| 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 | |