| name: GeoCoq_test |
| num_files: 136 |
| language: COQ |
| few_shot_data_path_for_retrieval: null |
| few_shot_metadata_filename_for_retrieval: null |
| dfs_data_path_for_retrieval: null |
| dfs_metadata_filename_for_retrieval: local.meta.json |
| theorem_cnt: 505 |
| datasets: |
| - project: <path-to-repo>/GeoCoq |
| files: |
| - path: theories/Main/Meta_theory/Models/hilbert_to_tarski.v |
| theorems: |
| - OS2__TS |
| - betH_expand |
| - strong_pasch |
| - bet_identity |
| - isosceles_congaH |
| - out2_out1 |
| - betH_outH2__betH |
| - pars__para |
| - same_side_not_incid |
| - bet_colH |
| - same_side_comm |
| - line_col |
| - congaH_commr |
| - congH_refl |
| - cong_trans |
| - outH_trivial |
| - colH_trans |
| - outH_dec |
| - H_euclidean_to_T_euclidean |
| - other_point_exists |
| - point3_online_exists |
| - path: theories/Algebraic/Counter_models/Planar/counter_model_bet_inner_transitivity.v |
| theorems: |
| - continuity |
| - point_equality_decidability |
| - proclus |
| - path: theories/Main/Meta_theory/Continuity/elementary_continuity_props.v |
| theorems: |
| - triangle_inequality1 |
| - euclid_22_aux |
| - one_point_line_circle__two_points_line_circle |
| - path: theories/Main/Annexes/suma.v |
| theorems: |
| - sams_lea2_suma2__lea456 |
| - sams_lea_lta789_suma2__lta456 |
| - sams_lea2_suma2__lea |
| - bet_suppa__suma |
| - trisuma_distincts |
| - col2_suma__col |
| - suma_suppa2__suma |
| - suma_assoc |
| - col_trisuma__bet |
| - acute_per_suma__nbet |
| - os2__sams |
| - bet__sams |
| - conga2_sams__sams |
| - sams_chara |
| - ts__suma_1 |
| - path: theories/Coinc/CongR.v |
| theorems: |
| - CTcong_comm |
| - CTcong_pseudo_refl |
| - eq_le2__eq2 |
| - path: theories/Main/Elements_statements/Book_1.v |
| theorems: |
| - prop_46 |
| - prop_2 |
| - prop_30 |
| - prop_28_2 |
| - prop_8 |
| - prop_3 |
| - prop_21_2 |
| - prop_29_1 |
| - prop_32_2 |
| - prop_20 |
| - prop_31 |
| - prop_5_2 |
| - path: theories/Main/Annexes/project.v |
| theorems: |
| - cong_conga3_cong3 |
| - project_to_projp |
| - projp_project_to_perp |
| - projp_preserves_bet |
| - projp_is_project |
| - path: theories/Algebraic/Counter_models/nD/counter_model_bet_symmetry.v |
| theorems: |
| - segment_construction |
| - path: theories/Main/Annexes/coplanar.v |
| theorems: |
| - ncoplanar_perm_11 |
| - reflect__coplanar |
| - coplanar_perm_11 |
| - ncoplanar_perm_10 |
| - coplanar_perm_9 |
| - ncop__ncols |
| - ncoplanar_perm_13 |
| - ncoplanar_perm_17 |
| - ncoplanar_perm_4 |
| - midpoint__coplanar |
| - ts__coplanar |
| - path: theories/Coinc/CoincR.v |
| theorems: |
| - CoappDup |
| - memCPAuxOK |
| - interp_CP |
| - path: theories/Main/Annexes/saccheri.v |
| theorems: |
| - t22_14__oah |
| - sac__pars1234 |
| - t22_14__bet_aux |
| - mid2_sac__lam6521 |
| - t22_7__cong |
| - sac__par1234 |
| - path: theories/Algebraic/Counter_models/nD/counter_model_cong_identity.v |
| theorems: |
| - continuity |
| - five_segment |
| - euclid |
| - cong_pseudo_reflexivity |
| - path: theories/Main/Highschool/orientation.v |
| theorems: |
| - per_preserves_bet |
| - proj3_col |
