| name: GeoCoq_eval | |
| num_files: 92 | |
| 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: 208 | |
| datasets: | |
| - project: <path-to-repo>/GeoCoq | |
| files: | |
| - path: theories/Algebraic/Counter_models/Planar/counter_model_cong_pseudo_reflexivity.v | |
| theorems: | |
| - cong_inner_transitivity | |
| - segment_construction | |
| - path: theories/Main/Annexes/quadrilaterals_inter_dec.v | |
| theorems: | |
| - rmb_perp | |
| - half_plgs | |
| - par_strict_cong_mid | |
| - Plg_perm | |
| - path: theories/Main/Tarski_dev/Ch05_bet_le.v | |
| theorems: | |
| - lt_comm | |
| - le_reflexivity | |
| - path: theories/Coinc/Utils/sets.v | |
| theorems: | |
| - leb_dec | |
| - lt | |
| - sortOK | |
| - path: theories/Main/Annexes/coplanar.v | |
| theorems: | |
| - reflectl__coplanar | |
| - coplanar_perm_3 | |
| - path: theories/Main/Meta_theory/Models/beeson_to_tarski.v | |
| theorems: | |
| - IT_dec | |
| - BetT_dec | |
| - path: theories/Main/Tarski_dev/Ch11_angles.v | |
| theorems: | |
| - in_angle_out | |
| - cong_lt_per2__lt_1 | |
| - cong3_diff2 | |
| - cong__acute | |
| - t18_18_aux | |
| - suppa_sym | |
| - suppa__per | |
| - angle_construction_3 | |
| - col_orth__orth | |
| - orth_at_dec | |
| - out_suppa__bet | |
| - cop3_orth__orth | |
| - acute_sym | |
| - orth_at__ncop2 | |
| - bet__obtuse | |
| - lta_suppa2__lta | |
| - l11_62_existence_bis | |
| - l11_18_1 | |
| - path: theories/Main/Tarski_dev/Ch12_parallel.v | |
| theorems: | |
| - par_col4__par | |
| - par_not_col | |
| - par_strict_all_one_side | |
| - l12_17 | |
| - line_dec | |
| - par_col2_par | |
| - path: theories/Main/Tarski_dev/Ch10_line_reflexivity.v | |
| theorems: | |
| - osym_not_col | |
| - midpoint_preserves_image | |
| - l10_4 | |
| - path: theories/Main/Meta_theory/Models/hilbert_to_tarski.v | |
| theorems: | |
| - betH_trans | |
| - congH_perms | |
| - betH_colH | |
| - addition_betH | |
| - same_side_prime__plane | |
| - playfair_s_postulateH | |
| - betH_to_bet | |
| - path: theories/Main/Tarski_dev/Ch16_coordinates.v | |
| theorems: | |
| - l16_9_1 | |
| - path: theories/Main/Tarski_dev/Ch13_4_cos.v | |
| theorems: | |
| - lcos3_permut1 | |
| - lcos_not_lg_null | |
| - lcos2_uniqueness | |
| - lcos3_eq_trans | |
| - path: theories/Coinc/ColR.v | |
| theorems: | |
| - positive_dec | |
| - proper_7 | |
| - path: theories/Main/Annexes/sums.v | |
| theorems: | |
| - sums__eq34 | |
| - sums_sym | |
| - path: theories/Main/Tarski_dev/Ch03_bet.v | |
| theorems: | |
| - lower_dim_ex | |
| - path: theories/Main/Annexes/quadrilaterals.v | |
| theorems: | |
| - Rectangle_Parallelogram | |
| - col_cong_mid2 | |
| - col_cong_mid1 | |
| - mid_plg_2 | |
| - parallelogram_strict_not_col_2 | |
| - plg_to_parallelogram | |
| - path: theories/Algebraic/Counter_models/nD/counter_model_upper_dim.v | |
| theorems: | |
| - bet_nD'_2D | |
| - path: theories/Elements/OriginalProofs/euclidean_tactics.v | |
| theorems: | |
| - neq_or_eq | |
