coinc.ColR]
sp_ok_empty [lemma, in GeoCoq.Tactics.Coinc.ColR]
sp_ok [definition, in GeoCoq.Tactics.Coinc.ColR]
sqrt3 [definition, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
sqrt3_square [lemma, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
Square [definition, in GeoCoq.Tarski_dev.Annexes.quadrilaterals]
square_dist [definition, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
square_pos [lemma, in GeoCoq.Tarski_dev.Ch14_order]
square_distance_formula [lemma, in GeoCoq.Tarski_dev.Ch16_coordinates]
square_distance_formula_aux [lemma, in GeoCoq.Tarski_dev.Ch16_coordinates]
Square_Rhombus [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals_inter_dec]
square_perp_rectangle [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals_inter_dec]
Square_Parallelogram [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals]
Square_Rectangle [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals]
Square_not_triv_3 [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals]
Square_not_triv_2 [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals]
Square_not_triv [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals]
SS [module, in GeoCoq.Utils.sets]
SSWEqP [module, in GeoCoq.Tactics.Coinc.ColR]
SSWEqP [module, in GeoCoq.Tactics.Coinc.CoincR]
SSWP [module, in GeoCoq.Tactics.Coinc.ColR]
SSWP [module, in GeoCoq.Tactics.Coinc.CoincR]
ss_ok_empty [lemma, in GeoCoq.Tactics.Coinc.ColR]
ss_ok [definition, in GeoCoq.Tactics.Coinc.ColR]
ss_ok_empty [lemma, in GeoCoq.Tactics.Coinc.CoincR]
ss_ok_inter_ok2 [lemma, in GeoCoq.Tactics.Coinc.CoincR]
ss_ok_inter_ok1 [lemma, in GeoCoq.Tactics.Coinc.CoincR]
ss_ok [definition, in GeoCoq.Tactics.Coinc.CoincR]
ss_ok_empty_for_col [lemma, in GeoCoq.Tactics.Coinc.CoincR_for_col]
ss_ok_for_col [definition, in GeoCoq.Tactics.Coinc.CoincR_for_col]
STadd [definition, in GeoCoq.Utils.sets]
STadd_iff [lemma, in GeoCoq.Utils.sets]
STelt [definition, in GeoCoq.Utils.sets]
STempty [definition, in GeoCoq.Utils.sets]
STempty_b [lemma, in GeoCoq.Utils.sets]
STexists_mem_4 [lemma, in GeoCoq.Utils.sets]
STexists_ [definition, in GeoCoq.Utils.sets]
STmem [definition, in GeoCoq.Utils.sets]
stronger [definition, in GeoCoq.Utils.all_equiv]
stronger_parallel_postulates_ter [lemma, in GeoCoq.Meta_theory.Parallel_postulates.Euclid]
stronger_parallel_postulates_bis [lemma, in GeoCoq.Meta_theory.Parallel_postulates.Euclid]
stronger_parallel_postulates [lemma, in GeoCoq.Meta_theory.Parallel_postulates.Euclid]
strong_parallel_postulate_implies_tarski_s_euclid [lemma, in GeoCoq.Meta_theory.Parallel_postulates.SPP_tarski]
strong_parallel_postulate_implies_tarski_s_euclid_aux [lemma, in GeoCoq.Meta_theory.Parallel_postulates.SPP_tarski]
strong_parallel_postulate_SPP [lemma, in GeoCoq.Meta_theory.Parallel_postulates.Euclid]
strong_pasch [lemma, in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
strong_parallel_postulate_implies_inter_dec [lemma, in GeoCoq.Meta_theory.Parallel_postulates.SPP_ID]
strong_parallel_postulate [definition, in GeoCoq.Meta_theory.Parallel_postulates.Euclid_def]
STt [definition, in GeoCoq.Utils.sets]
st_ok_empty [lemma, in GeoCoq.Tactics.Coinc.CoincR]
st_ok [definition, in GeoCoq.Tactics.Coinc.CoincR]
st_ok_empty_for_col [lemma, in GeoCoq.Tactics.Coinc.CoincR_for_col]
st_ok_for_col [definition, in GeoCoq.Tactics.Coinc.CoincR_for_col]
SubF [definition, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
subF__eq0 [lemma, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
subF_morphism [instance, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
subst_sp_ok [lemma, in GeoCoq.Tactics.Coinc.ColR]
subst_in_sp [definition, in GeoCoq.Tactics.Coinc.ColR]
subst_in_sp_aux_2 [definition, in GeoCoq.Tactics.Coinc.ColR]
subst_in_sp_aux_1 [definition, in GeoCoq.Tactics.Coinc.ColR]
subst_ss_ok [lemma, in GeoCoq.Tactics.Coinc.ColR]
subst_in_ss [definition, in GeoCoq.Tactics.Coinc.ColR]
subst_in_ss_aux [definition, in GeoCoq.Tactics.Coinc.ColR]
subst_in_set [definition, in GeoCoq.Tactics.Coinc.ColR]
Sum [definition, in GeoCoq.Tarski_dev.Ch14_sum]
SumA [definition, in GeoCoq.Tarski_dev.Annexes.suma]
suma [library]
suma_dec [lemma, in GeoCoq.Tarski_dev.Annexes.suma]
suma_assoc [lemma, in GeoCoq.Tarski_dev.Annexes.suma]
suma_assoc_2 [lemma, in GeoCoq.Tarski_dev.Annexes.suma]
suma_assoc_1 [lemma, in GeoCoq.Tarski_dev.Annexes.suma]
suma_comm [lemma, in GeoCoq.Tarski_dev.Annexes.suma]
suma_right_comm [lemma, in GeoCoq.Tarski_dev.Annexes.suma]
suma_middle_comm [lemma, in GeoCoq.Tarski_dev.Annexes.suma]
suma_left_comm [lemma, in GeoCoq.Tarski_dev.Annexes.suma]
suma_sym [lemma, in GeoCoq.Tarski_dev.Annexes.suma]
suma_distincts [lemma, in GeoCoq.Tarski_dev.Annexes.suma]
suma2__conga [lemma, in GeoCoq.Tarski_dev.Annexes.suma]
Sumg [definition, in GeoCoq.Tarski_dev.Ch15_lengths]
Sump [definition, in GeoCoq.Tarski_dev.Ch14_sum]
sump_to_sum [lemma, in GeoCoq.Tarski_dev.Ch14_sum]
SumV [definition, in GeoCoq.Tarski_dev.Annexes.vectors]
SumV_exists [definition, in GeoCoq.Tarski_dev.Annexes.vectors]
sum_f [lemma, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
sum_col [lemma, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
sum_pos_pos [lemma, in GeoCoq.Tarski_dev.Ch14_order]
sum_uniqueness [lemma, in GeoCoq.Tarski_dev.Annexes.vectors]
sum_exists [lemma, in GeoCoq.Tarski_dev.Annexes.vectors]
sum_sym [lemma, in GeoCoq.Tarski_dev.Annexes.vectors]
sum_diff_diff [lemma, in GeoCoq.Tarski_dev.Ch14_sum]
sum_opp [lemma, in GeoCoq.Tarski_dev.Ch14_sum]
sum_diff2_diff_sum2_b [lemma, in GeoCoq.Tarski_dev.Ch14_sum]
sum_diff2_diff_sum2_a [lemma, in GeoCoq.Tarski_dev.Ch14_sum]
sum_diff_diff_b [lemma, in GeoCoq.Tarski_dev.Ch14_sum]
sum_diff_diff_a [lemma, in GeoCoq.Tarski_dev.Ch14_sum]
sum_abcd [lemma, in GeoCoq.Tarski_dev.Ch14_sum]
sum_B_exists [lemma, in GeoCoq.Tarski_dev.Ch14_sum]
sum_A_exists [lemma, in GeoCoq.Tarski_dev.Ch14_sum]
sum_to_sum3 [lemma, in GeoCoq.Tarski_dev.Ch14_sum]
sum_stable [lemma, in GeoCoq.Tarski_dev.Ch14_sum]
sum_diff [lemma, in GeoCoq.Tarski_dev.Ch14_sum]
sum_ar2 [lemma, in GeoCoq.Tarski_dev.Ch14_sum]
sum_x_axis_unit_change [lemma, in GeoCoq.Tarski_dev.Ch14_sum]
sum_y_axis_change [lemma, in GeoCoq.Tarski_dev.Ch14_sum]
sum_assoc [lemma, in GeoCoq.Tarski_dev.Ch14_sum]
sum_assoc_2 [lemma, in GeoCoq.Tarski_dev.Ch14_sum]
sum_assoc_1 [lemma, in GeoCoq.Tarski_dev.Ch14_sum]
sum_iff_cong [lemma, in GeoCoq.Tarski_dev.Ch14_sum]
sum_comm [lemma, in GeoCoq.Tarski_dev.Ch14_sum]
sum_cong2 [lemma, in GeoCoq.Tarski_dev.Ch14_sum]
sum_cong [lemma, in GeoCoq.Tarski_dev.Ch14_sum]
sum_plg [lemma, in GeoCoq.Tarski_dev.Ch14_sum]
sum_A_null [lemma, in GeoCoq.Tarski_dev.Ch14_sum]
sum_B_null [lemma, in GeoCoq.Tarski_dev.Ch14_sum]
sum_uniquenessA [lemma, in GeoCoq.Tarski_dev.Ch14_sum]
sum_uniquenessB [lemma, in GeoCoq.Tarski_dev.Ch14_sum]
sum_A_B_B [lemma, in GeoCoq.Tarski_dev.Ch14_sum]
sum_A_B_A [lemma, in GeoCoq.Tarski_dev.Ch14_sum]
sum_par_strict [lemma, in GeoCoq.Tarski_dev.Ch14_sum]
sum_A_O_eq [lemma, in GeoCoq.Tarski_dev.Ch14_sum]
sum_O_B_eq [lemma, in GeoCoq.Tarski_dev.Ch14_sum]
sum_O_B [lemma, in GeoCoq.Tarski_dev.Ch14_sum]
sum_A_O [lemma, in GeoCoq.Tarski_dev.Ch14_sum]
sum_O_O [lemma, in GeoCoq.Tarski_dev.Ch14_sum]
sum_uniqueness [lemma, in GeoCoq.Tarski_dev.Ch14_sum]
sum_exists [lemma, in GeoCoq.Tarski_dev.Ch14_sum]
sum_to_sump [lemma, in GeoCoq.Tarski_dev.Ch14_sum]
sum22 [definition, in GeoCoq.Tarski_dev.Ch14_sum]
sum22_comm [lemma, in GeoCoq.Tarski_dev.Ch14_sum]
sum22_permut [lemma, in GeoCoq.Tarski_dev.Ch14_sum]
sum22_col [lemma, in GeoCoq.Tarski_dev.Ch14_sum]
sum3 [definition, in GeoCoq.Tarski_dev.Ch14_sum]
sum3_to_sum4 [lemma, in GeoCoq.Tarski_dev.Ch14_sum]
sum3_uniqueness [lemma, in GeoCoq.Tarski_dev.Ch14_sum]
sum3_exists [lemma, in GeoCoq.Tarski_dev.Ch14_sum]
sum3_comm_2_3 [lemma, in GeoCoq.Tarski_dev.Ch14_sum]
sum3_comm_1_2 [lemma, in GeoCoq.Tarski_dev.Ch14_sum]
sum3_permut [lemma, in GeoCoq.Tarski_dev.Ch14_sum]
sum3_col [lemma, in GeoCoq.Tarski_dev.Ch14_sum]
Sum4 [definition, in GeoCoq.Tarski_dev.Ch14_sum]
sum4_comm [lemma, in GeoCoq.Tarski_dev.Ch14_sum]
sum4_permut [lemma, in GeoCoq.Tarski_dev.Ch14_sum]
sum4_equiv [lemma, in GeoCoq.Tarski_dev.Ch14_sum]
sum4_col [lemma, in GeoCoq.Tarski_dev.Ch14_sum]
supplement_AM_CongA [lemma, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
swap_diff [lemma, in GeoCoq.Tarski_dev.Ch07_midpoint]
SWP [module, in GeoCoq.Utils.sets]
symmetric_point_uniqueness [lemma, in GeoCoq.Tarski_dev.Ch07_midpoint]
symmetric_point_construction [lemma, in GeoCoq.Tarski_dev.Ch07_midpoint]
symmetry_preserves_bet [lemma, in GeoCoq.Highschool.orientation]
symmetry_preseves_bet2 [lemma, in GeoCoq.Highschool.orientation]
symmetry_preseves_bet1 [lemma, in GeoCoq.Highschool.orientation]
symmetry_preserves_midpoint [lemma, in GeoCoq.Tarski_dev.Ch07_midpoint]
symmetry_preserves_per [lemma, in GeoCoq.Tarski_dev.Ch13_1]
symmetry_preserves_conga [lemma, in GeoCoq.Tarski_dev.Annexes.project]
symmetry_preserves_one_side [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals]
symmetry_preserves_two_sides [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals]
symmetry_preserves_bet [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals]
symmetry_preseves_bet2 [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals]
symmetry_preseves_bet1 [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals]
sym_preserve_diff [lemma, in GeoCoq.Tarski_dev.Ch09_plane]
sym_sym [lemma, in GeoCoq.Tarski_dev.Ch09_plane]
sym_par [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals]
Szmielew [section, in GeoCoq.Meta_theory.Parallel_postulates.szmielew]
szmielew [library]
szmielew_s_theorem [lemma, in GeoCoq.Meta_theory.Parallel_postulates.szmielew]