| - cong_le_le |
| - proj_par |
| - midpoint_col |
| - path: theories/Main/Meta_theory/Models/tarski_to_euclid.v |
| theorems: |
| - Euclid_follows_from_Tarski_euclidean |
| - InCirc_not_OnCirc |
| - nCol_not_Col |
| - path: theories/Main/Meta_theory/Continuity/grad.v |
| theorems: |
| - grad_neq__neq12 |
| - gradexp_le__reach |
| - grad_sum |
| - path: theories/Algebraic/POF_to_Tarski.v |
| theorems: |
| - cong_eq |
| - bet_betS |
| - ratioP_aux |
| - ratio_cp'_aux_2 |
| - dot_ge0 |
| - betS_ratio |
| - ratio_bet' |
| - addrBBB |
| - bet_axx |
| - betEP' |
| - ratiop0 |
| - bet_symmetry |
| - extension_eq |
| - quad_eq0 |
| - row2_eq0 |
| - eq_div_scale |
| - betS_sym |
| - ratioNN |
| - betE_xax |
| - path: theories/Algebraic/Counter_models/Planar/counter_model_lower_dim.v |
| theorems: |
| - continuity |
| - bet_symmetry |
| - path: theories/Main/Meta_theory/Models/tarski_to_hilbert.v |
| theorems: |
| - incident_col |
| - incidentp_eqp |
| - cop_plane_aux |
| - col_incident |
| - eqp_incidentp |
| - incidentp_Proper |
| - Hilbert_2D_follows_from_Tarski_2D |
| - path: theories/Main/Annexes/circles.v |
| theorems: |
| - bet_chord__diam_or_ncol |
| - bet_incs2__incs |
| - onc__inc |
| - outcs__outc |
| - diam_uniqueness |
| - path: theories/Elements/OriginalProofs/lemma_congruencetransitive.v |
| theorems: |
| - lemma_congruencetransitive |
| - path: theories/Main/Annexes/quadrilaterals_inter_dec.v |
| theorems: |
| - perp_rmb |
| - plg_par |
| - plg_cong_2 |
| - plgs_mid |
| - parallelogram_to_plg |
| - plg_not_comm_1 |
| - perp3__perp |
| - degenerated_rect_eq |
| - plg_mid |
| - plg_per_rect4 |
| - cop_perp3__rect |
| - path: theories/Main/Highschool/SegmTrisect.v |
| theorems: |
| - SegmTrisectSecondThirdUniqueness |
| - path: theories/Algebraic/Counter_models/nD/counter_model_euclid.v |
| theorems: |
| - cauchy_schwartz' |
| - cong_abdc |
| - E_in_disk_aux |
| - dist_lt1 |
| - cauchy_schwartz_eq' |
| - a'nD_eq0 |
| - bc_neq_nD |
| - cong'_cdab |
| - five_segment_holds_aux2 |
| - norm_point_subr_gt0 |
| - segment_addition |
| - triangle_ineq |
| - seg_aux7 |
| - bet_symmetry_vector |
| - c'nD_in_unit_disk |
| - i1'_in_unit_disk |
| - dist_eq1 |
| - cong_identity_holds |
| - segment_construction_holds_aux |
| - i_neq_i1 |
| - Rcf_to_GI_PED |
| - omd_i1i1 |
| - path: theories/Main/Tarski_dev/Ch14_sum.v |
| theorems: |
| - sum_cong |
| - opp0 |
| - cong_sum |
| - sum4_equiv |
| - proj_pars |
| - grid_not_par |
| - diff_uniquenessA |
| - sum_stable |
| - change_grid_sum |
| - double_not_null_not_nul |
| - pj_trivial |
| - sum_diff |
| - path: theories/Elements/OriginalProofs/lemma_ray.v |
| theorems: |
| - lemma_ray |
| - path: theories/Main/Tarski_dev/Ch11_angles.v |
| theorems: |
| - l11_19 |
| - l11_61 |
| - triangle_strict_reverse_inequality |
| - not_and_lta |
| - conga_dec |
| - l11_61_bis |
| - triangle_strict_inequality_2 |
| - l11_62_unicity |
| - gta_distincts |
| - col_orth_at__orth_at |
| - conga_obtuse__obtuse |
| - l11_21_a |
| - suppa2__conga123 |
| - inangle_one_side2 |
| - conga_preserves_in_angle |
| - l11_46 |
| - l11_60_bis |