| - path: theories/Algebraic/Counter_models/nD/counter_model_euclid.v | |
| theorems: | |
| - cong_abab | |
| - i2'_in_unit_disk | |
| - one_side_cong'_eq | |
| - p_scalar_point_lt1 | |
| - d'_in_unit_disk | |
| - lower_dim | |
| - nbet_bca | |
| - path: theories/Main/Annexes/suma.v | |
| theorems: | |
| - bet2_suma__out | |
| - sams_nos__nts | |
| - inangle__sams | |
| - conga3_suma__suma | |
| - suma_assoc_2 | |
| - out213__suma | |
| - sams_suma__out546 | |
| - trisuma_perm_231 | |
| - path: theories/Algebraic/Counter_models/nD/counter_model_five_segment.v | |
| theorems: | |
| - bet_symmetry | |
| - path: theories/Main/Tarski_dev/Ch08_orthogonality.v | |
| theorems: | |
| - per_distinct_1 | |
| - l8_16_1 | |
| - l8_16_2 | |
| - perp_exists | |
| - col_per2_cases | |
| - perp_proj | |
| - l8_8 | |
| - path: theories/Main/Tarski_dev/Ch02_cong.v | |
| theorems: | |
| - cong_symmetry | |
| - path: theories/Algebraic/Counter_models/Planar/counter_model_bet_inner_transitivity.v | |
| theorems: | |
| - segment_construction | |
| - path: theories/Main/Tarski_dev/Ch14_sum.v | |
| theorems: | |
| - sum_exists | |
| - path: theories/Algebraic/Counter_models/nD/gupta_inspired_to_independent_version.v | |
| theorems: | |
| - segment_constructionG_f | |
| - path: theories/Main/Meta_theory/Continuity/completeness.v | |
| theorems: | |
| - extension_to_plane__plane | |
| - path: theories/Main/Meta_theory/Models/tarski_to_euclid.v | |
| theorems: | |
| - Euclid_neutral_ruler_compass_follows_from_Tarski_ruler_and_compass | |
| - inside | |
| - path: theories/Main/Tarski_dev/Ch16_coordinates_with_functions.v | |
| theorems: | |
| - signed_area_perm | |
| - twice_signed_area_perm | |
| - Col_AM_Col | |
| - path: theories/Main/Meta_theory/Continuity/first_order.v | |
| theorems: | |
| - fof__fof1 | |
| - fof1__fof | |
| - path: theories/Main/Tarski_dev/Ch13_1.v | |
| theorems: | |
| - symmetry_preserves_per | |
| - path: theories/Main/Annexes/Tagged_predicates.v | |
| theorems: | |
| - NCol_tagged_NCol | |
| - Diff_tagged_Diff | |
| - Par_Par_tagged | |
| - path: theories/Main/Elements_statements/Book_1.v | |
| theorems: | |
| - prop_27 | |
| - path: theories/Main/Tarski_dev/Ch13_2_length.v | |
| theorems: | |
| - lg_null_instance | |
| - path: theories/Main/Tarski_dev/Ch14_order.v | |
| theorems: | |
| - neg_not_pos | |
| - col_2_le_or_ge | |
| - path: theories/Main/Highschool/concyclic.v | |
| theorems: | |
| - concyclic_perm_17 | |
| - path: theories/Algebraic/POF_to_Tarski.v | |
| theorems: | |
| - upper_dim_aux | |
| - extension_contraction | |
| - c2D_neq0 | |
| - betS_inner_transitivity | |
| - bet_colF | |
| - mulmx_tr | |
| - cong_perp_aux1 | |
| - euclid'' | |
| - contraction_betS | |
| - path: theories/Main/Tarski_dev/Ch15_lengths.v | |
| theorems: | |
| - signEq_refl | |
| - pyth_context | |
| - bet_leP | |
| - ltP_pos | |
| - path: theories/Algebraic/coplanarity.v | |
| theorems: | |
| - l9_33 | |
| - path: theories/Main/Tarski_dev/Ch13_5_Pappus_Pascal.v | |
| theorems: | |