T

T [definition, in GeoCoq.Meta_theory.Models.tarski_to_beeson]
T [section, in GeoCoq.Meta_theory.Models.tarski_to_hilbert]
tactics_axioms [library]
Tagged [definition, in GeoCoq.Tactics.Coinc.ColR]
Tagged [definition, in GeoCoq.Tactics.Coinc.CoincR]
Tagged_predicates [section, in GeoCoq.Tarski_dev.Annexes.Tagged_predicates]
Tagged_predicates [library]
tailCP [definition, in GeoCoq.Utils.arity]
tailCPbis [definition, in GeoCoq.Utils.arity]
tailDefaultCP [definition, in GeoCoq.Utils.arity]
Tarski_2D_euclidean [record, in GeoCoq.Axioms.tarski_axioms]
Tarski_2D [record, in GeoCoq.Axioms.tarski_axioms]
Tarski_neutral_dimensionless_with_decidable_point_equality [record, in GeoCoq.Axioms.tarski_axioms]
Tarski_neutral_dimensionless [record, in GeoCoq.Axioms.tarski_axioms]
Tarski_to_intuitionistic_Tarski [section, in GeoCoq.Meta_theory.Models.tarski_to_beeson]
Tarski_is_a_Coinc_theory_for_col [instance, in GeoCoq.Tactics.Coinc.tarski_to_coinc_theory_for_col]
Tarski_is_a_Coinc_predicates_for_col [instance, in GeoCoq.Tactics.Coinc.tarski_to_coinc_theory_for_col]
Tarski_is_a_Arity_for_col [instance, in GeoCoq.Tactics.Coinc.tarski_to_coinc_theory_for_col]
Tarski_is_a_Coinc_theory_for_col [section, in GeoCoq.Tactics.Coinc.tarski_to_coinc_theory_for_col]
tarski_s_euclid_remove_degenerated_cases [lemma, in GeoCoq.Meta_theory.Parallel_postulates.tarski_s_euclid_remove_degenerated_cases]
tarski_s_euclid_remove_degenerated_cases [section, in GeoCoq.Meta_theory.Parallel_postulates.tarski_s_euclid_remove_degenerated_cases]
tarski_s_euclid_implies_euclid_5 [lemma, in GeoCoq.Meta_theory.Parallel_postulates.tarski_euclid]
tarski_euclid [section, in GeoCoq.Meta_theory.Parallel_postulates.tarski_euclid]
Tarski_follows_from_Makarios_Variant' [instance, in GeoCoq.Meta_theory.Models.tarski_to_makarios]
Tarski_follows_from_Makarios_Variant [instance, in GeoCoq.Meta_theory.Models.tarski_to_makarios]
tarski_s_euclid_implies_playfair [lemma, in GeoCoq.Meta_theory.Parallel_postulates.tarski_playfair]
tarski_playfair [section, in GeoCoq.Meta_theory.Parallel_postulates.tarski_playfair]
Tarski_is_a_Col_theory [instance, in GeoCoq.Tactics.Coinc.tarski_to_col_theory]
Tarski_is_a_Col_theory [section, in GeoCoq.Tactics.Coinc.tarski_to_col_theory]
Tarski_is_a_Coinc_theory_for_concy [instance, in GeoCoq.Tactics.Coinc.tarski_to_coinc_theory_for_concyclic]
Tarski_is_a_Coinc_theory_for_cocyclic [section, in GeoCoq.Tactics.Coinc.tarski_to_coinc_theory_for_concyclic]
Tarski_2D_follows_from_Hilbert2D [instance, in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
Tarski_neutral_dimensionless_with_decidable_point_equality_follows_from_Hilbert2D [instance, in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
Tarski_neutral_dimensionless_follows_from_Hilbert2D [instance, in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
Tarski_is_a_Coinc_theory_for_cop [instance, in GeoCoq.Tactics.Coinc.tarski_to_coinc_theory_for_cop]
Tarski_is_a_Coinc_theory_for_cop [section, in GeoCoq.Tactics.Coinc.tarski_to_coinc_theory_for_cop]
Tarski_neutral_dimensionless_variant [record, in GeoCoq.Axioms.makarios_variant_axioms]
tarski_s_parallel_postulate [definition, in GeoCoq.Meta_theory.Parallel_postulates.Euclid_def]
tarski_s_euclid [lemma, in GeoCoq.Tarski_dev.Ch12_parallel_inter_dec]
tarski_euclid [library]
tarski_to_hilbert [library]
tarski_to_makarios [library]
tarski_to_coinc_theory_for_concyclic [library]
tarski_axioms [library]
tarski_to_coinc_theory_for_cop [library]
tarski_to_beeson [library]
tarski_to_coinc_theory_for_col [library]
tarski_s_euclid_remove_degenerated_cases [library]
tarski_to_col_theory [library]
tarski_playfair [library]
Tarski83_to_Makarios_variant [section, in GeoCoq.Meta_theory.Models.tarski_to_makarios]
TCP_tarski [section, in GeoCoq.Meta_theory.Parallel_postulates.TCP_tarski]
TCP_tarski [library]
test_col_ok [lemma, in GeoCoq.Tactics.Coinc.ColR]
test_col [definition, in GeoCoq.Tactics.Coinc.ColR]
test_coinc_ok [lemma, in GeoCoq.Tactics.Coinc.CoincR]
test_coinc [definition, in GeoCoq.Tactics.Coinc.CoincR]
test_coinc_ok_for_col [lemma, in GeoCoq.Tactics.Coinc.CoincR_for_col]
test_coinc_for_col [definition, in GeoCoq.Tactics.Coinc.CoincR_for_col]
TG_to_TID [instance, in GeoCoq.Meta_theory.Models.independent_tarski_to_tarski]
TG_to_T [instance, in GeoCoq.Meta_theory.Models.independent_tarski_to_tarski]
TG2D_euclidean_to_T2D_euclidean [instance, in GeoCoq.Meta_theory.Models.independent_tarski_to_tarski]
TG2D_to_T2D [instance, in GeoCoq.Meta_theory.Models.independent_tarski_to_tarski]
thales [lemma, in GeoCoq.Tarski_dev.Ch15_lengths]
thales_converse_postulate__thales_existence [lemma, in GeoCoq.Meta_theory.Parallel_postulates.thales_converse_postulate_thales_existence]
thales_converse_postulate_thales_existence [section, in GeoCoq.Meta_theory.Parallel_postulates.thales_converse_postulate_thales_existence]
thales_converse_postulate__weak_triangle_circumscription_principle [lemma, in GeoCoq.Meta_theory.Parallel_postulates.thales_converse_postulate_weak_triangle_circumscription_principle]
thales_converse_postulate_weak_triangle_circumscription_principle [section, in GeoCoq.Meta_theory.Parallel_postulates.thales_converse_postulate_weak_triangle_circumscription_principle]
thales_postulate__thales_converse_postulate [lemma, in GeoCoq.Meta_theory.Parallel_postulates.thales_postulate_thales_converse_postulate]
thales_postulate_thales_converse_postulate [section, in GeoCoq.Meta_theory.Parallel_postulates.thales_postulate_thales_converse_postulate]
thales_existence__rah [lemma, in GeoCoq.Meta_theory.Parallel_postulates.thales_existence_rah]
thales_existence_rah [section, in GeoCoq.Meta_theory.Parallel_postulates.thales_existence_rah]
thales_converse_postulate [definition, in GeoCoq.Meta_theory.Parallel_postulates.Euclid_def]
thales_postulate [definition, in GeoCoq.Meta_theory.Parallel_postulates.Euclid_def]
thales_existence_rah [library]
thales_postulate_thales_converse_postulate [library]
thales_converse_postulate_thales_existence [library]
thales_converse_postulate_weak_triangle_circumscription_principle [library]
third_point [lemma, in GeoCoq.Tarski_dev.Ch05_bet_le]
three_hypotheses_aux [lemma, in GeoCoq.Tarski_dev.Annexes.saccheri]
three_medians_intersect [lemma, in GeoCoq.Highschool.gravityCenter]
th12 [lemma, in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
th14 [lemma, in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
th15 [lemma, in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
th17 [lemma, in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
th18_aux [lemma, in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
th19 [lemma, in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
Tpoint [projection, in GeoCoq.Axioms.tarski_axioms]
TpointG [projection, in GeoCoq.Axioms.independent_tarski_axioms]
TriangleMidpointsTheorems [section, in GeoCoq.Tarski_dev.Annexes.midpoint_theorems]
Triangles [section, in GeoCoq.Highschool.triangles]
triangles [library]
Triangles.ABC [section, in GeoCoq.Highschool.triangles]
Triangles.ABC.A [variable, in GeoCoq.Highschool.triangles]
Triangles.ABC.B [variable, in GeoCoq.Highschool.triangles]
Triangles.ABC.C [variable, in GeoCoq.Highschool.triangles]
triangle_circumscription_implies_tarski_s_euclid [lemma, in GeoCoq.Meta_theory.Parallel_postulates.TCP_tarski]
triangle_circumscription_implies_tarski_s_euclid_aux [lemma, in GeoCoq.Meta_theory.Parallel_postulates.TCP_tarski]
triangle__existential_triangle [lemma, in GeoCoq.Meta_theory.Parallel_postulates.triangle_existential_triangle]
triangle_existential_triangle [section, in GeoCoq.Meta_theory.Parallel_postulates.triangle_existential_triangle]
triangle_mid_par_cong_1 [lemma, in GeoCoq.Tarski_dev.Annexes.midpoint_theorems]
triangle_mid_par_cong [lemma, in GeoCoq.Tarski_dev.Annexes.midpoint_theorems]
triangle_mid_par [lemma, in GeoCoq.Tarski_dev.Annexes.midpoint_theorems]
triangle_mid_par_flat [lemma, in GeoCoq.Tarski_dev.Annexes.midpoint_theorems]
triangle_mid_par_flat_cong [lemma, in GeoCoq.Tarski_dev.Annexes.midpoint_theorems]
triangle_mid_par_flat_cong_2 [lemma, in GeoCoq.Tarski_dev.Annexes.midpoint_theorems]
triangle_mid_par_flat_cong_1 [lemma, in GeoCoq.Tarski_dev.Annexes.midpoint_theorems]
triangle_mid_par_flat_cong_aux [lemma, in GeoCoq.Tarski_dev.Annexes.midpoint_theorems]
triangle_mid_par_strict_cong [lemma, in GeoCoq.Tarski_dev.Annexes.midpoint_theorems]
triangle_mid_par_strict_cong_simp [lemma, in GeoCoq.Tarski_dev.Annexes.midpoint_theorems]
triangle_mid_par_strict_cong_2 [lemma, in GeoCoq.Tarski_dev.Annexes.midpoint_theorems]
triangle_mid_par_strict_cong_1 [lemma, in GeoCoq.Tarski_dev.Annexes.midpoint_theorems]
triangle_par_mid [lemma, in GeoCoq.Tarski_dev.Annexes.midpoint_theorems]
triangle_mid_par_strict_cong_aux [lemma, in GeoCoq.Tarski_dev.Annexes.midpoint_theorems]
triangle_mid_par_strict [lemma, in GeoCoq.Tarski_dev.Annexes.midpoint_theorems]
triangle_area [lemma, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
triangle_reverse_inequality [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
triangle_strict_reverse_inequality [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
triangle_inequality_2 [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
triangle_strict_inequality_2 [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
triangle_inequality [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
triangle_strict_inequality [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
triangle_mid_par [lemma, in GeoCoq.Tarski_dev.Ch13_1]
triangle_par [lemma, in GeoCoq.Tarski_dev.Annexes.project]
triangle__playfair_bis [lemma, in GeoCoq.Meta_theory.Parallel_postulates.triangle_playfair_bis]
triangle_playfair_bis [section, in GeoCoq.Meta_theory.Parallel_postulates.triangle_playfair_bis]
triangle_postulate [definition, in GeoCoq.Meta_theory.Parallel_postulates.Euclid_def]
triangle_circumscription_principle [definition, in GeoCoq.Meta_theory.Parallel_postulates.Euclid_def]
triangle_playfair_bis [library]
triangle_existential_triangle [library]
triangular_equality_bis [lemma, in GeoCoq.Tarski_dev.Ch15_lengths]
triangular_equality [lemma, in GeoCoq.Tarski_dev.Ch15_lengths]
triangular_equality_equiv [lemma, in GeoCoq.Tarski_dev.Ch15_lengths]
Triple [record, in GeoCoq.Utils.aux]
TriSumA [definition, in GeoCoq.Tarski_dev.Annexes.suma]
trisuma_perm_132 [lemma, in GeoCoq.Tarski_dev.Annexes.suma]
trisuma_perm_213 [lemma, in GeoCoq.Tarski_dev.Annexes.suma]
trisuma_perm_321 [lemma, in GeoCoq.Tarski_dev.Annexes.suma]
trisuma_perm_312 [lemma, in GeoCoq.Tarski_dev.Annexes.suma]
trisuma_perm_231 [lemma, in GeoCoq.Tarski_dev.Annexes.suma]
trisuma_distincts [lemma, in GeoCoq.Tarski_dev.Annexes.suma]
trisuma2__conga [lemma, in GeoCoq.Tarski_dev.Annexes.suma]
TS [definition, in GeoCoq.Tarski_dev.Ch09_plane]
tST [definition, in GeoCoq.Utils.sets]
ts_per_per_ts [lemma, in GeoCoq.Tarski_dev.Ch13_1]
TS_upper_dim_bis [lemma, in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
TS_upper_dim [lemma, in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
ts_ts_os [lemma, in GeoCoq.Tarski_dev.Ch09_plane]
ts_cong_par_cong_par [lemma, in GeoCoq.Tarski_dev.Annexes.quadrilaterals_inter_dec]
ts2__ex_bet2 [lemma, in GeoCoq.Tarski_dev.Ch09_plane]
TwoF [definition, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
two_points_on_line [projection, in GeoCoq.Axioms.hilbert_axioms]
two_distinct_points [lemma, in GeoCoq.Tarski_dev.Ch03_bet]
two_sides_in_angle [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
two_sides_not_col [lemma, in GeoCoq.Tarski_dev.Ch09_plane]
two_sides_dec [lemma, in GeoCoq.Tarski_dev.Ch10_line_reflexivity_2D]
T_dec [lemma, in GeoCoq.Meta_theory.Models.tarski_to_beeson]
T_Bet [lemma, in GeoCoq.Meta_theory.Models.tarski_to_beeson]
T_42 [section, in GeoCoq.Highschool.midpoint_thales]
_ =l= _ (type_scope) [notation, in GeoCoq.Meta_theory.Models.tarski_to_hilbert]
T1_4 [section, in GeoCoq.Tarski_dev.Ch02_cong]
T1_3 [section, in GeoCoq.Tarski_dev.Ch02_cong]
T1_2 [section, in GeoCoq.Tarski_dev.Ch02_cong]
T1_1 [section, in GeoCoq.Tarski_dev.Ch02_cong]
T10 [section, in GeoCoq.Tarski_dev.Ch10_line_reflexivity]
T10_2D [section, in GeoCoq.Tarski_dev.Ch10_line_reflexivity_2D]
T11_2 [section, in GeoCoq.Tarski_dev.Ch11_angles]
T11_1 [section, in GeoCoq.Tarski_dev.Ch11_angles]
T12_3 [section, in GeoCoq.Tarski_dev.Ch12_parallel]
T12_2' [section, in GeoCoq.Tarski_dev.Ch12_parallel]
T12_2 [section, in GeoCoq.Tarski_dev.Ch12_parallel]
T12_1 [section, in GeoCoq.Tarski_dev.Ch12_parallel]
T13 [section, in GeoCoq.Tarski_dev.Ch12_parallel_inter_dec]
T14_prod.Grid.grid_ok [variable, in GeoCoq.Tarski_dev.Ch14_prod]
T14_prod.Grid.E' [variable, in GeoCoq.Tarski_dev.Ch14_prod]
T14_prod.Grid.E [variable, in GeoCoq.Tarski_dev.Ch14_prod]
T14_prod.Grid.O [variable, in GeoCoq.Tarski_dev.Ch14_prod]
T14_prod.Grid [section, in GeoCoq.Tarski_dev.Ch14_prod]
T14_prod [section, in GeoCoq.Tarski_dev.Ch14_prod]
T14_sum.Grid.grid_ok [variable, in GeoCoq.Tarski_dev.Ch14_sum]
T14_sum.Grid.E' [variable, in GeoCoq.Tarski_dev.Ch14_sum]
T14_sum.Grid.E [variable, in GeoCoq.Tarski_dev.Ch14_sum]
T14_sum.Grid.O [variable, in GeoCoq.Tarski_dev.Ch14_sum]
T14_sum.Grid [section, in GeoCoq.Tarski_dev.Ch14_sum]
T14_sum [section, in GeoCoq.Tarski_dev.Ch14_sum]
T15 [section, in GeoCoq.Tarski_dev.Ch15_lengths]
T16 [section, in GeoCoq.Tarski_dev.Ch16_coordinates]
T17 [section, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
T17.E [variable, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
T17.E' [variable, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
T17.ncolOEE' [variable, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
T17.O [variable, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
T18 [section, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
t18_19 [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
t18_18 [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
t18_18_aux [lemma, in GeoCoq.Tarski_dev.Ch11_angles]
T18.E [variable, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
T18.E' [variable, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
T18.ncolOEE' [variable, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
T18.O [variable, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
T18.orthonormal_grid [variable, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
T18.SS [variable, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
T18.U1 [variable, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
T18.U2 [variable, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
_ =F= _ (FScope) [notation, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
_ <= _ (FScope) [notation, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
_ / _ (FScope) [notation, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
_ - _ (FScope) [notation, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
_ * _ (FScope) [notation, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
_ + _ (FScope) [notation, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
- _ (FScope) [notation, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
0 (FScope) [notation, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
1 (FScope) [notation, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
2 (FScope) [notation, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
T2_5 [section, in GeoCoq.Tarski_dev.Ch03_bet]
T2_4 [section, in GeoCoq.Tarski_dev.Ch03_bet]
T2_3 [section, in GeoCoq.Tarski_dev.Ch03_bet]
T2_2 [section, in GeoCoq.Tarski_dev.Ch03_bet]
T2_1 [section, in GeoCoq.Tarski_dev.Ch03_bet]
t2_8 [lemma, in GeoCoq.Tarski_dev.Ch06_out_lines]
t22_20 [lemma, in GeoCoq.Tarski_dev.Annexes.saccheri]
t22_17__aah [lemma, in GeoCoq.Tarski_dev.Annexes.saccheri]
t22_17__oah [lemma, in GeoCoq.Tarski_dev.Annexes.saccheri]
t22_17__rah [lemma, in GeoCoq.Tarski_dev.Annexes.saccheri]
t22_14__oah [lemma, in GeoCoq.Tarski_dev.Annexes.saccheri]
t22_14__aah [lemma, in GeoCoq.Tarski_dev.Annexes.saccheri]
t22_14__rah [lemma, in GeoCoq.Tarski_dev.Annexes.saccheri]
t22_14__nisi [lemma, in GeoCoq.Tarski_dev.Annexes.saccheri]
t22_14__nisi_aux [lemma, in GeoCoq.Tarski_dev.Annexes.saccheri]
t22_14__isi_nbet [lemma, in GeoCoq.Tarski_dev.Annexes.saccheri]
t22_14__isi_nbet_aux [lemma, in GeoCoq.Tarski_dev.Annexes.saccheri]
t22_14__bet [lemma, in GeoCoq.Tarski_dev.Annexes.saccheri]
t22_14__bet_aux [lemma, in GeoCoq.Tarski_dev.Annexes.saccheri]
t22_12__oah [lemma, in GeoCoq.Tarski_dev.Annexes.saccheri]
t22_12__aah [lemma, in GeoCoq.Tarski_dev.Annexes.saccheri]
t22_12__rah [lemma, in GeoCoq.Tarski_dev.Annexes.saccheri]
t22_11__obtuse [lemma, in GeoCoq.Tarski_dev.Annexes.saccheri]
t22_11__acute [lemma, in GeoCoq.Tarski_dev.Annexes.saccheri]
t22_11__per [lemma, in GeoCoq.Tarski_dev.Annexes.saccheri]
t22_9__obtuse [lemma, in GeoCoq.Tarski_dev.Annexes.saccheri]
t22_9__acute [lemma, in GeoCoq.Tarski_dev.Annexes.saccheri]
t22_9__per [lemma, in GeoCoq.Tarski_dev.Annexes.saccheri]
t22_8__lt5612 [lemma, in GeoCoq.Tarski_dev.Annexes.saccheri]
t22_8__lt1256 [lemma, in GeoCoq.Tarski_dev.Annexes.saccheri]
t22_8__cong [lemma, in GeoCoq.Tarski_dev.Annexes.saccheri]
t22_8__obtuse [lemma, in GeoCoq.Tarski_dev.Annexes.saccheri]
t22_8__acute [lemma, in GeoCoq.Tarski_dev.Annexes.saccheri]
t22_8__per [lemma, in GeoCoq.Tarski_dev.Annexes.saccheri]
t22_7__lt1256 [lemma, in GeoCoq.Tarski_dev.Annexes.saccheri]
t22_7__lt5612 [lemma, in GeoCoq.Tarski_dev.Annexes.saccheri]
t22_7__cong [lemma, in GeoCoq.Tarski_dev.Annexes.saccheri]
t22_7__obtuse [lemma, in GeoCoq.Tarski_dev.Annexes.saccheri]
t22_7__acute [lemma, in GeoCoq.Tarski_dev.Annexes.saccheri]
t22_7__per [lemma, in GeoCoq.Tarski_dev.Annexes.saccheri]
t22_16_2 [lemma, in GeoCoq.Meta_theory.Parallel_postulates.legendre]
t22_16_2aux1 [lemma, in GeoCoq.Meta_theory.Parallel_postulates.legendre]
t22_16_2aux [lemma, in GeoCoq.Meta_theory.Parallel_postulates.legendre]
t22_16_1bis [lemma, in GeoCoq.Meta_theory.Parallel_postulates.legendre]
t22_16_1 [lemma, in GeoCoq.Meta_theory.Parallel_postulates.legendre]
t22_24 [lemma, in GeoCoq.Meta_theory.Parallel_postulates.archimedes]
t22_24_aux1 [lemma, in GeoCoq.Meta_theory.Parallel_postulates.archimedes]
t22_24_aux [lemma, in GeoCoq.Meta_theory.Parallel_postulates.archimedes]
t22_23 [lemma, in GeoCoq.Meta_theory.Parallel_postulates.archimedes]
t22_23_aux [lemma, in GeoCoq.Meta_theory.Parallel_postulates.archimedes]
t22_19 [lemma, in GeoCoq.Meta_theory.Parallel_postulates.archimedes]
t22_18 [lemma, in GeoCoq.Meta_theory.Parallel_postulates.archimedes]
t22_18_aux2 [lemma, in GeoCoq.Meta_theory.Parallel_postulates.archimedes]
t22_18_aux1 [lemma, in GeoCoq.Meta_theory.Parallel_postulates.archimedes]
T3 [section, in GeoCoq.Tarski_dev.Ch04_cong_bet]
T4_4 [section, in GeoCoq.Tarski_dev.Ch04_col]
T4_3 [section, in GeoCoq.Tarski_dev.Ch04_col]
T4_2 [section, in GeoCoq.Tarski_dev.Ch04_col]
T4_1 [section, in GeoCoq.Tarski_dev.Ch04_col]
T5 [section, in GeoCoq.Tarski_dev.Ch05_bet_le]
T6_2 [section, in GeoCoq.Tarski_dev.Ch06_out_lines]
T6_1 [section, in GeoCoq.Tarski_dev.Ch06_out_lines]
T7_2 [section, in GeoCoq.Tarski_dev.Ch07_midpoint]
T7_1 [section, in GeoCoq.Tarski_dev.Ch07_midpoint]
T8_5 [section, in GeoCoq.Tarski_dev.Ch08_orthogonality]
T8_4 [section, in GeoCoq.Tarski_dev.Ch08_orthogonality]
T8_3 [section, in GeoCoq.Tarski_dev.Ch08_orthogonality]
T8_2 [section, in GeoCoq.Tarski_dev.Ch08_orthogonality]
T8_1 [section, in GeoCoq.Tarski_dev.Ch08_orthogonality]
T9 [section, in GeoCoq.Tarski_dev.Ch09_plane]