| - angle_partition |
| - cong2_conga_obtuse__cong_conga2 |
| - lea_line |
| - conga_sym |
| - obtuse_chara |
| - conga_preserves_lta |
| - symmetry_preserves_conga |
| - in_angle_reverse |
| - out2__conga |
| - cong2_per2__cong |
| - l11_3 |
| - l11_31_2 |
| - cong_lt_per2__lt |
| - path: theories/Main/Meta_theory/Models/tarski_to_beeson.v |
| theorems: |
| - inner_pasch_B |
| - ColB_Col |
| - five_segment_B |
| - path: theories/Main/Tarski_dev/Ch12_parallel.v |
| theorems: |
| - par_strict_par |
| - col_perp2_ncol__col |
| - not_par_strict_id |
| - Par_strict_cases |
| - Par_perm |
| - par_strict_not_col_2 |
| - par_strict_right_comm |
| - path: theories/Main/Tarski_dev/Ch13_5_Pappus_Pascal.v |
| theorems: |
| - l13_10 |
| - l13_10_aux2 |
| - lcos2_lcos |
| - path: theories/Main/Annexes/half_angles.v |
| theorems: |
| - halfa_chara2 |
| - out_preserves_halfa |
| - ghalfa_right_comm |
| - ghalfa_exists |
| - cop_halfa_perp__os |
| - acute_ghalfa2_sams_suma2__ghalfa456 |
| - path: theories/Algebraic/Counter_models/nD/bet_identity.v |
| theorems: |
| - g2_5 |
| - g2_11 |
| - g2_1 |
| - path: theories/Main/Tarski_dev/Ch02_cong.v |
| theorems: |
| - not_cong_3421 |
| - cong_4312 |
| - cong_reflexivity |
| - distinct |
| - path: theories/Main/Annexes/quadrilaterals.v |
| theorems: |
| - Square_not_triv |
| - Rhombus_Rectangle_Square |
| - Square_Rectangle |
| - Square_not_triv_3 |
| - Square_not_triv_2 |
| - bet_cong_bet |
| - sym_par |
| - bet_half_bet |
| - mid_plg_1 |
| - path: theories/Main/Tarski_dev/Ch10_line_reflexivity.v |
| theorems: |
| - midpoint_preserves_per |
| - l10_2_existence_spec |
| - is_image_is_image_spec |
| - ex_sym |
| - l10_4_spec |
| - image_in_gen_is_image |
| - is_image_spec_col_cong |
| - path: theories/Main/Highschool/incenter.v |
| theorems: |
| - incenter_permut312 |
| - path: theories/Main/Tactics/CoincR_for_cop.v |
| theorems: |
| - ss_ok_empty_for_cop |
| - path: theories/Main/Highschool/triangles.v |
| theorems: |
| - equilateral_strict_swap_3 |
| - equilateral_strict_swap_2 |
| - equilateral_isosceles_1 |
| - isosceles_sym |
| - equilateral_swap_2 |
| - equilateral_strict_swap_5 |
| - equilateral_strict__not_col |
| - path: theories/Main/Annexes/sums.v |
| theorems: |
| - sums_assoc_2 |
| - sums_diff_1 |
| - le2_sums2__le34 |
| - path: theories/Main/Annexes/tangency.v |
| theorems: |
| - TangentCC_Col |
| - interccat__neq |
| - tangent_construction |
| - path: theories/Main/Tarski_dev/Ch16_coordinates_with_functions.v |
| theorems: |
| - signed_area_AAB |
| - characterization_of_collinearity_F |
| - put_neg_in_goal |
| - twice_signed_area_AAB |
| - SubF |
| - twice_signed_area_ABA |
| - characterization_of_perpendicularity_F |
| - AM_lower_dim |
| - signed_area_sum |
| - signed_area_ABA |
| - characterization_of_equality_F |
| - OF |
| - path: theories/Main/Tarski_dev/Ch06_out_lines.v |
| theorems: |
| - bet2_le2__le1346 |
| - l6_11_existence |
| - bet_out |
| - out_bet__out |
| - bet2_le2__le2356 |
| - l6_4_2 |
| - path: theories/Main/Tarski_dev/Ch12_parallel_inter_dec.v |
| theorems: |
| - parallel_uniqueness |