U

UnitTests [section, in GeoCoq.Tactics.UnitTests.unit_tests_2]
UnitTests [section, in GeoCoq.Tactics.UnitTests.unit_tests]
unit_tests_2 [library]
unit_tests [library]
universal_posidonius_postulate__perpendicular_transversal_postulate [lemma, in GeoCoq.Meta_theory.Parallel_postulates.universal_posidonius_postulate_par_perp_perp]
universal_posidonius_postulate_perpendicular_transversal_postulate [section, in GeoCoq.Meta_theory.Parallel_postulates.universal_posidonius_postulate_par_perp_perp]
universal_posidonius_postulate [definition, in GeoCoq.Meta_theory.Parallel_postulates.Euclid_def]
universal_posidonius_postulate_par_perp_perp [library]
upper_dim [projection, in GeoCoq.Axioms.tarski_axioms]
upper_dimG [projection, in GeoCoq.Axioms.independent_tarski_axioms]
upper_dimT [lemma, in GeoCoq.Meta_theory.Models.independent_tarski_to_tarski]
upper_dim [lemma, in GeoCoq.Meta_theory.Counter_models.counter_model_segment_construction]
upper_dim_implies_all_coplanar [lemma, in GeoCoq.Meta_theory.Dimension_axioms.upper_dim]
upper_dim_implies_one_or_two_sides [lemma, in GeoCoq.Meta_theory.Dimension_axioms.upper_dim]
upper_dim_implies_not_one_side_two_sides [lemma, in GeoCoq.Meta_theory.Dimension_axioms.upper_dim]
upper_dim_implies_two_sides_dec [lemma, in GeoCoq.Meta_theory.Dimension_axioms.upper_dim]
upper_dim_implies_not_two_sides_one_side [lemma, in GeoCoq.Meta_theory.Dimension_axioms.upper_dim]
upper_dim_implies_not_two_sides_one_side_aux [lemma, in GeoCoq.Meta_theory.Dimension_axioms.upper_dim]
upper_dim_implies_col_perp_perp_col [lemma, in GeoCoq.Meta_theory.Dimension_axioms.upper_dim]
upper_dim_implies_per_per_col [lemma, in GeoCoq.Meta_theory.Dimension_axioms.upper_dim]
upper_dim_axiom [definition, in GeoCoq.Meta_theory.Dimension_axioms.upper_dim]
Upper_dim [section, in GeoCoq.Meta_theory.Dimension_axioms.upper_dim]
upper_dim [lemma, in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
upper_dim [lemma, in GeoCoq.Meta_theory.Counter_models.counter_model_bet_identity]
upper_dim [library]


V

V [projection, in GeoCoq.Utils.aux]
varignon [lemma, in GeoCoq.Highschool.varignon]
Varignon [section, in GeoCoq.Highschool.varignon]
varignon [library]
varignon_aux [lemma, in GeoCoq.Highschool.varignon]
varignon_aux_aux [lemma, in GeoCoq.Highschool.varignon]
varignon' [lemma, in GeoCoq.Highschool.varignon]
vect [definition, in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
Vectors [section, in GeoCoq.Tarski_dev.Annexes.vectors]
vectors [library]
vector_same_dir_cong [lemma, in GeoCoq.Tarski_dev.Annexes.vectors]
vector_uniqueness [lemma, in GeoCoq.Tarski_dev.Annexes.vectors]
vector_construction_uniqueness [lemma, in GeoCoq.Tarski_dev.Annexes.vectors]
vector_construction [lemma, in GeoCoq.Tarski_dev.Annexes.vectors]
V1 [projection, in GeoCoq.Utils.aux]
V2 [projection, in GeoCoq.Utils.aux]


W

wd [projection, in GeoCoq.Tactics.Coinc.tactics_axioms]
wd_perm_2 [projection, in GeoCoq.Tactics.Coinc.tactics_axioms]
wd_perm_1 [projection, in GeoCoq.Tactics.Coinc.tactics_axioms]
weak_triangle_circumscription_principle__bachmann_s_lotschnittaxiom [lemma, in GeoCoq.Meta_theory.Parallel_postulates.weak_triangle_circumscription_principle_bachmann_s_lotschnittaxiom]
weak_triangle_circumscription_principle_bachmann_s_lotschnittaxiom [section, in GeoCoq.Meta_theory.Parallel_postulates.weak_triangle_circumscription_principle_bachmann_s_lotschnittaxiom]
weak_triangle_circumscription_principle [definition, in GeoCoq.Meta_theory.Parallel_postulates.Euclid_def]
weak_triangle_circumscription_principle_bachmann_s_lotschnittaxiom [library]


other

Something [notation, in GeoCoq.Utils.general_tactics]



Notation Index

L

_ =l= _ [in GeoCoq.Tarski_dev.Ch13_2_length]


T

_ =l= _ (type_scope) [in GeoCoq.Meta_theory.Models.tarski_to_hilbert]
_ =F= _ (FScope) [in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
_ <= _ (FScope) [in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
_ / _ (FScope) [in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
_ - _ (FScope) [in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
_ * _ (FScope) [in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
_ + _ (FScope) [in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
- _ (FScope) [in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
0 (FScope) [in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
1 (FScope) [in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
2 (FScope) [in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]


other

Something [in GeoCoq.Utils.general_tactics]



Module Index

P

PosOrder [in GeoCoq.Utils.sets]
PosSort [in GeoCoq.Utils.sets]
PosSort [in GeoCoq.Tactics.Coinc.CoincR]


S

S [in GeoCoq.Utils.sets]
SetOfPairsOfPositiveOrderedType [in GeoCoq.Utils.sets]
SetOfSetsOfPositiveOrderedType [in GeoCoq.Utils.sets]
SP [in GeoCoq.Utils.sets]
SPWEqP [in GeoCoq.Tactics.Coinc.ColR]
SS [in GeoCoq.Utils.sets]
SSWEqP [in GeoCoq.Tactics.Coinc.ColR]
SSWEqP [in GeoCoq.Tactics.Coinc.CoincR]
SSWP [in GeoCoq.Tactics.Coinc.ColR]
SSWP [in GeoCoq.Tactics.Coinc.CoincR]
SWP [in GeoCoq.Utils.sets]



Variable Index

B

Beeson_2.Bet_stability [in GeoCoq.Tarski_dev.Ch03_bet]
Beeson_1.Cong_stability [in GeoCoq.Tarski_dev.Ch03_bet]


T

Triangles.ABC.A [in GeoCoq.Highschool.triangles]
Triangles.ABC.B [in GeoCoq.Highschool.triangles]
Triangles.ABC.C [in GeoCoq.Highschool.triangles]
T14_prod.Grid.grid_ok [in GeoCoq.Tarski_dev.Ch14_prod]
T14_prod.Grid.E' [in GeoCoq.Tarski_dev.Ch14_prod]
T14_prod.Grid.E [in GeoCoq.Tarski_dev.Ch14_prod]
T14_prod.Grid.O [in GeoCoq.Tarski_dev.Ch14_prod]
T14_sum.Grid.grid_ok [in GeoCoq.Tarski_dev.Ch14_sum]
T14_sum.Grid.E' [in GeoCoq.Tarski_dev.Ch14_sum]
T14_sum.Grid.E [in GeoCoq.Tarski_dev.Ch14_sum]
T14_sum.Grid.O [in GeoCoq.Tarski_dev.Ch14_sum]
T17.E [in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
T17.E' [in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
T17.ncolOEE' [in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
T17.O [in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
T18.E [in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
T18.E' [in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
T18.ncolOEE' [in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
T18.O [in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
T18.orthonormal_grid [in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
T18.SS [in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
T18.U1 [in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
T18.U2 [in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]



Library Index

A

all_equiv
alternate_interior_angles_proclus
alternate_interior_angles_consecutive_interior_angles
alternate_interior_angles_playfair_bis
alternate_interior_angles_triangle
angle_archimedes
archimedes
aristotle_greenberg
arity
aux


B

bachmann_s_lotschnittaxiom_existential_inverse_projection_postulate
bachmann_s_lotschnittaxiom_weak_triangle_circumscription_principle
beeson_s_axioms
bisector


C

Ch02_cong
Ch03_bet
Ch04_cong_bet
Ch04_col
Ch05_bet_le
Ch06_out_lines
Ch07_midpoint
Ch08_orthogonality
Ch09_plane
Ch10_line_reflexivity_2D
Ch10_line_reflexivity
Ch11_angles
Ch12_parallel_inter_dec
Ch12_parallel
Ch13_4_cos
Ch13_6_Desargues_Hessenberg
Ch13_3_angles
Ch13_5_Pappus_Pascal
Ch13_2_length
Ch13_1
Ch14_order
Ch14_sum
Ch14_prod
Ch15_lengths
Ch15_pyth_rel
Ch16_coordinates
Ch16_coordinates_with_functions
circumcenter
CoincR
CoincR_for_col
ColR
concyclic
consecutive_interior_angles_alternate_interior_angles
Coplanar_perm
Coplanar_trans
counter_model_segment_construction
counter_model_bet_identity


E

equivalence_between_decidability_properties_of_basic_relations
Euclid
Euclid_def
euclid_5_original_euclid
Euler_line
exercises
existential_inverse_projection_postulate_legendre_s_postulate
existential_playfair_rah
existential_saccheri_rah
existential_triangle_rah


G

general_tactics
gravityCenter


H

hilbert_axioms
hilbert_to_tarski


I

incenter
independent_tarski_to_tarski
independent_tarski_axioms
inverse_projection_postulate_proclus_bis


L

legendre


M

makarios_variant_axioms
midpoint_thales
midpoint_playfair
midpoint_theorems


O

orientation
original_spp_inverse_projection_postulate
original_euclid_original_spp
orthocenter


P

par_perp_2_par_par_perp_perp
par_perp_perp_playfair
par_perp_perp_par_perp_2_par
par_perp_perp_TCP
par_trans_playfair
par_trans_NID
Permutations
perp_bisect
playfair_alternate_interior_angles
playfair_universal_posidonius_postulate
playfair_existential_playfair
playfair_bis_playfair
playfair_par_trans
playfair_midpoint
posidonius_postulate_rah
proclus_bis_proclus
proclus_aristotle
proclus_SPP
project


Q

quadrilaterals
quadrilaterals_inter_dec


R

rah_existential_saccheri
rah_similar
rah_posidonius_postulate
rah_triangle
rah_rectangle_principle
rah_thales_postulate
rectangle_principle_rectangle_existence
rectangle_existence_rah


S

saccheri
sets
similar_rah
SPP_ID
SPP_tarski
suma
szmielew


T

tactics_axioms
Tagged_predicates
tarski_euclid
tarski_to_hilbert
tarski_to_makarios
tarski_to_coinc_theory_for_concyclic
tarski_axioms
tarski_to_coinc_theory_for_cop
tarski_to_beeson
tarski_to_coinc_theory_for_col
tarski_s_euclid_remove_degenerated_cases
tarski_to_col_theory
tarski_playfair
TCP_tarski
thales_existence_rah
thales_postulate_thales_converse_postulate
thales_converse_postulate_thales_existence
thales_converse_postulate_weak_triangle_circumscription_principle
triangles
triangle_playfair_bis
triangle_existential_triangle


U

unit_tests_2
unit_tests
universal_posidonius_postulate_par_perp_perp
upper_dim


V

varignon
vectors


W

weak_triangle_circumscription_principle_bachmann_s_lotschnittaxiom



Lemma Index

A

aah__hpp [in GeoCoq.Meta_theory.Parallel_postulates.szmielew]
absolute_exterior_angle_theorem [in GeoCoq.Tarski_dev.Annexes.saccheri]
acute_col_out [in GeoCoq.Tarski_dev.Ch13_3_angles]
acute_not_bet [in GeoCoq.Tarski_dev.Ch13_3_angles]
acute_col_perp__out [in GeoCoq.Tarski_dev.Ch12_parallel]
acute_sac__aah [in GeoCoq.Tarski_dev.Annexes.saccheri]
acute_sac__lt [in GeoCoq.Tarski_dev.Annexes.saccheri]
acute_comp_not_acute [in GeoCoq.Tarski_dev.Ch13_4_cos]
acute_not_obtuse [in GeoCoq.Tarski_dev.Ch13_4_cos]
acute_archi_aux2 [in GeoCoq.Meta_theory.Parallel_postulates.angle_archimedes]
acute_archi_aux1 [in GeoCoq.Meta_theory.Parallel_postulates.angle_archimedes]
acute_archi_aux [in GeoCoq.Meta_theory.Parallel_postulates.angle_archimedes]
acute_not_per [in GeoCoq.Tarski_dev.Ch11_angles]
acute_trivial [in GeoCoq.Tarski_dev.Ch11_angles]
acute_chara [in GeoCoq.Tarski_dev.Ch11_angles]
acute_obtuse__lta [in GeoCoq.Tarski_dev.Ch11_angles]
acute_per__lta [in GeoCoq.Tarski_dev.Ch11_angles]
acute_conga__acute [in GeoCoq.Tarski_dev.Ch11_angles]
acute_distincts [in GeoCoq.Tarski_dev.Ch11_angles]
acute_distinct [in GeoCoq.Tarski_dev.Ch11_angles]
acute_lea_acute [in GeoCoq.Tarski_dev.Ch11_angles]
acute_sym [in GeoCoq.Tarski_dev.Ch11_angles]
acute_bet_obtuse [in GeoCoq.Tarski_dev.Ch13_1]
acute_suma__nbet [in GeoCoq.Tarski_dev.Annexes.suma]
acute__isi [in GeoCoq.Tarski_dev.Annexes.suma]
addition_betH [in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
allButLastCPTl [in GeoCoq.Utils.arity]
all_eqaa [in GeoCoq.Tarski_dev.Ch13_3_angles]
all_eqa [in GeoCoq.Tarski_dev.Ch13_3_angles]
all_one_side_par_strict [in GeoCoq.Tarski_dev.Ch12_parallel]
all_equiv_equiv [in GeoCoq.Utils.all_equiv]
all_coplanar_upper_dim [in GeoCoq.Meta_theory.Dimension_axioms.upper_dim]
all_coplanar_implies_upper_dim [in GeoCoq.Meta_theory.Dimension_axioms.upper_dim]
all_eql [in GeoCoq.Tarski_dev.Ch13_2_length]
all_coplanar [in GeoCoq.Tarski_dev.Ch10_line_reflexivity_2D]
alternate_interior__triangle [in GeoCoq.Meta_theory.Parallel_postulates.alternate_interior_angles_triangle]
alternate_interior__playfair_bis [in GeoCoq.Meta_theory.Parallel_postulates.alternate_interior_angles_playfair_bis]
alternate_interior__playfair_aux [in GeoCoq.Meta_theory.Parallel_postulates.alternate_interior_angles_playfair_bis]
alternate_interior__proclus [in GeoCoq.Meta_theory.Parallel_postulates.alternate_interior_angles_proclus]
alternate_interior__consecutive_interior [in GeoCoq.Meta_theory.Parallel_postulates.alternate_interior_angles_consecutive_interior_angles]
altitude_intersect [in GeoCoq.Highschool.orthocenter]
altitude_is_perp_bisect [in GeoCoq.Highschool.orthocenter]
AM_perp_AM_Par_AM_perp [in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
AM_Perp_triv2 [in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
AM_Perp_triv1 [in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
AM_Perp_AM_Perp_AM_Par [in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
AM_lower_dim [in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
AM_Par_ratio_AM_Par [in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
anga_col_null [in GeoCoq.Tarski_dev.Ch13_3_angles]
anga_not_lg_null [in GeoCoq.Tarski_dev.Ch13_3_angles]
anga_col_out [in GeoCoq.Tarski_dev.Ch13_3_angles]
anga_out_anga [in GeoCoq.Tarski_dev.Ch13_3_angles]
anga_conga_anga [in GeoCoq.Tarski_dev.Ch13_3_angles]
anga_const_o [in GeoCoq.Tarski_dev.Ch13_3_angles]
anga_not_flat [in GeoCoq.Tarski_dev.Ch13_3_angles]
anga_acute [in GeoCoq.Tarski_dev.Ch13_3_angles]
anga_const [in GeoCoq.Tarski_dev.Ch13_3_angles]
anga_distincts [in GeoCoq.Tarski_dev.Ch13_3_angles]
anga_not_null_lg [in GeoCoq.Tarski_dev.Ch13_3_angles]
anga_sym [in GeoCoq.Tarski_dev.Ch13_3_angles]
anga_distinct [in GeoCoq.Tarski_dev.Ch13_3_angles]
anga_conga [in GeoCoq.Tarski_dev.Ch13_3_angles]
anga_is_ang [in GeoCoq.Tarski_dev.Ch13_3_angles]
anga_exists [in GeoCoq.Tarski_dev.Ch13_3_angles]
angles_archi_aux1 [in GeoCoq.Meta_theory.Parallel_postulates.angle_archimedes]
angles_archi_aux [in GeoCoq.Meta_theory.Parallel_postulates.angle_archimedes]
angle_bisector [in GeoCoq.Tarski_dev.Ch11_angles]
angle_partition [in GeoCoq.Tarski_dev.Ch11_angles]
angle_construction_3 [in GeoCoq.Tarski_dev.Ch11_angles]
angle_construction_2 [in GeoCoq.Tarski_dev.Ch11_angles]
angle_construction_1 [in GeoCoq.Tarski_dev.Ch11_angles]
ang_not_lg_null [in GeoCoq.Tarski_dev.Ch13_3_angles]
ang_cong_ang [in GeoCoq.Tarski_dev.Ch13_3_angles]
ang_const_o [in GeoCoq.Tarski_dev.Ch13_3_angles]
ang_distincts [in GeoCoq.Tarski_dev.Ch13_3_angles]
ang_not_null_lg [in GeoCoq.Tarski_dev.Ch13_3_angles]
ang_sym [in GeoCoq.Tarski_dev.Ch13_3_angles]
ang_const [in GeoCoq.Tarski_dev.Ch13_3_angles]
ang_distinct [in GeoCoq.Tarski_dev.Ch13_3_angles]
ang_conga [in GeoCoq.Tarski_dev.Ch13_3_angles]
ang_exists [in GeoCoq.Tarski_dev.Ch13_3_angles]
another_point [in GeoCoq.Meta_theory.Models.tarski_to_beeson]
another_point [in GeoCoq.Tarski_dev.Ch03_bet]
app_2_n_app_eq [in GeoCoq.Utils.arity]
app_app_2_n_default [in GeoCoq.Utils.arity]
app_app_2_n [in GeoCoq.Utils.arity]
app_2_n_app_default [in GeoCoq.Utils.arity]
app_2_n_app [in GeoCoq.Utils.arity]
app_1_n_app_eq [in GeoCoq.Utils.arity]
app_app_1_n [in GeoCoq.Utils.arity]
app_1_n_app [in GeoCoq.Utils.arity]
app_n_1_app_eq [in GeoCoq.Utils.arity]
app_app_n_1 [in GeoCoq.Utils.arity]
app_n_1_app [in GeoCoq.Utils.arity]
archi__gradaexp_destruction [in GeoCoq.Meta_theory.Parallel_postulates.angle_archimedes]
archi__grada_destruction [in GeoCoq.Meta_theory.Parallel_postulates.angle_archimedes]
archi_in_angles [in GeoCoq.Meta_theory.Parallel_postulates.angle_archimedes]
archi_in_acute_angles [in GeoCoq.Meta_theory.Parallel_postulates.angle_archimedes]
archi__acute_or_right [in GeoCoq.Meta_theory.Parallel_postulates.archimedes]
archi__obtuse_case_elimination [in GeoCoq.Meta_theory.Parallel_postulates.archimedes]
aristotle__greenberg [in GeoCoq.Meta_theory.Parallel_postulates.aristotle_greenberg]
axiom_A2a [in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
axiom_A2b [in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
axiom_euclid_uniqueness [in GeoCoq.Meta_theory.Models.tarski_to_hilbert]
axiom_conga_refl [in GeoCoq.Meta_theory.Models.tarski_to_hilbert]
axiom_inter_dec [in GeoCoq.Meta_theory.Models.tarski_to_hilbert]
axiom_conga_permlr [in GeoCoq.Meta_theory.Models.tarski_to_hilbert]
axiom_congaH_outH_congaH [in GeoCoq.Meta_theory.Models.tarski_to_hilbert]
axiom_cong_permr [in GeoCoq.Meta_theory.Models.tarski_to_hilbert]
axiom_conga_comm [in GeoCoq.Meta_theory.Models.tarski_to_hilbert]
axiom_hcong_4_uniqueness [in GeoCoq.Meta_theory.Models.tarski_to_hilbert]
axiom_hcong_4_existence [in GeoCoq.Meta_theory.Models.tarski_to_hilbert]
axiom_cong_5' [in GeoCoq.Meta_theory.Models.tarski_to_hilbert]
axiom_hcong_3 [in GeoCoq.Meta_theory.Models.tarski_to_hilbert]
axiom_hcong_refl [in GeoCoq.Meta_theory.Models.tarski_to_hilbert]
axiom_hcong_trans [in GeoCoq.Meta_theory.Models.tarski_to_hilbert]
axiom_hcong_scott [in GeoCoq.Meta_theory.Models.tarski_to_hilbert]
axiom_hcong_1_uniqueness [in GeoCoq.Meta_theory.Models.tarski_to_hilbert]
axiom_hcong_1_existence [in GeoCoq.Meta_theory.Models.tarski_to_hilbert]
axiom_pasch [in GeoCoq.Meta_theory.Models.tarski_to_hilbert]
axiom_between_one [in GeoCoq.Meta_theory.Models.tarski_to_hilbert]
axiom_between_only_one [in GeoCoq.Meta_theory.Models.tarski_to_hilbert]
axiom_between_out [in GeoCoq.Meta_theory.Models.tarski_to_hilbert]
axiom_between_comm [in GeoCoq.Meta_theory.Models.tarski_to_hilbert]
axiom_between_diff [in GeoCoq.Meta_theory.Models.tarski_to_hilbert]
axiom_between_col [in GeoCoq.Meta_theory.Models.tarski_to_hilbert]
axiom_plan' [in GeoCoq.Meta_theory.Models.tarski_to_hilbert]
axiom_plan [in GeoCoq.Meta_theory.Models.tarski_to_hilbert]
axiom_two_points_on_line [in GeoCoq.Meta_theory.Models.tarski_to_hilbert]
axiom_line_uniqueness [in GeoCoq.Meta_theory.Models.tarski_to_hilbert]
axiom_Incid_dec [in GeoCoq.Meta_theory.Models.tarski_to_hilbert]
axiom_Incid_morphism [in GeoCoq.Meta_theory.Models.tarski_to_hilbert]
axiom_line_existence [in GeoCoq.Meta_theory.Models.tarski_to_hilbert]
axiom_five_segmentsH [in GeoCoq.Meta_theory.Models.hilbert_to_tarski]


B

bachmann_s_lotschnittaxiom__existential_inverse_projection_postulate [in GeoCoq.Meta_theory.Parallel_postulates.bachmann_s_lotschnittaxiom_existential_inverse_projection_postulate]
bachmann_s_lotschnittaxiom__weak_triangle_circumscription_principle [in GeoCoq.Meta_theory.Parallel_postulates.bachmann_s_lotschnittaxiom_weak_triangle_circumscription_principle]
BetH_Bet [in GeoCoq.Meta_theory.Models.tarski_to_beeson]
betH_congH2__False [in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
betH_outH2__betH [in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
betH_outH__outH [in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
betH_congH3_outH_betH [in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
betH_not_congH [in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
betH_dec [in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
betH_trans0 [in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
betH_trans [in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
betH_trans2 [in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
betH_trans1 [in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
betH_expand [in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
betH_colH [in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
betH_line [in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
betH_to_bet [in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
betH_distincts [in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
betH2_out [in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
BetSEq [in GeoCoq.Meta_theory.Parallel_postulates.Euclid_def]
BetT_id [in GeoCoq.Meta_theory.Models.tarski_to_beeson]
BetT_symmetry [in GeoCoq.Meta_theory.Models.tarski_to_beeson]
between_symmetry_B [in GeoCoq.Meta_theory.Models.tarski_to_beeson]
between_inner_transitivity_B [in GeoCoq.Meta_theory.Models.tarski_to_beeson]
between_identity_B [in GeoCoq.Meta_theory.Models.tarski_to_beeson]
between_cong_3 [in GeoCoq.Tarski_dev.Ch05_bet_le]
between_cong_2 [in GeoCoq.Tarski_dev.Ch05_bet_le]
between_cong [in GeoCoq.Tarski_dev.Ch05_bet_le]
between_exchange4 [in GeoCoq.Tarski_dev.Ch03_bet]
between_exchange2 [in GeoCoq.Tarski_dev.Ch03_bet]
between_inner_transitivity [in GeoCoq.Tarski_dev.Ch03_bet]
between_exchange3 [in GeoCoq.Tarski_dev.Ch03_bet]
between_equality [in GeoCoq.Tarski_dev.Ch03_bet]
between_trivial2 [in GeoCoq.Tarski_dev.Ch03_bet]
between_symmetry [in GeoCoq.Tarski_dev.Ch03_bet]
between_trivial [in GeoCoq.Tarski_dev.Ch03_bet]
between_trivialT [in GeoCoq.Meta_theory.Models.independent_tarski_to_tarski]
between_identityT [in GeoCoq.Meta_theory.Models.independent_tarski_to_tarski]
between_identity [in GeoCoq.Meta_theory.Counter_models.counter_model_segment_construction]
between_symmetry [in GeoCoq.Meta_theory.Models.tarski_to_makarios]
between_trivial [in GeoCoq.Meta_theory.Models.tarski_to_makarios]
between_symmetric [in GeoCoq.Tarski_dev.Ch11_angles]
between_one [in GeoCoq.Meta_theory.Models.tarski_to_hilbert]
between_one [in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
between_only_one' [in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
bet_flat_ang [in GeoCoq.Tarski_dev.Ch13_3_angles]
bet_id [in GeoCoq.Meta_theory.Models.tarski_to_beeson]
Bet_T [in GeoCoq.Meta_theory.Models.tarski_to_beeson]
bet_stability [in GeoCoq.Meta_theory.Models.tarski_to_beeson]
bet_half_bet [in GeoCoq.Highschool.orientation]
bet_double_bet [in GeoCoq.Highschool.orientation]
bet_le_le [in GeoCoq.Highschool.orientation]
bet_le_eq [in GeoCoq.Tarski_dev.Ch05_bet_le]
bet__le2313 [in GeoCoq.Tarski_dev.Ch05_bet_le]
bet__le1213 [in GeoCoq.Tarski_dev.Ch05_bet_le]
bet_cong_eq [in GeoCoq.Tarski_dev.Ch05_bet_le]
bet_dec [in GeoCoq.Tarski_dev.Ch05_bet_le]
bet_dec_eq_dec_b [in GeoCoq.Tarski_dev.Ch03_bet]
bet_neq32__neq [in GeoCoq.Tarski_dev.Ch03_bet]
bet_neq23__neq [in GeoCoq.Tarski_dev.Ch03_bet]
bet_neq21__neq [in GeoCoq.Tarski_dev.Ch03_bet]
bet_neq12__neq [in GeoCoq.Tarski_dev.Ch03_bet]
Bet_perm [in GeoCoq.Tarski_dev.Ch03_bet]
Bet_cases [in GeoCoq.Tarski_dev.Ch03_bet]
bet_col [in GeoCoq.Tarski_dev.Ch03_bet]
bet_decG [in GeoCoq.Meta_theory.Models.independent_tarski_to_tarski]
bet_leP [in GeoCoq.Tarski_dev.Ch15_lengths]
bet_lt21_le31 [in GeoCoq.Tarski_dev.Ch14_order]
bet_lt21_le32 [in GeoCoq.Tarski_dev.Ch14_order]
bet_lt12_le13 [in GeoCoq.Tarski_dev.Ch14_order]
bet_lt12_le23 [in GeoCoq.Tarski_dev.Ch14_order]
bet_cong3 [in GeoCoq.Tarski_dev.Ch02_cong]
bet_col1 [in GeoCoq.Tarski_dev.Ch07_midpoint]
bet_le__lt [in GeoCoq.Tarski_dev.Ch11_angles]
bet_obtuse__acute [in GeoCoq.Tarski_dev.Ch11_angles]
bet_acute__obtuse [in GeoCoq.Tarski_dev.Ch11_angles]
bet__obtuse [in GeoCoq.Tarski_dev.Ch11_angles]
bet_lea__bet [in GeoCoq.Tarski_dev.Ch11_angles]
bet_in_angle_bet [in GeoCoq.Tarski_dev.Ch11_angles]
bet_conga_bet [in GeoCoq.Tarski_dev.Ch11_angles]
bet_out_out_bet [in GeoCoq.Tarski_dev.Ch06_out_lines]
bet_out [in GeoCoq.Tarski_dev.Ch06_out_lines]
Bet_Between_H [in GeoCoq.Meta_theory.Models.tarski_to_hilbert]
bet_betCood [in GeoCoq.Tarski_dev.Ch16_coordinates]
bet_betCood_aux [in GeoCoq.Tarski_dev.Ch16_coordinates]
bet_trans [in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
bet_comm [in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
bet_cong3_bet [in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
bet_disjoint [in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
bet_colH [in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
bet_identity [in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
bet_same_dir2 [in GeoCoq.Tarski_dev.Annexes.vectors]
bet_same_dir1 [in GeoCoq.Tarski_dev.Annexes.vectors]
Bet_tagged_Bet [in GeoCoq.Tarski_dev.Annexes.Tagged_predicates]
Bet_Bet_tagged [in GeoCoq.Tarski_dev.Annexes.Tagged_predicates]
bet_dec_eq_dec [in GeoCoq.Meta_theory.Decidability.equivalence_between_decidability_properties_of_basic_relations]
bet_cong_bet [in GeoCoq.Tarski_dev.Annexes.quadrilaterals]
bet_half_bet [in GeoCoq.Tarski_dev.Annexes.quadrilaterals]
bet_double_bet [in GeoCoq.Tarski_dev.Annexes.quadrilaterals]
bet_le_le [in GeoCoq.Tarski_dev.Annexes.quadrilaterals]
bet_suma__per [in GeoCoq.Tarski_dev.Annexes.suma]
bet_per_suma__per123 [in GeoCoq.Tarski_dev.Annexes.suma]
bet_per_suma__per456 [in GeoCoq.Tarski_dev.Annexes.suma]
bet_suma__isi [in GeoCoq.Tarski_dev.Annexes.suma]
bet2_lta__lta [in GeoCoq.Tarski_dev.Ch11_angles]
bet2_out_out [in GeoCoq.Tarski_dev.Ch06_out_lines]
bet2_le2__le1245 [in GeoCoq.Tarski_dev.Ch06_out_lines]
bet2_le2__le2356 [in GeoCoq.Tarski_dev.Ch06_out_lines]
bet2_le2__le1346 [in GeoCoq.Tarski_dev.Ch06_out_lines]
bet2_cong_bet [in GeoCoq.Tarski_dev.Annexes.quadrilaterals]
bet3_cong3_bet [in GeoCoq.Tarski_dev.Annexes.quadrilaterals]
bisector_perp_equality [in GeoCoq.Highschool.bisector]
bisector_foot_out_out [in GeoCoq.Highschool.bisector]
bisector_existence [in GeoCoq.Highschool.bisector]