| - l12_23 |
| - not_par_one_not_par |
| - par_dec |
| - l12_20_bis |
| - path: theories/Algebraic/coplanarity.v |
| theorems: |
| - Cop_3412 |
| - Cop_3214 |
| - Cop_4213 |
| - Copl_4312 |
| - Copl_3142 |
| - Cop_2413 |
| - Copl_1324 |
| - Cop_1243 |
| - Cop_4123 |
| - Copl_1432 |
| - Copl_2134 |
| - Copl_1342 |
| - path: theories/Main/Tarski_dev/Ch10_line_reflexivity_2.v |
| theorems: |
| - cong_cop_mid_perp__col |
| - ex_perp_cop |
| - image_gen_preserves_inter |
| - image_preserves_midpoint |
| - path: theories/Elements/OriginalProofs/proposition_37.v |
| theorems: |
| - proposition_37 |
| - path: theories/Main/Tarski_dev/Ch15_lengths.v |
| theorems: |
| - thales |
| - l15_7 |
| - sign_dec |
| - length_id_2 |
| - cong2_lea__le |
| - signeq__prod_pos |
| - image_preserves_out |
| - pythagoras_obtuse_or_per |
| - path: theories/Main/Tarski_dev/Ch13_3_angles.v |
| theorems: |
| - anga_col_out |
| - ang_distincts |
| - not_conga_is_anga |
| - anga_acute |
| - is_null_ang_out |
| - is_ang_distinct |
| - is_anga_conga_is_anga |
| - null_ang |
| - anga_distinct |
| - not_null_not_col |
| - all_eqaa |
| - path: theories/Main/Meta_theory/Continuity/archimedes.v |
| theorems: |
| - t22_23_aux |
| - t22_18_aux2 |
| - t22_18_aux1 |
| - path: theories/Main/Tarski_dev/Ch03_bet.v |
| theorems: |
| - bet_neq23__neq |
| - path: theories/Main/Tarski_dev/Ch13_4_cos.v |
| theorems: |
| - lcos_eq_refl |
| - lcos2_comm |
| - lcos3_lg_anga |
| - lcos_eq_sym |
| - is_null_anga_dec |
| - lcos2_exists |
| - null_lcos |
| - l13_6 |
| - obtuse_not_acute |
| - path: theories/Elements/OriginalProofs/proposition_44.v |
| theorems: |
| - proposition_44 |
| - path: theories/Main/Tarski_dev/Ch16_coordinates.v |
| theorems: |
| - bet_betCood_aux |
| - exists_grid |
| - cong_3_2_cong_4 |
| - square_distance_formula |
| - characterization_of_congruence |
| - coordinates_of_point |
| - path: theories/Algebraic/Counter_models/Planar/counter_model_cong_pseudo_reflexivity.v |
| theorems: |
| - point_equality_decidability |
| - path: theories/Elements/OriginalProofs/proposition_07.v |
| theorems: |
| - proposition_07 |
| - path: theories/Elements/OriginalProofs/lemma_21helper.v |
| theorems: |
| - lemma_21helper |
| - path: theories/Algebraic/tcp_ndc.v |
| theorems: |
| - tcp_os_mab_mmac_b_ssa |
| - tcp_os_b_ssa_mab_mac |
| - tcp_os_b_sa_mmab_mac |
| - tcp_ncol_inplane_2_4 |
| - path: theories/Main/Highschool/bisector.v |
| theorems: |
| - bisector_foot_out_out |
| - path: theories/Main/Meta_theory/Continuity/completeness.v |
| theorems: |
| - extension_reverse_bet |
| - col2_diff_inj_line__diff |
| - path: theories/Algebraic/Counter_models/counter_model_bet_identity.v |
| theorems: |
| - segment_construction |
| - not_between_identity |
| - cong_aux_4 |
| - euclid |
| - path: theories/Algebraic/Counter_models/Planar/counter_model_bet_symmetry.v |
| theorems: |
| - cong_inner_transitivity |
| - path: theories/Main/Tarski_dev/Ch09_plane.v |
| theorems: |
| - os_out_os |
| - osp_transitivity |
| - cop_out__osp |
| - l9_17 |
| - two_sides_not_col |
| - ex_ncol_cop2 |
| - mid_preserves_col |
| - cop3_osp__osp |
| - ts2__ex_bet2 |
| - invert_two_sides |
| - cop__one_or_two_sides |
| - one_side_reflexivity |
| - bet_cop2__cop |
| - cop_osp__ex_cop2 |
| - path: theories/Algebraic/Counter_models/nD/counter_model_cong_inner_transitivity.v |
| theorems: |
| - euclid |
| - cong_identity |
| - path: theories/Algebraic/Counter_models/Planar/counter_model_upper_dim.v |
| theorems: |
| - lower_dim |
| - path: theories/Main/Highschool/gravityCenter.v |
| theorems: |
| - intersection_two_medians_exist_unique |
| - is_gravity_center_third |
| - path: theories/Main/Highschool/sesamath_exercises.v |
| theorems: |
| - sesamath_4ieme_G2_ex42 |
| - sesamath_4ieme_G2_ex45 |
| - sesamath_4ieme_G2_ex44_1 |
| - sesamath_4ieme_G2_ex37 |
| - sesamath_4ieme_G2_ex40 |
| - path: theories/Main/Tarski_dev/Ch13_1.v |
| theorems: |
| - perp2_preserves_bet23 |
| - triangle_mid_par |
| - path: theories/Coinc/Utils/arity.v |
| theorems: |
| - InNth |
| - InCPOK |
| - listInd |
| - consTailCPOK |
| - circPermNIdAux |
| - CPLRec |
| - lastCPIn |
| - consHeadCP |
| - path: theories/Main/Meta_theory/Parallel_postulates/thales_converse_postulate_thales_existence.v |
| theorems: |
| - thales_converse_postulate__thales_existence |
| - path: theories/Main/Annexes/vectors.v |
| theorems: |
| - one_side_col_out |
| - same_dir_id |
| - sum_sym |
| - plg_plg_bet |
| - is_to_ise |
| - path: theories/Algebraic/Counter_models/nD/counter_model_upper_dim.v |
| theorems: |
| - oP |
| - path: theories/Elements/OriginalProofs/lemma_linereflectionisometry.v |
| theorems: |
| - lemma_linereflectionisometry |
| - path: theories/Main/Tarski_dev/Ch14_order.v |
| theorems: |
| - pos_inv_pos |
| - path: theories/Main/Meta_theory/Models/gupta_inspired_to_tarski.v |
| theorems: |
| - g2_5 |
| - path: theories/Main/Meta_theory/Models/tarski_to_gupta_inspired.v |
| theorems: |
| - inner_pasch' |
| - path: theories/Main/Meta_theory/Models/tarski_to_coinc_theory_for_concyclic.v |
| theorems: |
| - not_col_perm_1 |
| - concy_3 |
| - path: theories/Main/Annexes/Tagged_predicates.v |
| theorems: |
| - Mid_tagged_Mid |
| - path: theories/Main/Meta_theory/Parallel_postulates/TCP_tarski.v |
| theorems: |
| - impossible_case_4_2 |
| - impossible_two_sides_not_col |
| - path: theories/Algebraic/Counter_models/nD/counter_model_lower_dim.v |
| theorems: |
| - lower_dim |
| - path: theories/Main/Tarski_dev/Ch08_orthogonality.v |
| theorems: |
| - perp_cong |
| - perp_in_perp |
| - l8_14_2_1b_bis |
| - per_dec |
| - perp_col2 |
| - perp_in_col_perp_in |
| - l8_3 |
| - per_perp_in |
| - path: theories/Elements/OriginalProofs/proposition_30.v |
| theorems: |
| - proposition_30 |
| - parnotmeet |
| - path: theories/Main/Meta_theory/Parallel_postulates/rah_rectangle_principle.v |
| theorems: |
| - rah__rectangle_principle |
| - path: theories/Elements/OriginalProofs/lemma_collinearitypreserved.v |
| theorems: |
| - lemma_collinearitypreserved |
| - path: theories/Elements/OriginalProofs/proposition_43.v |
| theorems: |
| - proposition_43 |
| - path: theories/Main/Meta_theory/Models/beeson_to_tarski.v |
| theorems: |