C

Cd_Cd_EqF [in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
Cd_Col [in GeoCoq.Tarski_dev.Ch16_coordinates]
centroid_theorem [in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
change_grid_prod [in GeoCoq.Tarski_dev.Ch14_prod]
change_grid_prod1 [in GeoCoq.Tarski_dev.Ch14_prod]
change_grid_prod_l_O [in GeoCoq.Tarski_dev.Ch14_prod]
change_grid_sum [in GeoCoq.Tarski_dev.Ch14_sum]
change_grid_sum_0 [in GeoCoq.Tarski_dev.Ch14_sum]
characterization_of_perpendicularity_F [in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
characterization_of_perpendicularity_F_bis [in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
characterization_of_parallelism_F [in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
characterization_of_parallelism_F_bis [in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
characterization_of_parallelism_F_aux [in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
characterization_of_right_triangle_F [in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
characterization_of_midpoint_F [in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
characterization_of_neq_F [in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
characterization_of_equality_F_bis [in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
characterization_of_equality_F_aux [in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
characterization_of_neq_F_bis [in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
characterization_of_equality_F [in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
characterization_of_collinearity_F [in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
characterization_of_betweenness_F [in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
characterization_of_congruence_F [in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
characterization_of_collinearity [in GeoCoq.Tarski_dev.Ch16_coordinates]
characterization_of_betweenness [in GeoCoq.Tarski_dev.Ch16_coordinates]
characterization_of_betweenness_aux [in GeoCoq.Tarski_dev.Ch16_coordinates]
characterization_of_congruence [in GeoCoq.Tarski_dev.Ch16_coordinates]
chasles [in GeoCoq.Tarski_dev.Annexes.vectors]
chasles_ratios [in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
circPermNConsOK [in GeoCoq.Utils.arity]
circPermNConsTlOK [in GeoCoq.Utils.arity]
circPermNCPOK [in GeoCoq.Utils.arity]
circPermNCP0 [in GeoCoq.Utils.arity]
circPermNId [in GeoCoq.Utils.arity]
circPermNIdAux [in GeoCoq.Utils.arity]
circPermNIdFirst [in GeoCoq.Utils.arity]
circPermPerm [in GeoCoq.Utils.arity]
circumcenter_per [in GeoCoq.Highschool.circumcenter]
circumcenter_intersect [in GeoCoq.Highschool.circumcenter]
circumcenter_perp_all [in GeoCoq.Highschool.circumcenter]
circumcenter_perp [in GeoCoq.Highschool.circumcenter]
circumcenter_cong [in GeoCoq.Highschool.circumcenter]
CoappDup [in GeoCoq.Tactics.Coinc.CoincR]
CoappDupAux [in GeoCoq.Tactics.Coinc.CoincR]
CoappDupPerm [in GeoCoq.Tactics.Coinc.CoincR]
ColB_Col [in GeoCoq.Meta_theory.Models.tarski_to_beeson]
ColH_bets [in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
colH_trans [in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
colH_dec [in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
colH_trivial121 [in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
colH_trivial122 [in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
colH_trivial112 [in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
colH_trivial111 [in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
colH_permut_321 [in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
colH_permut_132 [in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
colH_permut_213 [in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
colH_permut_312 [in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
colH_permut_231 [in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
collect_diffs [in GeoCoq.Tactics.Coinc.ColR]
collect_cols [in GeoCoq.Tactics.Coinc.ColR]
collect_wds [in GeoCoq.Tactics.Coinc.CoincR]
collect_coincs [in GeoCoq.Tactics.Coinc.CoincR]
collect_wds_for_col [in GeoCoq.Tactics.Coinc.CoincR_for_col]
collect_coincs_for_col [in GeoCoq.Tactics.Coinc.CoincR_for_col]
cols_coincide [in GeoCoq.Meta_theory.Models.tarski_to_hilbert]
cols_coincide_2 [in GeoCoq.Meta_theory.Models.tarski_to_hilbert]
cols_coincide_1 [in GeoCoq.Meta_theory.Models.tarski_to_hilbert]
Col_dec [in GeoCoq.Meta_theory.Models.tarski_to_beeson]
col_proj_proj [in GeoCoq.Highschool.orientation]
col_proj_col [in GeoCoq.Highschool.orientation]
Col_dec [in GeoCoq.Tarski_dev.Ch05_bet_le]
col_3 [in GeoCoq.Tactics.Coinc.tarski_to_coinc_theory_for_col]
col_bd [in GeoCoq.Tactics.Coinc.tarski_to_coinc_theory_for_col]
col_perm_2 [in GeoCoq.Tactics.Coinc.tarski_to_coinc_theory_for_col]
col_perm_1 [in GeoCoq.Tactics.Coinc.tarski_to_coinc_theory_for_col]
col_par [in GeoCoq.Tarski_dev.Ch12_parallel]
col_not_col_not_par [in GeoCoq.Tarski_dev.Ch12_parallel]
Col_decG [in GeoCoq.Meta_theory.Models.independent_tarski_to_tarski]
col_permut321 [in GeoCoq.Tarski_dev.Annexes.midpoint_theorems]
col_permut312 [in GeoCoq.Tarski_dev.Annexes.midpoint_theorems]
col_permut231 [in GeoCoq.Tarski_dev.Annexes.midpoint_theorems]
col_permut213 [in GeoCoq.Tarski_dev.Annexes.midpoint_theorems]
col_permut132 [in GeoCoq.Tarski_dev.Annexes.midpoint_theorems]
Col_AM_Col [in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
col_defect__out [in GeoCoq.Meta_theory.Parallel_postulates.legendre]
col_2_le_or_ge [in GeoCoq.Tarski_dev.Ch14_order]
col_pos_or_neg [in GeoCoq.Tarski_dev.Ch14_order]
col_coplanar [in GeoCoq.Tarski_dev.Coplanar_perm]
col_perp_perp_col [in GeoCoq.Tarski_dev.Ch11_angles]
col_conga_col [in GeoCoq.Tarski_dev.Ch11_angles]
col_in_angle_out [in GeoCoq.Tarski_dev.Ch11_angles]
col_in_angle [in GeoCoq.Tarski_dev.Ch11_angles]
col_per_perp [in GeoCoq.Tarski_dev.Ch08_orthogonality]
col_col_per_per [in GeoCoq.Tarski_dev.Ch08_orthogonality]
col_out2_col [in GeoCoq.Tarski_dev.Ch06_out_lines]
col_transitivity_2 [in GeoCoq.Tarski_dev.Ch06_out_lines]
col_transitivity_1 [in GeoCoq.Tarski_dev.Ch06_out_lines]
col_incident [in GeoCoq.Meta_theory.Models.tarski_to_hilbert]
col_disjoint_bet [in GeoCoq.Meta_theory.Models.tarski_to_hilbert]
col_upper_dim [in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
col_2_par_projp2_cong [in GeoCoq.Tarski_dev.Annexes.project]
col_par_projp2_eq [in GeoCoq.Tarski_dev.Annexes.project]
col_projp_eq [in GeoCoq.Tarski_dev.Annexes.project]
Col_tagged_Col [in GeoCoq.Tarski_dev.Annexes.Tagged_predicates]
Col_Col_tagged [in GeoCoq.Tarski_dev.Annexes.Tagged_predicates]
col_two_sides_bet [in GeoCoq.Tarski_dev.Ch09_plane]
col_one_side_out [in GeoCoq.Tarski_dev.Ch09_plane]
col_one_side [in GeoCoq.Tarski_dev.Ch09_plane]
col_two_sides [in GeoCoq.Tarski_dev.Ch09_plane]
col_eq [in GeoCoq.Tarski_dev.Ch09_plane]
col_preserves_two_sides [in GeoCoq.Tarski_dev.Ch09_plane]
col_cong_cong [in GeoCoq.Tarski_dev.Annexes.quadrilaterals_inter_dec]
col_cong_mid2 [in GeoCoq.Tarski_dev.Annexes.quadrilaterals]
col_cong_mid1 [in GeoCoq.Tarski_dev.Annexes.quadrilaterals]
col_bet2_cong2 [in GeoCoq.Tarski_dev.Annexes.quadrilaterals]
col_bet2_cong1 [in GeoCoq.Tarski_dev.Annexes.quadrilaterals]
col_cong2_bet4 [in GeoCoq.Tarski_dev.Annexes.quadrilaterals]
col_cong2_bet3 [in GeoCoq.Tarski_dev.Annexes.quadrilaterals]
col_cong2_bet2 [in GeoCoq.Tarski_dev.Annexes.quadrilaterals]
col_cong2_bet1 [in GeoCoq.Tarski_dev.Annexes.quadrilaterals]
col_cong_bet [in GeoCoq.Tarski_dev.Annexes.quadrilaterals]
col_not_plgs [in GeoCoq.Tarski_dev.Annexes.quadrilaterals]
col_cong_mid [in GeoCoq.Tarski_dev.Annexes.quadrilaterals]
col_trisuma__bet [in GeoCoq.Tarski_dev.Annexes.suma]
col_par_par_col [in GeoCoq.Tarski_dev.Ch12_parallel_inter_dec]
col_cong_3_cong_3_eq [in GeoCoq.Tarski_dev.Ch04_col]
col_trivial_3 [in GeoCoq.Tarski_dev.Ch04_col]
col_trivial_2 [in GeoCoq.Tarski_dev.Ch04_col]
col_trivial_1 [in GeoCoq.Tarski_dev.Ch04_col]
Col_perm [in GeoCoq.Tarski_dev.Ch04_col]
Col_cases [in GeoCoq.Tarski_dev.Ch04_col]
col_permutation_5 [in GeoCoq.Tarski_dev.Ch04_col]
col_permutation_4 [in GeoCoq.Tarski_dev.Ch04_col]
col_permutation_3 [in GeoCoq.Tarski_dev.Ch04_col]
col_permutation_2 [in GeoCoq.Tarski_dev.Ch04_col]
col_permutation_1 [in GeoCoq.Tarski_dev.Ch04_col]
col123_124__col234 [in GeoCoq.Tarski_dev.Annexes.midpoint_theorems]
col123_124__col134 [in GeoCoq.Tarski_dev.Annexes.midpoint_theorems]
col123__nos [in GeoCoq.Tarski_dev.Ch09_plane]
col124__nos [in GeoCoq.Tarski_dev.Ch09_plane]
col2_os__os [in GeoCoq.Tarski_dev.Ch09_plane]
col3 [in GeoCoq.Tarski_dev.Ch06_out_lines]
compareListSpec [in GeoCoq.Utils.sets]
compare_spec [in GeoCoq.Utils.sets]
compatibility_of_prod_with_order [in GeoCoq.Tarski_dev.Ch14_order]
compatibility_of_sum_with_order [in GeoCoq.Tarski_dev.Ch14_order]
concyclic_1123 [in GeoCoq.Highschool.concyclic]
concyclic_perm_23 [in GeoCoq.Highschool.concyclic]
concyclic_perm_22 [in GeoCoq.Highschool.concyclic]
concyclic_perm_21 [in GeoCoq.Highschool.concyclic]
concyclic_perm_20 [in GeoCoq.Highschool.concyclic]
concyclic_perm_19 [in GeoCoq.Highschool.concyclic]
concyclic_perm_18 [in GeoCoq.Highschool.concyclic]
concyclic_perm_17 [in GeoCoq.Highschool.concyclic]
concyclic_perm_16 [in GeoCoq.Highschool.concyclic]
concyclic_perm_15 [in GeoCoq.Highschool.concyclic]
concyclic_perm_14 [in GeoCoq.Highschool.concyclic]
concyclic_perm_13 [in GeoCoq.Highschool.concyclic]
concyclic_perm_12 [in GeoCoq.Highschool.concyclic]
concyclic_perm_11 [in GeoCoq.Highschool.concyclic]
concyclic_perm_10 [in GeoCoq.Highschool.concyclic]
concyclic_perm_9 [in GeoCoq.Highschool.concyclic]
concyclic_perm_8 [in GeoCoq.Highschool.concyclic]
concyclic_perm_7 [in GeoCoq.Highschool.concyclic]
concyclic_perm_6 [in GeoCoq.Highschool.concyclic]
concyclic_perm_5 [in GeoCoq.Highschool.concyclic]
concyclic_perm_4 [in GeoCoq.Highschool.concyclic]
concyclic_perm_3 [in GeoCoq.Highschool.concyclic]
concyclic_perm_2 [in GeoCoq.Highschool.concyclic]
concyclic_perm_1 [in GeoCoq.Highschool.concyclic]
concyclic_trans [in GeoCoq.Highschool.concyclic]
concyclic_gen_pseudo_trans [in GeoCoq.Tactics.Coinc.tarski_to_coinc_theory_for_concyclic]
concyclic_gen_1123 [in GeoCoq.Tactics.Coinc.tarski_to_coinc_theory_for_concyclic]
concyclic_gen_2134 [in GeoCoq.Tactics.Coinc.tarski_to_coinc_theory_for_concyclic]
concyclic_gen_2341 [in GeoCoq.Tactics.Coinc.tarski_to_coinc_theory_for_concyclic]
concyclic_not_col_or_eq [in GeoCoq.Highschool.Euler_line]
concyclic_not_col_or_eq_aux [in GeoCoq.Highschool.Euler_line]
concy_3 [in GeoCoq.Tactics.Coinc.tarski_to_coinc_theory_for_concyclic]
concy_trans_1 [in GeoCoq.Tactics.Coinc.tarski_to_coinc_theory_for_concyclic]
concy_bd [in GeoCoq.Tactics.Coinc.tarski_to_coinc_theory_for_concyclic]
concy_perm_2 [in GeoCoq.Tactics.Coinc.tarski_to_coinc_theory_for_concyclic]
concy_perm_1 [in GeoCoq.Tactics.Coinc.tarski_to_coinc_theory_for_concyclic]
congaH_commr [in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
congaH_sym [in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
congaH_existence_congH [in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
conga_per2_os__cong [in GeoCoq.Tarski_dev.Annexes.saccheri]
conga_bet_conga [in GeoCoq.Tarski_dev.Ch15_lengths]
conga_defect__defect [in GeoCoq.Meta_theory.Parallel_postulates.legendre]
conga_distinct [in GeoCoq.Tarski_dev.Ch11_angles]
conga_dec [in GeoCoq.Tarski_dev.Ch11_angles]
conga_sym_equiv [in GeoCoq.Tarski_dev.Ch11_angles]
conga_preserves_gta [in GeoCoq.Tarski_dev.Ch11_angles]
conga_preserves_lta [in GeoCoq.Tarski_dev.Ch11_angles]
conga__lea456123 [in GeoCoq.Tarski_dev.Ch11_angles]
conga__lea [in GeoCoq.Tarski_dev.Ch11_angles]
conga_preserves_in_angle [in GeoCoq.Tarski_dev.Ch11_angles]
conga_ex_cong3 [in GeoCoq.Tarski_dev.Ch11_angles]
conga_line [in GeoCoq.Tarski_dev.Ch11_angles]
conga_comm [in GeoCoq.Tarski_dev.Ch11_angles]
conga_left_comm [in GeoCoq.Tarski_dev.Ch11_angles]
conga_right_comm [in GeoCoq.Tarski_dev.Ch11_angles]
conga_trivial_1 [in GeoCoq.Tarski_dev.Ch11_angles]
conga_pseudo_refl [in GeoCoq.Tarski_dev.Ch11_angles]
conga_trans [in GeoCoq.Tarski_dev.Ch11_angles]
conga_diff56 [in GeoCoq.Tarski_dev.Ch11_angles]
conga_diff45 [in GeoCoq.Tarski_dev.Ch11_angles]
conga_diff2 [in GeoCoq.Tarski_dev.Ch11_angles]
conga_diff1 [in GeoCoq.Tarski_dev.Ch11_angles]
conga_sym [in GeoCoq.Tarski_dev.Ch11_angles]
conga_refl [in GeoCoq.Tarski_dev.Ch11_angles]
conga_preserves_obtuse [in GeoCoq.Tarski_dev.Ch13_1]
conga_to_par_os [in GeoCoq.Tarski_dev.Annexes.quadrilaterals_inter_dec]
conga_to_par_ts [in GeoCoq.Tarski_dev.Annexes.quadrilaterals_inter_dec]
conga_trisuma__trisuma [in GeoCoq.Tarski_dev.Annexes.suma]
conga_isi_nos__nts [in GeoCoq.Tarski_dev.Annexes.suma]
conga2_grada__grada [in GeoCoq.Meta_theory.Parallel_postulates.angle_archimedes]
conga2_isi__isi [in GeoCoq.Tarski_dev.Annexes.suma]
conga3_defect__defect [in GeoCoq.Meta_theory.Parallel_postulates.legendre]
conga3_trisuma__trisuma [in GeoCoq.Tarski_dev.Annexes.suma]
conga3_suma__suma [in GeoCoq.Tarski_dev.Annexes.suma]
congH_colH_betH [in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
congH_perml [in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
congH_perms [in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
congH_permlr [in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
congH_sym [in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
congH_refl [in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
congH_perm [in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
cong_stability_eq_stability [in GeoCoq.Meta_theory.Models.tarski_to_beeson]
cong_stability [in GeoCoq.Meta_theory.Models.tarski_to_beeson]
cong_le_le [in GeoCoq.Highschool.orientation]
cong_identity_inv [in GeoCoq.Highschool.orientation]
cong__le [in GeoCoq.Tarski_dev.Ch05_bet_le]
Cong_dec [in GeoCoq.Tarski_dev.Ch05_bet_le]
cong_dec_eq_dec_b [in GeoCoq.Tarski_dev.Ch03_bet]
cong_conga_perp [in GeoCoq.Tarski_dev.Ch12_parallel]
cong_trivial_identityT [in GeoCoq.Meta_theory.Models.independent_tarski_to_tarski]
cong_inner_transitivityT [in GeoCoq.Meta_theory.Models.independent_tarski_to_tarski]
cong_inner_transitivity [in GeoCoq.Meta_theory.Counter_models.counter_model_segment_construction]
cong_identity [in GeoCoq.Meta_theory.Counter_models.counter_model_segment_construction]
cong_pseudo_reflexivity [in GeoCoq.Meta_theory.Counter_models.counter_model_segment_construction]
cong_mid__suma [in GeoCoq.Tarski_dev.Annexes.saccheri]
cong_sac__per [in GeoCoq.Tarski_dev.Annexes.saccheri]
Cong_AM_Cong [in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
cong_pseudo_reflexivity [in GeoCoq.Meta_theory.Models.tarski_to_makarios]
cong_left_commutativity [in GeoCoq.Meta_theory.Models.tarski_to_makarios]
cong_symmetry [in GeoCoq.Meta_theory.Models.tarski_to_makarios]
cong_reflexivity [in GeoCoq.Meta_theory.Models.tarski_to_makarios]
Cong_perm [in GeoCoq.Tarski_dev.Ch02_cong]
Cong_cases [in GeoCoq.Tarski_dev.Ch02_cong]
cong_3_swap_2 [in GeoCoq.Tarski_dev.Ch02_cong]
cong_3_swap [in GeoCoq.Tarski_dev.Ch02_cong]
cong_3_sym [in GeoCoq.Tarski_dev.Ch02_cong]
cong_diff_4 [in GeoCoq.Tarski_dev.Ch02_cong]
cong_diff_3 [in GeoCoq.Tarski_dev.Ch02_cong]
cong_diff_2 [in GeoCoq.Tarski_dev.Ch02_cong]
cong_diff [in GeoCoq.Tarski_dev.Ch02_cong]
cong_commutativity [in GeoCoq.Tarski_dev.Ch02_cong]
cong_reverse_identity [in GeoCoq.Tarski_dev.Ch02_cong]
cong_trivial_identity [in GeoCoq.Tarski_dev.Ch02_cong]
cong_4321 [in GeoCoq.Tarski_dev.Ch02_cong]
cong_4312 [in GeoCoq.Tarski_dev.Ch02_cong]
cong_3421 [in GeoCoq.Tarski_dev.Ch02_cong]
cong_right_commutativity [in GeoCoq.Tarski_dev.Ch02_cong]
cong_left_commutativity [in GeoCoq.Tarski_dev.Ch02_cong]
cong_transitivity [in GeoCoq.Tarski_dev.Ch02_cong]
cong_symmetry [in GeoCoq.Tarski_dev.Ch02_cong]
cong_reflexivity [in GeoCoq.Tarski_dev.Ch02_cong]
cong_mid2__cong13 [in GeoCoq.Tarski_dev.Ch07_midpoint]
cong_cong_half_2 [in GeoCoq.Tarski_dev.Ch07_midpoint]
cong_cong_half_1 [in GeoCoq.Tarski_dev.Ch07_midpoint]
cong_col_mid [in GeoCoq.Tarski_dev.Ch07_midpoint]
cong_perp_conga [in GeoCoq.Tarski_dev.Ch13_1]
cong_preserves_bet [in GeoCoq.Tarski_dev.Ch06_out_lines]
cong_3_3_cong_5 [in GeoCoq.Tarski_dev.Ch16_coordinates]
cong_3_2_cong_4 [in GeoCoq.Tarski_dev.Ch16_coordinates]
cong_permT [in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
cong_transitivity [in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
cong_preserves_bet [in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
cong_preserves_col_stronger [in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
cong_preserves_col [in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
cong_trans [in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
cong_sym [in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
cong_distincts [in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
cong_inner_transitivity [in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
cong_identity [in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
cong_aux_6 [in GeoCoq.Meta_theory.Counter_models.counter_model_bet_identity]
cong_aux_5 [in GeoCoq.Meta_theory.Counter_models.counter_model_bet_identity]
cong_aux_4 [in GeoCoq.Meta_theory.Counter_models.counter_model_bet_identity]
cong_aux_3 [in GeoCoq.Meta_theory.Counter_models.counter_model_bet_identity]
cong_aux_2 [in GeoCoq.Meta_theory.Counter_models.counter_model_bet_identity]
cong_aux [in GeoCoq.Meta_theory.Counter_models.counter_model_bet_identity]
cong_sym [in GeoCoq.Meta_theory.Counter_models.counter_model_bet_identity]
cong_inner_transitivity [in GeoCoq.Meta_theory.Counter_models.counter_model_bet_identity]
cong_identity [in GeoCoq.Meta_theory.Counter_models.counter_model_bet_identity]
cong_pseudo_reflexivity [in GeoCoq.Meta_theory.Counter_models.counter_model_bet_identity]
cong_conga3_cong3 [in GeoCoq.Tarski_dev.Annexes.project]
cong_perp_bisect_col [in GeoCoq.Tarski_dev.Annexes.perp_bisect]
cong_perp_bisect [in GeoCoq.Tarski_dev.Annexes.perp_bisect]
Cong_tagged_Cong [in GeoCoq.Tarski_dev.Annexes.Tagged_predicates]
Cong_Cong_tagged [in GeoCoq.Tarski_dev.Annexes.Tagged_predicates]
cong_dec_eq_dec [in GeoCoq.Meta_theory.Decidability.equivalence_between_decidability_properties_of_basic_relations]
cong_le_le [in GeoCoq.Tarski_dev.Annexes.quadrilaterals]
cong_identity_inv [in GeoCoq.Tarski_dev.Annexes.quadrilaterals]
cong_sum [in GeoCoq.Tarski_dev.Ch14_sum]
cong2_lt__lt [in GeoCoq.Tarski_dev.Ch05_bet_le]
cong2_sac2__cong [in GeoCoq.Tarski_dev.Annexes.saccheri]
cong2_lam2__conga [in GeoCoq.Tarski_dev.Annexes.saccheri]
cong2_lam2__cong [in GeoCoq.Tarski_dev.Annexes.saccheri]
cong2_conga_cong [in GeoCoq.Tarski_dev.Ch11_angles]
cong3_symmetry [in GeoCoq.Tarski_dev.Ch05_bet_le]
cong3_bet_eq [in GeoCoq.Tarski_dev.Ch04_cong_bet]
cong3_transitivity [in GeoCoq.Tarski_dev.Ch02_cong]
cong3_preserves_out [in GeoCoq.Tarski_dev.Ch11_angles]
cong3_conga2 [in GeoCoq.Tarski_dev.Ch11_angles]
cong3_conga [in GeoCoq.Tarski_dev.Ch11_angles]
cong3_diff2 [in GeoCoq.Tarski_dev.Ch11_angles]
cong3_diff [in GeoCoq.Tarski_dev.Ch11_angles]
cong3_par2_par [in GeoCoq.Tarski_dev.Annexes.quadrilaterals_inter_dec]
cong3_id [in GeoCoq.Tarski_dev.Annexes.quadrilaterals]
consecutive_interior__alternate_interior [in GeoCoq.Meta_theory.Parallel_postulates.consecutive_interior_angles_alternate_interior_angles]
consHdInterpOK [in GeoCoq.Tactics.Coinc.CoincR]
consHdTlTlHd [in GeoCoq.Utils.arity]
consHeadCPHd [in GeoCoq.Utils.arity]
consHeadCPOK [in GeoCoq.Utils.arity]
consHeadCPTl [in GeoCoq.Utils.arity]
consTailCPAbl [in GeoCoq.Utils.arity]
consTailCPLast [in GeoCoq.Utils.arity]
consTailCPOK [in GeoCoq.Utils.arity]
consTailCPTl [in GeoCoq.Utils.arity]
consTailCPTlD [in GeoCoq.Utils.arity]
consTailOK [in GeoCoq.Utils.arity]
consTailPerm [in GeoCoq.Utils.arity]
consTlHdHdTl [in GeoCoq.Utils.arity]
construction_uniquenessT [in GeoCoq.Meta_theory.Models.independent_tarski_to_tarski]
construction_uniqueness [in GeoCoq.Tarski_dev.Ch02_cong]
construction_uniqueness [in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
construct_triangle [in GeoCoq.Highschool.orthocenter]
construct_intersection [in GeoCoq.Highschool.orthocenter]
coordinates_of_point_F [in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
coordinates_of_point_f [in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
coordinates_of_point [in GeoCoq.Tarski_dev.Ch16_coordinates]
coord_exchange_axes [in GeoCoq.Tarski_dev.Ch16_coordinates]
coplanar_pseudo_trans [in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1 [in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4 [in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_3 [in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_3_3 [in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_3_3_3 [in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_3_3_2 [in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_3_3_2_3 [in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_3_3_2_2 [in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_3_3_2_1 [in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_3_3_1 [in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_3_2 [in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_3_2_3 [in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_3_2_3_3 [in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_3_2_3_2 [in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_3_2_3_1 [in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_3_2_2 [in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_3_2_1 [in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_3_2_1_3 [in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_3_2_1_2 [in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_3_2_1_1 [in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_3_1 [in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_3_1_3 [in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_3_1_3_3 [in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_3_1_3_2 [in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_3_1_3_1 [in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_3_1_2 [in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_3_1_1 [in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_3_1_1_3 [in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_3_1_1_2 [in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_3_1_1_1 [in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_2 [in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_2_3 [in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_2_3_3 [in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_2_3_2 [in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_2_3_2_3 [in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_2_3_2_2 [in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_2_3_2_1 [in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_2_3_1 [in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_2_2 [in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_2_2_3 [in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_2_2_3_3 [in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_2_2_3_2 [in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_2_2_3_1 [in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_2_2_2 [in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_2_2_1 [in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_2_2_1_3 [in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_2_2_1_2 [in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_2_2_1_1 [in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_2_1 [in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_2_1_3 [in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_2_1_3_3 [in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_2_1_3_2 [in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_2_1_3_1 [in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_2_1_2 [in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_2_1_2_3 [in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_2_1_2_2 [in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_2_1_2_1 [in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_2_1_1 [in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_2_1_1_3 [in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_2_1_1_2 [in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_2_1_1_1 [in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_1 [in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_1_3 [in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_1_3_3 [in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_1_3_3_3 [in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_1_3_3_2 [in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_1_3_3_1 [in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_1_3_2 [in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_1_3_2_3 [in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_1_3_2_2 [in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_1_3_2_1 [in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_1_3_1 [in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_1_3_1_3 [in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_1_3_1_2 [in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_1_3_1_1 [in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_1_2 [in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_1_2_3 [in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_1_2_2 [in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_1_2_2_3 [in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_1_2_2_2 [in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_1_2_2_1 [in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_1_2_1 [in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_1_1 [in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_1_1_3 [in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_1_1_2 [in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_1_1_2_3 [in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_1_1_2_2 [in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_1_1_2_1 [in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_4_1_1_1 [in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_3 [in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_3_3_3 [in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_3_3_3_3 [in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_3_3_3_3_3 [in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_3_3_3_3_2 [in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_3_3_3_3_1 [in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_3_3_3_2 [in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_3_3_3_2_3 [in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_3_3_3_2_2 [in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_3_3_3_2_1 [in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_3_3_3_1 [in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_3_3_3_1_3 [in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_3_3_3_1_2 [in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_3_3_3_1_1 [in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_3_2_3 [in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_3_2_2 [in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_3_1_3 [in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_3_1_2 [in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_3_1_2_3 [in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_3_1_2_3_3 [in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_3_1_2_3_2 [in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_3_1_2_3_1 [in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_3_1_2_2 [in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_3_1_2_2_3 [in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_3_1_2_2_2 [in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_3_1_2_2_1 [in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_3_1_2_1 [in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_3_1_2_1_3 [in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_3_1_2_1_2 [in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_3_1_2_1_1 [in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_3_1_1 [in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_2 [in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_2_3_3 [in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_2_3_3_2_2 [in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_2_3_3_1_3 [in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_2_3_3_1_2 [in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_2_3_3_1_1 [in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_2_2_3 [in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_2_2_2 [in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_2_2_2_2_2 [in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_2_2_2_1_3 [in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_2_2_2_1_2 [in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_2_2_2_1_1 [in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_2_1_3 [in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_2_1_3_3_3 [in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_2_1_3_2_3 [in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_2_1_3_2_2 [in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_2_1_3_1_3 [in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_2_1_3_1_2 [in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_2_1_3_1_1 [in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_2_1_2 [in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_2_1_1 [in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_2_1_1_2_2 [in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_2_1_1_1_3 [in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_2_1_1_1_2 [in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_2_1_1_1_1 [in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_1 [in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_1_3_3 [in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_1_2_3 [in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_1_2_2 [in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_1_1_3 [in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_1_1_2 [in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trans_1_aux_1_1_1 [in GeoCoq.Tarski_dev.Coplanar_trans]
coplanar_trivial [in GeoCoq.Tarski_dev.Coplanar_perm]
coplanar_perm_23 [in GeoCoq.Tarski_dev.Coplanar_perm]
coplanar_perm_22 [in GeoCoq.Tarski_dev.Coplanar_perm]
coplanar_perm_21 [in GeoCoq.Tarski_dev.Coplanar_perm]
coplanar_perm_20 [in GeoCoq.Tarski_dev.Coplanar_perm]
coplanar_perm_19 [in GeoCoq.Tarski_dev.Coplanar_perm]
coplanar_perm_18 [in GeoCoq.Tarski_dev.Coplanar_perm]
coplanar_perm_17 [in GeoCoq.Tarski_dev.Coplanar_perm]
coplanar_perm_16 [in GeoCoq.Tarski_dev.Coplanar_perm]
coplanar_perm_15 [in GeoCoq.Tarski_dev.Coplanar_perm]
coplanar_perm_14 [in GeoCoq.Tarski_dev.Coplanar_perm]
coplanar_perm_13 [in GeoCoq.Tarski_dev.Coplanar_perm]
coplanar_perm_12 [in GeoCoq.Tarski_dev.Coplanar_perm]
coplanar_perm_11 [in GeoCoq.Tarski_dev.Coplanar_perm]
coplanar_perm_10 [in GeoCoq.Tarski_dev.Coplanar_perm]
coplanar_perm_9 [in GeoCoq.Tarski_dev.Coplanar_perm]
coplanar_perm_8 [in GeoCoq.Tarski_dev.Coplanar_perm]
coplanar_perm_7 [in GeoCoq.Tarski_dev.Coplanar_perm]
coplanar_perm_6 [in GeoCoq.Tarski_dev.Coplanar_perm]
coplanar_perm_5 [in GeoCoq.Tarski_dev.Coplanar_perm]
coplanar_perm_4 [in GeoCoq.Tarski_dev.Coplanar_perm]
coplanar_perm_3 [in GeoCoq.Tarski_dev.Coplanar_perm]
coplanar_perm_2 [in GeoCoq.Tarski_dev.Coplanar_perm]
coplanar_perm_1 [in GeoCoq.Tarski_dev.Coplanar_perm]
cop_per_per_col [in GeoCoq.Meta_theory.Dimension_axioms.upper_dim]
cop_3 [in GeoCoq.Tactics.Coinc.tarski_to_coinc_theory_for_cop]
cop_bd [in GeoCoq.Tactics.Coinc.tarski_to_coinc_theory_for_cop]
cop_perm_2 [in GeoCoq.Tactics.Coinc.tarski_to_coinc_theory_for_cop]
cop_perm_1 [in GeoCoq.Tactics.Coinc.tarski_to_coinc_theory_for_cop]
co_side [in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
CPCPL [in GeoCoq.Utils.arity]
CPLCP [in GeoCoq.Utils.arity]
CPLHd [in GeoCoq.Utils.arity]
CPLHdTlOK [in GeoCoq.Utils.arity]
CPLOCPTlOK [in GeoCoq.Utils.sets]
CPLOK [in GeoCoq.Utils.arity]
CPLRec [in GeoCoq.Utils.arity]
CPToListOK [in GeoCoq.Utils.arity]
CPToListTl1 [in GeoCoq.Utils.arity]
CPToListTl2 [in GeoCoq.Utils.arity]
CPToSSHdTl [in GeoCoq.Tactics.Coinc.CoincR]
CPToSSOK [in GeoCoq.Tactics.Coinc.CoincR]
CPToSSOKAux [in GeoCoq.Tactics.Coinc.CoincR]
CP_ind [in GeoCoq.Utils.arity]
Cs_not_Col [in GeoCoq.Tarski_dev.Ch16_coordinates]
CTcol_trivial_2 [in GeoCoq.Tactics.Coinc.ColR]
CTcol_trivial_1 [in GeoCoq.Tactics.Coinc.ColR]
CTcol_permutation_4 [in GeoCoq.Tactics.Coinc.ColR]
CTcol_permutation_3 [in GeoCoq.Tactics.Coinc.ColR]
CTcol_permutation_2 [in GeoCoq.Tactics.Coinc.ColR]
CTcol_permutation_5 [in GeoCoq.Tactics.Coinc.ColR]
cut_two_sides [in GeoCoq.Meta_theory.Models.tarski_to_hilbert]
cut_same_side_cut [in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
cut_distinct [in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
cut_exists [in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
cut_comm [in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
cut'_comm [in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
cut2_not_cut [in GeoCoq.Meta_theory.Models.hilbert_to_tarski]