| - ICol_chara |
| - lower_dim |
| - ICol_dec |
| - path: theories/Main/Meta_theory/Models/tarski_to_coinc_theory_for_cop.v |
| theorems: |
| - Tarski_is_a_Coinc_predicates_for_cop |
| - path: theories/Algebraic/Counter_models/Planar/counter_model_five_segment.v |
| theorems: |
| - bet_inner_transitivity |
| - cong_identity |
| - nbetS_cab |
| - bet_1Dd |
| - path: theories/Main/Annexes/midpoint_theorems.v |
| theorems: |
| - col_permut132 |
| - col123_124__col134 |
| - path: theories/Main/Tactics/CoincR_for_col.v |
| theorems: |
| - ss_ok_empty_for_col |
| - path: theories/Algebraic/Counter_models/Planar/counter_model_cong_inner_transitivity.v |
| theorems: |
| - cong_pseudo_reflexivity |
| - path: theories/Main/Tarski_dev/Ch14_prod.v |
| theorems: |
| - prod_0_r |
| - prod_assoc1 |
| - prod_y_axis_change |
| - path: theories/Elements/OriginalProofs/lemma_erectedperpendicularunique.v |
| theorems: |
| - lemma_erectedperpendicularunique |
| - path: theories/Main/Meta_theory/Parallel_postulates/legendre.v |
| theorems: |
| - legendre_aux2 |
| - legendre_s_third_theorem |
| - path: theories/Algebraic/Counter_models/Planar/counter_model_euclid.v |
| theorems: |
| - lower_dim |
| - nbet_bca |
| - cong_identity |
| - path: theories/Main/Meta_theory/Parallel_postulates/thales_existence_rah.v |
| theorems: |
| - thales_existence__rah |
| - path: theories/Algebraic/Counter_models/nD/independent_version_to_tarski.v |
| theorems: |
| - altIT2D_to_T2D |
| - Estability |
| - path: theories/Main/Tarski_dev/Ch13_2_length.v |
| theorems: |
| - ex_points_lg_not_col |
| - is_len_cong |
| - lg_eql_lg |
| - path: theories/Main/Highschool/exercises.v |
| theorems: |
| - quadrileral_midpoints |
| - path: theories/Elements/OriginalProofs/proposition_24.v |
| theorems: |
| - proposition_24 |
| - path: theories/Main/Tarski_dev/Ch05_bet_le.v |
| theorems: |
| - cong__le3412 |
| - between_cong_2 |
| - nlt |
| - cong__nlt |
| - le__nlt |
| - path: theories/Elements/OriginalProofs/proposition_29B.v |
| theorems: |
| - proposition_29B |
| - path: theories/Elements/OriginalProofs/lemma_TGflip.v |
| theorems: |
| - lemma_TGflip |
| - path: theories/Coinc/Utils/sets.v |
| theorems: |
| - eq_equiv |
| - lt |
| - lt_trans |
| - STexists_mem_4 |
| - InCPOCP |
| - path: theories/Main/Meta_theory/Parallel_postulates/tarski_euclid.v |
| theorems: |
| - tarski_s_euclid_implies_euclid_5 |
| - path: theories/Main/Annexes/inscribed_angle.v |
| theorems: |
| - cop_obtuse_onc3__ts |
| - bet_cong__ghalfa |
| - path: theories/Elements/OriginalProofs/lemma_legsmallerhypotenuse.v |
| theorems: |
| - lemma_legsmallerhypotenuse |
| - path: theories/Main/Highschool/varignon.v |
| theorems: |
| - varignon_aux_aux |
| - path: theories/Elements/OriginalProofs/proposition_28C.v |
| theorems: |
| - proposition_28C |
| - path: theories/Algebraic/Counter_models/nD/independent_version_to_beeson.v |
| theorems: |
| - ITcong_inner_transitivity |
| - path: theories/Coinc/ColR.v |
| theorems: |
| - CTcol_permutation_5 |
| - proper_3 |
| - path: theories/Main/Meta_theory/Parallel_postulates/rah_posidonius_postulate.v |