D

defect_ncol_out__rah [in GeoCoq.Meta_theory.Parallel_postulates.legendre]
defect_perm_132 [in GeoCoq.Meta_theory.Parallel_postulates.legendre]
defect_perm_213 [in GeoCoq.Meta_theory.Parallel_postulates.legendre]
defect_perm_321 [in GeoCoq.Meta_theory.Parallel_postulates.legendre]
defect_perm_312 [in GeoCoq.Meta_theory.Parallel_postulates.legendre]
defect_perm_231 [in GeoCoq.Meta_theory.Parallel_postulates.legendre]
defect_distincts [in GeoCoq.Meta_theory.Parallel_postulates.legendre]
defect2__conga [in GeoCoq.Meta_theory.Parallel_postulates.legendre]
degenerated_rect_eq [in GeoCoq.Tarski_dev.Annexes.quadrilaterals_inter_dec]
Diff_Col_ColB [in GeoCoq.Meta_theory.Models.tarski_to_beeson]
diff_perm_2 [in GeoCoq.Tactics.Coinc.tarski_to_coinc_theory_for_col]
diff_perm_1 [in GeoCoq.Tactics.Coinc.tarski_to_coinc_theory_for_col]
diff_f [in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
diff_col [in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
diff_not_col_col_par4_mid [in GeoCoq.Highschool.orthocenter]
diff_2_le_le [in GeoCoq.Tarski_dev.Ch14_order]
diff_pos_diff_neg [in GeoCoq.Tarski_dev.Ch14_order]
diff_per_diff [in GeoCoq.Tarski_dev.Ch08_orthogonality]
diff_2_prod [in GeoCoq.Tarski_dev.Ch14_prod]
diff_of_squares [in GeoCoq.Tarski_dev.Ch14_prod]
Diff_perm [in GeoCoq.Tarski_dev.Annexes.Tagged_predicates]
Diff_tagged_Diff [in GeoCoq.Tarski_dev.Annexes.Tagged_predicates]
Diff_Diff_tagged [in GeoCoq.Tarski_dev.Annexes.Tagged_predicates]
diff_col_ex3 [in GeoCoq.Tarski_dev.Ch09_plane]
diff_bet_ex3 [in GeoCoq.Tarski_dev.Ch09_plane]
diff_col_ex [in GeoCoq.Tarski_dev.Ch09_plane]
diff_to_plg [in GeoCoq.Tarski_dev.Ch14_sum]
diff_stable [in GeoCoq.Tarski_dev.Ch14_sum]
diff_opp [in GeoCoq.Tarski_dev.Ch14_sum]
diff_sum [in GeoCoq.Tarski_dev.Ch14_sum]
diff_null_eq [in GeoCoq.Tarski_dev.Ch14_sum]
diff_uniquenessB [in GeoCoq.Tarski_dev.Ch14_sum]
diff_uniquenessA [in GeoCoq.Tarski_dev.Ch14_sum]
diff_O_A_opp [in GeoCoq.Tarski_dev.Ch14_sum]
diff_O_A [in GeoCoq.Tarski_dev.Ch14_sum]
diff_A_O [in GeoCoq.Tarski_dev.Ch14_sum]
diff_uniqueness [in GeoCoq.Tarski_dev.Ch14_sum]
diff_exists [in GeoCoq.Tarski_dev.Ch14_sum]
diff_null [in GeoCoq.Tarski_dev.Ch14_sum]
diff_ar2 [in GeoCoq.Tarski_dev.Ch14_sum]
distinct [in GeoCoq.Tarski_dev.Ch08_orthogonality]
distinct [in GeoCoq.Tarski_dev.Ch09_plane]
distr_l_diff [in GeoCoq.Tarski_dev.Ch14_prod]
distr_r [in GeoCoq.Tarski_dev.Ch14_prod]
distr_l [in GeoCoq.Tarski_dev.Ch14_prod]
div_f [in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
div_col [in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
div_uniqueness [in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
div_exists [in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
double_not_null_not_nul [in GeoCoq.Tarski_dev.Ch14_sum]
double_null_null [in GeoCoq.Tarski_dev.Ch14_sum]


E

eqA_preserves_anga [in GeoCoq.Tarski_dev.Ch13_3_angles]
eqA_preserves_ang [in GeoCoq.Tarski_dev.Ch13_3_angles]
eqbListEqList [in GeoCoq.Utils.sets]
eqbST_eqST [in GeoCoq.Utils.sets]
eqListOK [in GeoCoq.Utils.sets]
eqListRefl [in GeoCoq.Utils.sets]
eqListSortOCP [in GeoCoq.Utils.sets]
eqListSym [in GeoCoq.Utils.sets]
eqListTrans [in GeoCoq.Utils.sets]
eql_lcos_null [in GeoCoq.Tarski_dev.Ch13_4_cos]
eqo_refl [in GeoCoq.Highschool.orientation]
eqo_one_side [in GeoCoq.Highschool.orientation]
eqo_eq_o [in GeoCoq.Highschool.orientation]
eqST_dec [in GeoCoq.Utils.sets]
equality_foot_out_out [in GeoCoq.Highschool.bisector]
equilateral_strict_conga_3 [in GeoCoq.Highschool.triangles]
equilateral_strict_conga_2 [in GeoCoq.Highschool.triangles]
equilateral_strict_conga_1 [in GeoCoq.Highschool.triangles]
equilateral_strict__not_col [in GeoCoq.Highschool.triangles]
equilateral_strict_swap_5 [in GeoCoq.Highschool.triangles]
equilateral_strict_swap_4 [in GeoCoq.Highschool.triangles]
equilateral_strict_swap_3 [in GeoCoq.Highschool.triangles]
equilateral_strict_swap_2 [in GeoCoq.Highschool.triangles]
equilateral_strict_swap_1 [in GeoCoq.Highschool.triangles]
equilateral_strict_neq [in GeoCoq.Highschool.triangles]
equilateral_isosceles_3 [in GeoCoq.Highschool.triangles]
equilateral_isosceles_2 [in GeoCoq.Highschool.triangles]
equilateral_isosceles_1 [in GeoCoq.Highschool.triangles]
equilateral_swap_rot [in GeoCoq.Highschool.triangles]
equilateral_swap_2 [in GeoCoq.Highschool.triangles]
equilateral_rot_2 [in GeoCoq.Highschool.triangles]
equilateral_swap [in GeoCoq.Highschool.triangles]
equilateral_rot [in GeoCoq.Highschool.triangles]
equilateral_cong [in GeoCoq.Highschool.triangles]
equilateral_strict_equilateral [in GeoCoq.Highschool.triangles]
equivalence_of_aristotle_greenberg_and_decidability_of_intersection [in GeoCoq.Meta_theory.Parallel_postulates.Euclid]
equivalence_between_decidability_properties_of_basic_relations [in GeoCoq.Meta_theory.Decidability.equivalence_between_decidability_properties_of_basic_relations]
equivalent_parallel_postulates_without_any_continuity_bis [in GeoCoq.Meta_theory.Parallel_postulates.Euclid]
equivalent_parallel_postulates_assuming_greenberg_s_postulate [in GeoCoq.Meta_theory.Parallel_postulates.Euclid]
equivalent_parallel_postulates_without_decidability_of_intersection_of_lines_bis [in GeoCoq.Meta_theory.Parallel_postulates.Euclid]
equivalent_parallel_postulates_with_decidability_of_intersection_of_lines [in GeoCoq.Meta_theory.Parallel_postulates.Euclid]
equivalent_parallel_postulates_without_any_continuity [in GeoCoq.Meta_theory.Parallel_postulates.Euclid]
equivalent_parallel_postulates_without_decidability_of_intersection_of_lines [in GeoCoq.Meta_theory.Parallel_postulates.Euclid]
eqv_cong [in GeoCoq.Tarski_dev.Annexes.project]
eqv_eq_project [in GeoCoq.Tarski_dev.Annexes.project]
eqv_project_eq_eq [in GeoCoq.Tarski_dev.Annexes.project]
eqv_mid [in GeoCoq.Tarski_dev.Annexes.vectors]
eqv_sum [in GeoCoq.Tarski_dev.Annexes.vectors]
eqv_opp_null [in GeoCoq.Tarski_dev.Annexes.vectors]
eqv_par [in GeoCoq.Tarski_dev.Annexes.vectors]
eqv_permut [in GeoCoq.Tarski_dev.Annexes.vectors]
eqv_trivial [in GeoCoq.Tarski_dev.Annexes.vectors]
eqv_comm [in GeoCoq.Tarski_dev.Annexes.vectors]
eqv_trans [in GeoCoq.Tarski_dev.Annexes.vectors]
eqv_sym [in GeoCoq.Tarski_dev.Annexes.vectors]
eqv_refl [in GeoCoq.Tarski_dev.Annexes.vectors]
eq_eq_tagged [in GeoCoq.Tactics.Coinc.ColR]
eq_dec_points_from_classic [in GeoCoq.Meta_theory.Models.tarski_to_beeson]
eq_dec [in GeoCoq.Meta_theory.Models.tarski_to_beeson]
eq_o_refl [in GeoCoq.Highschool.orientation]
eq_o_one_side [in GeoCoq.Highschool.orientation]
eq_o_eqo [in GeoCoq.Highschool.orientation]
eq_dec_F [in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
eq_dec_points [in GeoCoq.Tarski_dev.Ch02_cong]
eq_conga_out [in GeoCoq.Tarski_dev.Ch11_angles]
eq_incident [in GeoCoq.Meta_theory.Models.tarski_to_hilbert]
eq_symmetry [in GeoCoq.Meta_theory.Models.tarski_to_hilbert]
eq_reflexivity [in GeoCoq.Meta_theory.Models.tarski_to_hilbert]
eq_transitivity [in GeoCoq.Meta_theory.Models.tarski_to_hilbert]
eq_points_coordinates [in GeoCoq.Tarski_dev.Ch16_coordinates]
eq_squares_eq_or_opp [in GeoCoq.Tarski_dev.Ch14_prod]
eq_dec_bet_dec [in GeoCoq.Meta_theory.Decidability.equivalence_between_decidability_properties_of_basic_relations]
eq_dec_implies_between_cong_3 [in GeoCoq.Meta_theory.Decidability.equivalence_between_decidability_properties_of_basic_relations]
eq_dec_cong_dec [in GeoCoq.Meta_theory.Decidability.equivalence_between_decidability_properties_of_basic_relations]
eq_dec_implies_between_cong [in GeoCoq.Meta_theory.Decidability.equivalence_between_decidability_properties_of_basic_relations]
eq_dec_implies_segment_construction_2 [in GeoCoq.Meta_theory.Decidability.equivalence_between_decidability_properties_of_basic_relations]
eq_dec_implies_l5_2 [in GeoCoq.Meta_theory.Decidability.equivalence_between_decidability_properties_of_basic_relations]
eq_dec_implies_l5_1 [in GeoCoq.Meta_theory.Decidability.equivalence_between_decidability_properties_of_basic_relations]
eq_dec_implies_l4_17 [in GeoCoq.Meta_theory.Decidability.equivalence_between_decidability_properties_of_basic_relations]
eq_dec_implies_l4_16 [in GeoCoq.Meta_theory.Decidability.equivalence_between_decidability_properties_of_basic_relations]
eq_dec_implies_l4_6 [in GeoCoq.Meta_theory.Decidability.equivalence_between_decidability_properties_of_basic_relations]
eq_dec_implies_l4_5 [in GeoCoq.Meta_theory.Decidability.equivalence_between_decidability_properties_of_basic_relations]
eq_dec_implies_l4_2 [in GeoCoq.Meta_theory.Decidability.equivalence_between_decidability_properties_of_basic_relations]
eq_dec_implies_point_construction_different [in GeoCoq.Meta_theory.Decidability.equivalence_between_decidability_properties_of_basic_relations]
eq_dec_implies_two_distinct_points [in GeoCoq.Meta_theory.Decidability.equivalence_between_decidability_properties_of_basic_relations]
eq_dec_implies_between_exchange4 [in GeoCoq.Meta_theory.Decidability.equivalence_between_decidability_properties_of_basic_relations]
eq_dec_implies_outer_transitivity_between2 [in GeoCoq.Meta_theory.Decidability.equivalence_between_decidability_properties_of_basic_relations]
eq_dec_implies_construction_uniqueness [in GeoCoq.Meta_theory.Decidability.equivalence_between_decidability_properties_of_basic_relations]
eq_dec_implies_l2_11 [in GeoCoq.Meta_theory.Decidability.equivalence_between_decidability_properties_of_basic_relations]
euclid [in GeoCoq.Meta_theory.Counter_models.counter_model_segment_construction]
euclid [in GeoCoq.Meta_theory.Counter_models.counter_model_bet_identity]
euclid_5__original_euclid [in GeoCoq.Meta_theory.Parallel_postulates.euclid_5_original_euclid]
Euler_line [in GeoCoq.Highschool.Euler_line]
Euler_line_special_case [in GeoCoq.Highschool.Euler_line]
existential_triangle__rah [in GeoCoq.Meta_theory.Parallel_postulates.existential_triangle_rah]
existential_saccheri__rah [in GeoCoq.Meta_theory.Parallel_postulates.existential_saccheri_rah]
existential_inverse_projection_postulate__legendre_s_postulate [in GeoCoq.Meta_theory.Parallel_postulates.existential_inverse_projection_postulate_legendre_s_postulate]
existential_playfair__rah [in GeoCoq.Meta_theory.Parallel_postulates.existential_playfair_rah]
exists_witness_ok [in GeoCoq.Tactics.Coinc.ColR]
exists_equilateral_triangle [in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
exists_Cong_Per [in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
exists_witness_ok [in GeoCoq.Tactics.Coinc.CoincR]
exists_not_incident [in GeoCoq.Meta_theory.Models.tarski_to_hilbert]
exists_coord [in GeoCoq.Tarski_dev.Ch16_coordinates]
exists_projp [in GeoCoq.Tarski_dev.Ch16_coordinates]
exists_grid [in GeoCoq.Tarski_dev.Ch16_coordinates]
exists_circumcenter [in GeoCoq.Highschool.circumcenter]
ex_anga [in GeoCoq.Tarski_dev.Ch13_3_angles]
ex_eqaa [in GeoCoq.Tarski_dev.Ch13_3_angles]
ex_points_anga [in GeoCoq.Tarski_dev.Ch13_3_angles]
ex_ang [in GeoCoq.Tarski_dev.Ch13_3_angles]
ex_eqa [in GeoCoq.Tarski_dev.Ch13_3_angles]
ex_points_ang [in GeoCoq.Tarski_dev.Ch13_3_angles]
ex_col1 [in GeoCoq.Highschool.orientation]
ex_col [in GeoCoq.Highschool.orientation]
ex_sym1 [in GeoCoq.Tarski_dev.Ch10_line_reflexivity]
ex_sym [in GeoCoq.Tarski_dev.Ch10_line_reflexivity]
ex_saccheri [in GeoCoq.Tarski_dev.Annexes.saccheri]
ex_defect [in GeoCoq.Meta_theory.Parallel_postulates.legendre]
ex_conga_ts [in GeoCoq.Tarski_dev.Ch11_angles]
ex_per_cong [in GeoCoq.Tarski_dev.Ch11_angles]
ex_col2 [in GeoCoq.Tarski_dev.Ch08_orthogonality]
ex_eqL [in GeoCoq.Tarski_dev.Ch13_2_length]
ex_lg [in GeoCoq.Tarski_dev.Ch13_2_length]
ex_eql [in GeoCoq.Tarski_dev.Ch13_2_length]
ex_points_lg_not_col [in GeoCoq.Tarski_dev.Ch13_2_length]
ex_point_lg_bet [in GeoCoq.Tarski_dev.Ch13_2_length]
ex_point_lg_out [in GeoCoq.Tarski_dev.Ch13_2_length]
ex_point_lg [in GeoCoq.Tarski_dev.Ch13_2_length]
ex_points_lg [in GeoCoq.Tarski_dev.Ch13_2_length]
ex_col3 [in GeoCoq.Tarski_dev.Annexes.quadrilaterals]
ex_trisuma [in GeoCoq.Tarski_dev.Annexes.suma]
ex_suma [in GeoCoq.Tarski_dev.Annexes.suma]


F

fieldF [in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
field_prop_1 [in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
field_prop_zero [in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
field_prop [in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
five_segment [in GeoCoq.Meta_theory.Models.tarski_to_beeson]
five_segment_B [in GeoCoq.Meta_theory.Models.tarski_to_beeson]
five_segment [in GeoCoq.Meta_theory.Counter_models.counter_model_segment_construction]
five_segment [in GeoCoq.Meta_theory.Models.tarski_to_makarios]
five_segment' [in GeoCoq.Meta_theory.Models.tarski_to_makarios]
five_segment_with_def [in GeoCoq.Tarski_dev.Ch02_cong]
five_segment [in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
five_segment [in GeoCoq.Meta_theory.Counter_models.counter_model_bet_identity]
fixLastCPOK [in GeoCoq.Utils.arity]
flat_ang [in GeoCoq.Tarski_dev.Ch13_3_angles]
flat_not_acute [in GeoCoq.Tarski_dev.Ch13_4_cos]
flat_all_lea [in GeoCoq.Tarski_dev.Ch13_1]
Fmult_integral [in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
fourth_point [in GeoCoq.Tarski_dev.Ch05_bet_le]


G

gea_total [in GeoCoq.Tarski_dev.Ch11_angles]
gea_dec [in GeoCoq.Tarski_dev.Ch11_angles]
gea_distincts [in GeoCoq.Tarski_dev.Ch11_angles]
ge_comm [in GeoCoq.Tarski_dev.Ch05_bet_le]
ge_right_comm [in GeoCoq.Tarski_dev.Ch05_bet_le]
ge_left_comm [in GeoCoq.Tarski_dev.Ch05_bet_le]
gradaexp_destruction_aux [in GeoCoq.Meta_theory.Parallel_postulates.angle_archimedes]
gradaexp__grada [in GeoCoq.Meta_theory.Parallel_postulates.angle_archimedes]
grada_out__out [in GeoCoq.Meta_theory.Parallel_postulates.angle_archimedes]
grada__lea [in GeoCoq.Meta_theory.Parallel_postulates.angle_archimedes]
grada_distincts [in GeoCoq.Meta_theory.Parallel_postulates.angle_archimedes]
grada2_isi_suma__grada [in GeoCoq.Meta_theory.Parallel_postulates.angle_archimedes]
gradexp_le__reach [in GeoCoq.Meta_theory.Parallel_postulates.archimedes]
gradexp__grad [in GeoCoq.Meta_theory.Parallel_postulates.archimedes]
gradexp2__gradexp456 [in GeoCoq.Meta_theory.Parallel_postulates.archimedes]
gradexp2__gradexp123 [in GeoCoq.Meta_theory.Parallel_postulates.archimedes]
grad__ex_gradexp_le [in GeoCoq.Meta_theory.Parallel_postulates.archimedes]
grad_sum [in GeoCoq.Meta_theory.Parallel_postulates.archimedes]
grad__le [in GeoCoq.Meta_theory.Parallel_postulates.archimedes]
grad_neq__neq12 [in GeoCoq.Meta_theory.Parallel_postulates.archimedes]
grad_neq__neq13 [in GeoCoq.Meta_theory.Parallel_postulates.archimedes]
grad__bet [in GeoCoq.Meta_theory.Parallel_postulates.archimedes]
grad112__eq [in GeoCoq.Meta_theory.Parallel_postulates.archimedes]
grad121__eq [in GeoCoq.Meta_theory.Parallel_postulates.archimedes]
grad2__grad456 [in GeoCoq.Meta_theory.Parallel_postulates.archimedes]
grad2__grad123 [in GeoCoq.Meta_theory.Parallel_postulates.archimedes]
gravity_center_change_triangle [in GeoCoq.Highschool.Euler_line]
grid_exchange_axes [in GeoCoq.Tarski_dev.Ch16_coordinates]
grid_not_par [in GeoCoq.Tarski_dev.Ch14_sum]
gta_dec [in GeoCoq.Tarski_dev.Ch11_angles]
gta_distincts [in GeoCoq.Tarski_dev.Ch11_angles]
gta_trans [in GeoCoq.Tarski_dev.Ch11_angles]
gta_to_lta [in GeoCoq.Tarski_dev.Ch13_1]
gt_comm [in GeoCoq.Tarski_dev.Ch05_bet_le]
gt_right_comm [in GeoCoq.Tarski_dev.Ch05_bet_le]
gt_left_comm [in GeoCoq.Tarski_dev.Ch05_bet_le]
g2_16 [in GeoCoq.Meta_theory.Models.independent_tarski_to_tarski]
g2_15 [in GeoCoq.Meta_theory.Models.independent_tarski_to_tarski]
g2_14 [in GeoCoq.Meta_theory.Models.independent_tarski_to_tarski]
g2_13 [in GeoCoq.Meta_theory.Models.independent_tarski_to_tarski]
g2_12 [in GeoCoq.Meta_theory.Models.independent_tarski_to_tarski]
g2_11 [in GeoCoq.Meta_theory.Models.independent_tarski_to_tarski]
g2_10 [in GeoCoq.Meta_theory.Models.independent_tarski_to_tarski]
g2_9 [in GeoCoq.Meta_theory.Models.independent_tarski_to_tarski]
g2_8 [in GeoCoq.Meta_theory.Models.independent_tarski_to_tarski]
g2_7 [in GeoCoq.Meta_theory.Models.independent_tarski_to_tarski]
g2_6 [in GeoCoq.Meta_theory.Models.independent_tarski_to_tarski]
g2_5 [in GeoCoq.Meta_theory.Models.independent_tarski_to_tarski]
g2_4 [in GeoCoq.Meta_theory.Models.independent_tarski_to_tarski]
g2_3 [in GeoCoq.Meta_theory.Models.independent_tarski_to_tarski]
g2_2 [in GeoCoq.Meta_theory.Models.independent_tarski_to_tarski]
g2_1 [in GeoCoq.Meta_theory.Models.independent_tarski_to_tarski]


H

half_plgs [in GeoCoq.Tarski_dev.Annexes.quadrilaterals_inter_dec]
hilbert_s_version_of_pasch_aux [in GeoCoq.Tarski_dev.Ch11_angles]
hilbert_s_version_of_pasch [in GeoCoq.Meta_theory.Parallel_postulates.midpoint_playfair]


I

identify_lines_ok [in GeoCoq.Tactics.Coinc.ColR]
identify_varieties_ok [in GeoCoq.Tactics.Coinc.CoincR]
image_col [in GeoCoq.Tarski_dev.Ch10_line_reflexivity]
image_in_col0 [in GeoCoq.Tarski_dev.Ch10_line_reflexivity]
image_image_in [in GeoCoq.Tarski_dev.Ch10_line_reflexivity]
image_in_gen_is_image [in GeoCoq.Tarski_dev.Ch10_line_reflexivity]
image_in_is_image_spec [in GeoCoq.Tarski_dev.Ch10_line_reflexivity]
image_id [in GeoCoq.Tarski_dev.Ch10_line_reflexivity]
image_preserves_out [in GeoCoq.Tarski_dev.Ch15_lengths]
image_preserves_col [in GeoCoq.Tarski_dev.Ch15_lengths]
image_preserves_bet1 [in GeoCoq.Tarski_dev.Ch15_lengths]
image_cong_col [in GeoCoq.Tarski_dev.Ch10_line_reflexivity_2D]
image_preserves_per [in GeoCoq.Tarski_dev.Ch10_line_reflexivity_2D]
image_preserves_midpoint [in GeoCoq.Tarski_dev.Ch10_line_reflexivity_2D]
image_gen_preserves_bet [in GeoCoq.Tarski_dev.Ch10_line_reflexivity_2D]
image_preserves_bet [in GeoCoq.Tarski_dev.Ch10_line_reflexivity_2D]
image_in_col [in GeoCoq.Tarski_dev.Ch10_line_reflexivity_2D]
impossible_case_8 [in GeoCoq.Meta_theory.Parallel_postulates.SPP_tarski]
impossible_case_7 [in GeoCoq.Meta_theory.Parallel_postulates.SPP_tarski]
impossible_case_6 [in GeoCoq.Meta_theory.Parallel_postulates.SPP_tarski]
impossible_case_5 [in GeoCoq.Meta_theory.Parallel_postulates.SPP_tarski]
impossible_two_sides_not_col [in GeoCoq.Meta_theory.Parallel_postulates.TCP_tarski]
impossible_case_4 [in GeoCoq.Meta_theory.Parallel_postulates.TCP_tarski]
impossible_case_4_2 [in GeoCoq.Meta_theory.Parallel_postulates.TCP_tarski]
impossible_case_4_1 [in GeoCoq.Meta_theory.Parallel_postulates.TCP_tarski]
impossible_case_3 [in GeoCoq.Meta_theory.Parallel_postulates.TCP_tarski]
impossible_case_2 [in GeoCoq.Meta_theory.Parallel_postulates.TCP_tarski]
impossible_case_1 [in GeoCoq.Meta_theory.Parallel_postulates.TCP_tarski]
inangle_dec [in GeoCoq.Tarski_dev.Ch11_angles]
inangle_one_side2 [in GeoCoq.Tarski_dev.Ch13_1]
inangle_one_side [in GeoCoq.Tarski_dev.Ch13_1]
inangle__isi [in GeoCoq.Tarski_dev.Annexes.suma]
inangle__suma [in GeoCoq.Tarski_dev.Annexes.suma]
incenter_dec [in GeoCoq.Highschool.incenter]
incenter_permut321 [in GeoCoq.Highschool.incenter]
incenter_permut312 [in GeoCoq.Highschool.incenter]
incenter_permut231 [in GeoCoq.Highschool.incenter]
incenter_permut213 [in GeoCoq.Highschool.incenter]
incenter_permut132 [in GeoCoq.Highschool.incenter]
incenter_exists [in GeoCoq.Highschool.incenter]
incident_col [in GeoCoq.Meta_theory.Models.tarski_to_hilbert]
incident_eq [in GeoCoq.Meta_theory.Models.tarski_to_hilbert]
Incid_line [in GeoCoq.Meta_theory.Models.tarski_to_hilbert]
Incid_not_Incid__not_colH [in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
InCPOCP [in GeoCoq.Utils.sets]
InCPOK [in GeoCoq.Utils.arity]
inner_pasch_B [in GeoCoq.Meta_theory.Models.tarski_to_beeson]
inner_paschT [in GeoCoq.Meta_theory.Models.independent_tarski_to_tarski]
inner_pasch [in GeoCoq.Meta_theory.Counter_models.counter_model_segment_construction]
inner_pasch_aux [in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
inner_pasch [in GeoCoq.Meta_theory.Counter_models.counter_model_bet_identity]
InNth [in GeoCoq.Utils.arity]
interp_CPOK [in GeoCoq.Tactics.Coinc.CoincR]
interp_CPTlOK [in GeoCoq.Tactics.Coinc.CoincR]
interp_CPHdOK [in GeoCoq.Tactics.Coinc.CoincR]
intersection_two_medians_exist_unique [in GeoCoq.Highschool.gravityCenter]
intersection_two_medians_exist [in GeoCoq.Highschool.gravityCenter]
inter_comm [in GeoCoq.Tarski_dev.Ch12_parallel]
inter_right_comm [in GeoCoq.Tarski_dev.Ch12_parallel]
inter_left_comm [in GeoCoq.Tarski_dev.Ch12_parallel]
inter_sym [in GeoCoq.Tarski_dev.Ch12_parallel]
inter_trivial [in GeoCoq.Tarski_dev.Ch12_parallel]
inter_uniqueness_not_par [in GeoCoq.Tarski_dev.Ch12_parallel]
inter_dec_plus_par_perp_perp_imply_triangle_circumscription [in GeoCoq.Meta_theory.Parallel_postulates.par_perp_perp_TCP]
inter_incid_uniquenessH [in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
inter_uniquenessH [in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
inter_dec [in GeoCoq.Tarski_dev.Ch12_parallel_inter_dec]
inverse_projection_postulate__proclus_bis [in GeoCoq.Meta_theory.Parallel_postulates.inverse_projection_postulate_proclus_bis]
invert_one_side [in GeoCoq.Tarski_dev.Ch09_plane]
invert_two_sides [in GeoCoq.Tarski_dev.Ch09_plane]
inv_f [in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
inv_uniqueness [in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
inv_col [in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
inv_exists_with_notation [in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]
inv_exists [in GeoCoq.Tarski_dev.Ch14_prod]
in_angle_reverse [in GeoCoq.Tarski_dev.Ch11_angles]
in_angle_asym [in GeoCoq.Tarski_dev.Ch11_angles]
in_angle_trans [in GeoCoq.Tarski_dev.Ch11_angles]
in_angle_line [in GeoCoq.Tarski_dev.Ch11_angles]
in_angle_trivial_2 [in GeoCoq.Tarski_dev.Ch11_angles]
in_angle_trivial_1 [in GeoCoq.Tarski_dev.Ch11_angles]
in_angle_one_side [in GeoCoq.Tarski_dev.Ch11_angles]
in_angle_out [in GeoCoq.Tarski_dev.Ch11_angles]
in_angle_two_sides [in GeoCoq.Tarski_dev.Ch11_angles]
ise_to_is [in GeoCoq.Tarski_dev.Annexes.vectors]
isi_dec [in GeoCoq.Tarski_dev.Annexes.suma]
isi_lta2_suma2__lta456 [in GeoCoq.Tarski_dev.Annexes.suma]
isi_lta2_suma2__lta123 [in GeoCoq.Tarski_dev.Annexes.suma]
isi_lea_lta789_suma2__lta456 [in GeoCoq.Tarski_dev.Annexes.suma]
isi_lea_lta789_suma2__lta123 [in GeoCoq.Tarski_dev.Annexes.suma]
isi_lea_lta123_suma2__lta456 [in GeoCoq.Tarski_dev.Annexes.suma]
isi_lea_lta456_suma2__lta123 [in GeoCoq.Tarski_dev.Annexes.suma]
isi_lea2_suma2__lea456 [in GeoCoq.Tarski_dev.Annexes.suma]
isi_lea2_suma2__lea123 [in GeoCoq.Tarski_dev.Annexes.suma]
isi_lta2_suma2__lta [in GeoCoq.Tarski_dev.Annexes.suma]
isi_lea_lta456_suma2__lta [in GeoCoq.Tarski_dev.Annexes.suma]
isi_lea_lta123_suma2__lta [in GeoCoq.Tarski_dev.Annexes.suma]
isi_suma__out546 [in GeoCoq.Tarski_dev.Annexes.suma]
isi_suma__out213 [in GeoCoq.Tarski_dev.Annexes.suma]
isi_lea2_suma2__conga456 [in GeoCoq.Tarski_dev.Annexes.suma]
isi_lea2_suma2__conga123 [in GeoCoq.Tarski_dev.Annexes.suma]
isi_assoc [in GeoCoq.Tarski_dev.Annexes.suma]
isi_assoc_2 [in GeoCoq.Tarski_dev.Annexes.suma]
isi_assoc_1 [in GeoCoq.Tarski_dev.Annexes.suma]
isi_lea2_suma2__lea [in GeoCoq.Tarski_dev.Annexes.suma]
isi_lea123_suma2__lea [in GeoCoq.Tarski_dev.Annexes.suma]
isi_lea456_suma2__lea [in GeoCoq.Tarski_dev.Annexes.suma]
isi_lea2__isi [in GeoCoq.Tarski_dev.Annexes.suma]
isi_suma__lea456789 [in GeoCoq.Tarski_dev.Annexes.suma]
isi_suma__lea123789 [in GeoCoq.Tarski_dev.Annexes.suma]
isi_comm [in GeoCoq.Tarski_dev.Annexes.suma]
isi_left_comm [in GeoCoq.Tarski_dev.Annexes.suma]
isi_right_comm [in GeoCoq.Tarski_dev.Annexes.suma]
isi_sym [in GeoCoq.Tarski_dev.Annexes.suma]
isi_distincts [in GeoCoq.Tarski_dev.Annexes.suma]
isi_chara [in GeoCoq.Tarski_dev.Annexes.suma]
isi123231 [in GeoCoq.Tarski_dev.Annexes.suma]
isi2_suma2__conga123 [in GeoCoq.Tarski_dev.Annexes.suma]
isi2_suma2__conga456 [in GeoCoq.Tarski_dev.Annexes.suma]
isosceles_congaH [in GeoCoq.Meta_theory.Models.hilbert_to_tarski]
isosceles_conga [in GeoCoq.Highschool.triangles]
isosceles_sym [in GeoCoq.Highschool.triangles]
is_null_all [in GeoCoq.Tarski_dev.Ch13_3_angles]
is_null_ang_out [in GeoCoq.Tarski_dev.Ch13_3_angles]
is_null_anga_out [in GeoCoq.Tarski_dev.Ch13_3_angles]
is_anga_distinct [in GeoCoq.Tarski_dev.Ch13_3_angles]
is_anga_conga_is_anga [in GeoCoq.Tarski_dev.Ch13_3_angles]
is_anga_conga [in GeoCoq.Tarski_dev.Ch13_3_angles]
is_anga_to_is_ang [in GeoCoq.Tarski_dev.Ch13_3_angles]
is_ang_distinct [in GeoCoq.Tarski_dev.Ch13_3_angles]
is_ang_conga_is_ang [in GeoCoq.Tarski_dev.Ch13_3_angles]
is_ang_conga [in GeoCoq.Tarski_dev.Ch13_3_angles]
is_image_spec_dec [in GeoCoq.Tarski_dev.Ch10_line_reflexivity]
is_image_spec_triv [in GeoCoq.Tarski_dev.Ch10_line_reflexivity]
is_image_rev [in GeoCoq.Tarski_dev.Ch10_line_reflexivity]
is_image_spec_rev [in GeoCoq.Tarski_dev.Ch10_line_reflexivity]
is_image_spec_col_cong [in GeoCoq.Tarski_dev.Ch10_line_reflexivity]
is_image_col_cong [in GeoCoq.Tarski_dev.Ch10_line_reflexivity]
is_image_is_image_spec [in GeoCoq.Tarski_dev.Ch10_line_reflexivity]
is_null_anga_dec [in GeoCoq.Tarski_dev.Ch13_4_cos]
is_length_exists [in GeoCoq.Tarski_dev.Ch15_lengths]
is_orthocenter_perm_5 [in GeoCoq.Highschool.orthocenter]
is_orthocenter_perm_4 [in GeoCoq.Highschool.orthocenter]
is_orthocenter_perm_3 [in GeoCoq.Highschool.orthocenter]
is_orthocenter_perm_2 [in GeoCoq.Highschool.orthocenter]
is_orthocenter_perm_1 [in GeoCoq.Highschool.orthocenter]
is_orthocenter_perm [in GeoCoq.Highschool.orthocenter]
is_orthocenter_cases [in GeoCoq.Highschool.orthocenter]
is_midpoint_id_2 [in GeoCoq.Tarski_dev.Ch07_midpoint]
is_midpoint_id [in GeoCoq.Tarski_dev.Ch07_midpoint]
is_midpoint_dec [in GeoCoq.Tarski_dev.Ch07_midpoint]
is_image_perp_in [in GeoCoq.Tarski_dev.Ch13_1]
is_to_ise [in GeoCoq.Tarski_dev.Annexes.vectors]
is_gravity_center_cases [in GeoCoq.Highschool.gravityCenter]
is_gravity_center_perm_5 [in GeoCoq.Highschool.gravityCenter]
is_gravity_center_perm_4 [in GeoCoq.Highschool.gravityCenter]
is_gravity_center_perm_3 [in GeoCoq.Highschool.gravityCenter]
is_gravity_center_perm_2 [in GeoCoq.Highschool.gravityCenter]
is_gravity_center_perm_1 [in GeoCoq.Highschool.gravityCenter]
is_gravity_center_perm [in GeoCoq.Highschool.gravityCenter]
is_gravity_center_third_reci [in GeoCoq.Highschool.gravityCenter]
is_gravity_center_third [in GeoCoq.Highschool.gravityCenter]
is_gravity_center_diff_3 [in GeoCoq.Highschool.gravityCenter]
is_gravity_center_diff_2 [in GeoCoq.Highschool.gravityCenter]
is_gravity_center_diff_1 [in GeoCoq.Highschool.gravityCenter]
is_gravity_center_col [in GeoCoq.Highschool.gravityCenter]
is_gravity_center_exist_unique [in GeoCoq.Highschool.gravityCenter]
is_len_cong_is_len [in GeoCoq.Tarski_dev.Ch13_2_length]
is_len_cong [in GeoCoq.Tarski_dev.Ch13_2_length]
is_circumcenter_uniqueness [in GeoCoq.Highschool.circumcenter]
is_circumcenter_perm_5 [in GeoCoq.Highschool.circumcenter]
is_circumcenter_perm_4 [in GeoCoq.Highschool.circumcenter]
is_circumcenter_perm_3 [in GeoCoq.Highschool.circumcenter]
is_circumcenter_perm_2 [in GeoCoq.Highschool.circumcenter]
is_circumcenter_perm_1 [in GeoCoq.Highschool.circumcenter]
is_circumcenter_perm [in GeoCoq.Highschool.circumcenter]
is_circumcenter_cases [in GeoCoq.Highschool.circumcenter]
IT_trivial2 [in GeoCoq.Meta_theory.Models.tarski_to_beeson]
IT_trivial [in GeoCoq.Meta_theory.Models.tarski_to_beeson]
IT_chara [in GeoCoq.Meta_theory.Models.tarski_to_beeson]