| theorems: |
| - rah__posidonius_aux |
| - path: theories/Main/Meta_theory/Parallel_postulates/parallel_postulates.v |
| theorems: |
| - equivalence_of_aristotle_greenberg_and_decidability_of_intersection |
| - equivalent_postulates_with_decidability_of_intersection_of_lines |
| - path: theories/Main/Annexes/perp_bisect.v |
| theorems: |
| - perp_bisect_is_on_perp_bisect |
| - perp_bisect_perp |
| - perp_bisect_existence |
| - path: theories/Elements/OriginalProofs/lemma_twolines.v |
| theorems: |
| - lemma_twolines |
| - path: theories/Algebraic/Counter_models/Planar/counter_model_cong_identity.v |
| theorems: |
| - five_segment |
| - path: theories/Coinc/Utils/general_tactics.v |
| theorems: |
| - ltac_something_show |
| - path: theories/Main/Tarski_dev/Ch07_midpoint.v |
| theorems: |
| - midpoint_def |
| - path: theories/Main/Meta_theory/Parallel_postulates/weak_tarski_s_parallel_postulate_weak_inverse_projection_postulate.v |
| theorems: |
| - weak_tarski_s_parallel_postulate__weak_inverse_projection_postulate |
| - path: theories/Elements/OriginalProofs/proposition_08.v |
| theorems: |
| - proposition_08 |
| - path: theories/Elements/OriginalProofs/proposition_02.v |
| theorems: |
| - proposition_02 |
| - path: theories/Elements/OriginalProofs/lemma_pointreflectionisometry.v |
| theorems: |
| - lemma_pointreflectionisometry |
| - path: theories/Elements/OriginalProofs/lemma_planeseparation.v |
| theorems: |
| - lemma_planeseparation |
| - path: theories/Algebraic/Counter_models/nD/counter_model_five_segment.v |
| theorems: |
| - row_mx_head |
| - path: theories/Main/Meta_theory/Parallel_postulates/SPP_tarski.v |
| theorems: |
| - impossible_case_7 |
| - strong_parallel_postulate_implies_tarski_s_euclid |
| - path: theories/Algebraic/Counter_models/nD/independence.v |
| theorems: |
| - big_pairs_andb_and |
| - path: theories/Main/Meta_theory/Models/tarski_to_coinc_theory_for_col.v |
| theorems: |
| - col_perm_1 |
| - path: theories/Main/Tactics/CoincR_for_concy.v |
| theorems: |
| - ss_ok_empty_for_concy |
| - path: theories/Main/Meta_theory/Models/tarski_to_makarios.v |
| theorems: |
| - five_segment' |
| - path: theories/Elements/OriginalProofs/proposition_12.v |
| theorems: |
| - proposition_12 |
| - path: theories/Elements/OriginalProofs/lemma_lessthancongruence2.v |
| theorems: |
| - lemma_lessthancongruence2 |
| - path: theories/Main/Tarski_dev/Ch15_pyth_rel.v |
| theorems: |
| - Ps_Col |
| - path: theories/Algebraic/Counter_models/nD/dimensional_axioms.v |
| theorems: |
| - nth_basis |
| - path: theories/Elements/OriginalProofs/lemma_collinear5.v |
| theorems: |
| - lemma_collinear5 |
| - path: theories/Elements/OriginalProofs/lemma_samenotopposite.v |
| theorems: |
| - lemma_samenotopposite |
| - path: theories/Elements/OriginalProofs/euclidean_tactics.v |
| theorems: |
| - nCol_notCol |
| - path: theories/Algebraic/Counter_models/nD/counter_model_segment_construction.v |
| theorems: |
| - ncol__nColT |
| - path: theories/Elements/OriginalProofs/lemma_samesidecollinear.v |
| theorems: |
| - lemma_samesidecollinear |
|
|