K

ker_par [in GeoCoq.Tarski_dev.Annexes.project]
ker_col [in GeoCoq.Tarski_dev.Annexes.project]
Kite_comm [in GeoCoq.Tarski_dev.Annexes.quadrilaterals]
KnuthAx1 [in GeoCoq.Tarski_dev.Ch16_coordinates_with_functions]


L

lam_obtuse__oah [in GeoCoq.Tarski_dev.Annexes.saccheri]
lam_acute__aah [in GeoCoq.Tarski_dev.Annexes.saccheri]
lam_per__rah [in GeoCoq.Tarski_dev.Annexes.saccheri]
lam__os [in GeoCoq.Tarski_dev.Annexes.saccheri]
lam_perm [in GeoCoq.Tarski_dev.Annexes.saccheri]
lam6521_mid2__sac [in GeoCoq.Tarski_dev.Annexes.saccheri]
lam6534_mid2__sac [in GeoCoq.Tarski_dev.Annexes.saccheri]
lastCPIn [in GeoCoq.Utils.arity]
lastCPTl [in GeoCoq.Utils.arity]
lastTailOK [in GeoCoq.Utils.arity]
lcos_lcos_col [in GeoCoq.Tarski_dev.Ch13_5_Pappus_Pascal]
lcos_per_anga [in GeoCoq.Tarski_dev.Ch13_5_Pappus_Pascal]
lcos_eq_lcos3_eq [in GeoCoq.Tarski_dev.Ch13_4_cos]
lcos_eq_lcos2_eq [in GeoCoq.Tarski_dev.Ch13_4_cos]
lcos_eq_trans [in GeoCoq.Tarski_dev.Ch13_4_cos]
lcos_eq_sym [in GeoCoq.Tarski_dev.Ch13_4_cos]
lcos_eq_refl [in GeoCoq.Tarski_dev.Ch13_4_cos]
lcos_eqa_lcos [in GeoCoq.Tarski_dev.Ch13_4_cos]
lcos_uniqueness [in GeoCoq.Tarski_dev.Ch13_4_cos]
lcos_exists [in GeoCoq.Tarski_dev.Ch13_4_cos]
lcos_lg [in GeoCoq.Tarski_dev.Ch13_4_cos]
lcos_per [in GeoCoq.Tarski_dev.Ch13_4_cos]
lcos_const_o [in GeoCoq.Tarski_dev.Ch13_4_cos]
lcos_not_lg_null [in GeoCoq.Tarski_dev.Ch13_4_cos]
lcos_eql_lcos [in GeoCoq.Tarski_dev.Ch13_4_cos]
lcos_lg_anga [in GeoCoq.Tarski_dev.Ch13_4_cos]
lcos_const_cb [in GeoCoq.Tarski_dev.Ch13_4_cos]
lcos_const_ab [in GeoCoq.Tarski_dev.Ch13_4_cos]
lcos_const_a [in GeoCoq.Tarski_dev.Ch13_4_cos]
lcos_lg_distincts [in GeoCoq.Tarski_dev.Ch13_4_cos]
lcos_const [in GeoCoq.Tarski_dev.Ch13_4_cos]
lcos_const1 [in GeoCoq.Tarski_dev.Ch13_4_cos]
lcos_const0 [in GeoCoq.Tarski_dev.Ch13_4_cos]
lcos_lg_not_null [in GeoCoq.Tarski_dev.Ch13_4_cos]
lcos2_lcos [in GeoCoq.Tarski_dev.Ch13_5_Pappus_Pascal]
lcos2_eq_lcos3_eq [in GeoCoq.Tarski_dev.Ch13_4_cos]
lcos2_lg_not_null [in GeoCoq.Tarski_dev.Ch13_4_cos]
lcos2_eq_trans [in GeoCoq.Tarski_dev.Ch13_4_cos]
lcos2_lg_anga [in GeoCoq.Tarski_dev.Ch13_4_cos]
lcos2_eql_lcos2 [in GeoCoq.Tarski_dev.Ch13_4_cos]
lcos2_uniqueness [in GeoCoq.Tarski_dev.Ch13_4_cos]
lcos2_eq_sym [in GeoCoq.Tarski_dev.Ch13_4_cos]
lcos2_eq_refl [in GeoCoq.Tarski_dev.Ch13_4_cos]
lcos2_exists' [in GeoCoq.Tarski_dev.Ch13_4_cos]
lcos2_exists [in GeoCoq.Tarski_dev.Ch13_4_cos]
lcos2_comm [in GeoCoq.Tarski_dev.Ch13_4_cos]
lcos3_lcos2 [in GeoCoq.Tarski_dev.Ch13_5_Pappus_Pascal]
lcos3_eq_trans [in GeoCoq.Tarski_dev.Ch13_4_cos]
lcos3_lg_not_null [in GeoCoq.Tarski_dev.Ch13_4_cos]
lcos3_lg_anga [in GeoCoq.Tarski_dev.Ch13_4_cos]
lcos3_eql_lcos3 [in GeoCoq.Tarski_dev.Ch13_4_cos]
lcos3_uniqueness [in GeoCoq.Tarski_dev.Ch13_4_cos]
lcos3_eq_sym [in GeoCoq.Tarski_dev.Ch13_4_cos]
lcos3_eq_refl [in GeoCoq.Tarski_dev.Ch13_4_cos]
lcos3_exists [in GeoCoq.Tarski_dev.Ch13_4_cos]
lcos3_permut2 [in GeoCoq.Tarski_dev.Ch13_4_cos]
lcos3_permut1 [in GeoCoq.Tarski_dev.Ch13_4_cos]
lcos3_permut3 [in GeoCoq.Tarski_dev.Ch13_4_cos]
lcos3_lcos_2_1 [in GeoCoq.Tarski_dev.Ch13_4_cos]
lcos3_lcos_1_2 [in GeoCoq.Tarski_dev.Ch13_4_cos]
lea__nlta [in GeoCoq.Tarski_dev.Ch11_angles]
lea_total [in GeoCoq.Tarski_dev.Ch11_angles]
lea_dec [in GeoCoq.Tarski_dev.Ch11_angles]
lea_in_angle [in GeoCoq.Tarski_dev.Ch11_angles]
lea_distincts [in GeoCoq.Tarski_dev.Ch11_angles]
lea_acute_obtuse [in GeoCoq.Tarski_dev.Ch11_angles]
lea_comm [in GeoCoq.Tarski_dev.Ch11_angles]
lea_right_comm [in GeoCoq.Tarski_dev.Ch11_angles]
lea_left_comm [in GeoCoq.Tarski_dev.Ch11_angles]
lea_asym [in GeoCoq.Tarski_dev.Ch11_angles]
lea_trans [in GeoCoq.Tarski_dev.Ch11_angles]
lea_refl [in GeoCoq.Tarski_dev.Ch11_angles]
lea_line [in GeoCoq.Tarski_dev.Ch11_angles]
lea_cases [in GeoCoq.Tarski_dev.Ch12_parallel_inter_dec]
lea121345 [in GeoCoq.Tarski_dev.Ch11_angles]
lea123456_lta__lta [in GeoCoq.Tarski_dev.Ch11_angles]
lea456789_lta__lta [in GeoCoq.Tarski_dev.Ch11_angles]
legendre_s_theorem [in GeoCoq.Meta_theory.Parallel_postulates.legendre]
legendre_aux2 [in GeoCoq.Meta_theory.Parallel_postulates.legendre]
legendre_aux1 [in GeoCoq.Meta_theory.Parallel_postulates.legendre]
legendre_aux [in GeoCoq.Meta_theory.Parallel_postulates.legendre]
legendre_aux2 [in GeoCoq.Meta_theory.Parallel_postulates.triangle_playfair_bis]
legendre_aux1 [in GeoCoq.Meta_theory.Parallel_postulates.triangle_playfair_bis]
lengthAtLeastOne [in GeoCoq.Utils.sets]
lengthNilOK [in GeoCoq.Utils.arity]
lengthOfCPToList [in GeoCoq.Utils.arity]
lengthOne [in GeoCoq.Utils.sets]
length_sym [in GeoCoq.Tarski_dev.Ch15_lengths]
length_existence [in GeoCoq.Tarski_dev.Ch15_lengths]
length_out [in GeoCoq.Tarski_dev.Ch15_lengths]
length_O [in GeoCoq.Tarski_dev.Ch15_lengths]
length_not_col_null [in GeoCoq.Tarski_dev.Ch15_lengths]
length_Ps [in GeoCoq.Tarski_dev.Ch15_lengths]
length_cong [in GeoCoq.Tarski_dev.Ch15_lengths]
length_uniqueness [in GeoCoq.Tarski_dev.Ch15_lengths]
length_leP_le_2 [in GeoCoq.Tarski_dev.Ch15_lengths]
length_leP_le_1 [in GeoCoq.Tarski_dev.Ch15_lengths]
length_Ar2 [in GeoCoq.Tarski_dev.Ch15_lengths]
length_eq_cong_2 [in GeoCoq.Tarski_dev.Ch15_lengths]
length_eq_cong_1 [in GeoCoq.Tarski_dev.Ch15_lengths]
length_id [in GeoCoq.Tarski_dev.Ch15_lengths]
length_id_2 [in GeoCoq.Tarski_dev.Ch15_lengths]
length_id_1 [in GeoCoq.Tarski_dev.Ch15_lengths]
length_pos [in GeoCoq.Tarski_dev.Ch15_lengths]
length_eq_or_opp [in GeoCoq.Tarski_dev.Ch16_coordinates]
leP_bet [in GeoCoq.Tarski_dev.Ch15_lengths]
leP_sum_leP [in GeoCoq.Tarski_dev.Ch14_order]
leP_trans [in GeoCoq.Tarski_dev.Ch14_order]
leP_asym [in GeoCoq.Tarski_dev.Ch14_order]
leP_refl [in GeoCoq.Tarski_dev.Ch14_order]
le_cong_le [in GeoCoq.Highschool.orientation]
le_comm [in GeoCoq.Highschool.orientation]
le_right_comm [in GeoCoq.Highschool.orientation]
le_left_comm [in GeoCoq.Highschool.orientation]
le__nlt [in GeoCoq.Tarski_dev.Ch05_bet_le]
le_comm [in GeoCoq.Tarski_dev.Ch05_bet_le]
le_right_comm [in GeoCoq.Tarski_dev.Ch05_bet_le]
le_left_comm [in GeoCoq.Tarski_dev.Ch05_bet_le]
le_zero [in GeoCoq.Tarski_dev.Ch05_bet_le]
le_cases [in GeoCoq.Tarski_dev.Ch05_bet_le]
le_trivial [in GeoCoq.Tarski_dev.Ch05_bet_le]
le_anti_symmetry [in GeoCoq.Tarski_dev.Ch05_bet_le]
le_transitivity [in GeoCoq.Tarski_dev.Ch05_bet_le]
le_reflexivity [in GeoCoq.Tarski_dev.Ch05_bet_le]
le_bet [in GeoCoq.Tarski_dev.Ch05_bet_le]
le_pos_prod_le [in GeoCoq.Tarski_dev.Ch14_order]
le_mid2__le12 [in GeoCoq.Tarski_dev.Ch07_midpoint]
le_mid2__le13 [in GeoCoq.Tarski_dev.Ch07_midpoint]
le_cong_le [in GeoCoq.Tarski_dev.Annexes.quadrilaterals]
le_comm [in GeoCoq.Tarski_dev.Annexes.quadrilaterals]
le_right_comm [in GeoCoq.Tarski_dev.Annexes.quadrilaterals]
le_left_comm [in GeoCoq.Tarski_dev.Annexes.quadrilaterals]
le1221 [in GeoCoq.Tarski_dev.Ch05_bet_le]
le1234_lt__lt [in GeoCoq.Tarski_dev.Ch05_bet_le]
le3456_lt__lt [in GeoCoq.Tarski_dev.Ch05_bet_le]
lg_eql_lg [in GeoCoq.Tarski_dev.Ch13_2_length]
lg_null_dec [in GeoCoq.Tarski_dev.Ch13_2_length]
lg_null_trivial [in GeoCoq.Tarski_dev.Ch13_2_length]
lg_null_instance [in GeoCoq.Tarski_dev.Ch13_2_length]
lg_sym [in GeoCoq.Tarski_dev.Ch13_2_length]
lg_cong_lg [in GeoCoq.Tarski_dev.Ch13_2_length]
lg_cong [in GeoCoq.Tarski_dev.Ch13_2_length]
lg_exists [in GeoCoq.Tarski_dev.Ch13_2_length]
line_dec [in GeoCoq.Tarski_dev.Ch12_parallel]
listInd [in GeoCoq.Utils.arity]
ListToCPTl [in GeoCoq.Utils.arity]
lower_dim [in GeoCoq.Meta_theory.Models.tarski_to_beeson]
lower_dim_B [in GeoCoq.Meta_theory.Models.tarski_to_beeson]
lower_dim_ex [in GeoCoq.Tarski_dev.Ch03_bet]
lower_dim [in GeoCoq.Meta_theory.Counter_models.counter_model_segment_construction]
lower_dim_ex [in