| - lcos_per_anga | |
| - l13_10_aux4 | |
| - path: theories/Main/Annexes/vectors.v | |
| theorems: | |
| - eqv_refl | |
| - path: theories/Elements/OriginalProofs/proposition_47A.v | |
| theorems: | |
| - proposition_47A | |
| - path: theories/Algebraic/Counter_models/Planar/counter_model_cong_inner_transitivity.v | |
| theorems: | |
| - euclid | |
| - path: theories/Elements/OriginalProofs/proposition_30B.v | |
| theorems: | |
| - proposition_30B | |
| - path: theories/Main/Tarski_dev/Ch13_3_angles.v | |
| theorems: | |
| - is_anga_distinct | |
| - anga_not_null_lg | |
| - eqA_preserves_ang | |
| - anga_conga_anga | |
| - path: theories/Main/Annexes/half_angles.v | |
| theorems: | |
| - col_halfa__out | |
| - ghalfa_preserves_conga_1 | |
| - ghalfa__acute | |
| - path: theories/Main/Annexes/project.v | |
| theorems: | |
| - project_preserves_eqv | |
| - projp_col | |
| - projp2_col | |
| - path: theories/Main/Meta_theory/Continuity/first_order_dedekind_circle_circle.v | |
| theorems: | |
| - fod__circle_circle | |
| - path: theories/Algebraic/Counter_models/Planar/counter_model_lower_dim.v | |
| theorems: | |
| - euclid | |
| - bet_inner_transitivity | |
| - path: theories/Algebraic/Counter_models/nD/counter_model_bet_inner_transitivity.v | |
| theorems: | |
| - col__Col_13 | |
| - cong_inner_transitivity | |
| - path: theories/Algebraic/Counter_models/Planar/counter_model_euclid.v | |
| theorems: | |
| - betR_abc | |
| - c'_norm | |
| - path: theories/Main/Meta_theory/Continuity/dedekind_cantor.v | |
| theorems: | |
| - nested__diff | |
| - path: theories/Main/Tarski_dev/Ch09_plane.v | |
| theorems: | |
| - col_cop2__cop | |
| - l9_38 | |
| - coplanar_pseudo_trans | |
| - one_side_symmetry | |
| - per_col_eq | |
| - l9_19 | |
| - path: theories/Main/Annexes/circles.v | |
| theorems: | |
| - circle_circle_os | |
| - outc_eq | |
| - ray_cut_chord | |
| - bet_inc2__inc | |
| - onc2_per__mid | |
| - Prop_7_8_uniqueness | |
| - path: theories/Main/Meta_theory/Decidability/equivalence_between_decidability_properties_of_basic_relations.v | |
| theorems: | |
| - bet_dec_eq_dec | |
| - path: theories/Main/Meta_theory/Models/tarski_to_hilbert.v | |
| theorems: | |
| - between_one | |
| - OS_same_side' | |
| - path: theories/Main/Tarski_dev/Ch04_col.v | |
| theorems: | |
| - col_permutation_5 | |
| - path: theories/Algebraic/Counter_models/nD/counter_model_cong_pseudo_reflexivity.v | |
| theorems: | |
| - segment_construction | |
| - bet_inner_transitivity | |
| - path: theories/Main/Meta_theory/Parallel_postulates/parallel_postulates.v | |
| theorems: | |
| - equivalent_postulates_without_decidability_of_intersection_of_lines_bis | |
| - path: theories/Main/Tarski_dev/Ch14_prod.v | |
| theorems: | |
| - prod_x_axis_unit_change | |
| - path: theories/Elements/OriginalProofs/lemma_ray5.v | |
| theorems: | |
| - lemma_ray5 | |
| - path: theories/Main/Meta_theory/Parallel_postulates/par_trans_NID.v | |
| theorems: | |
| - playfair__playfair_quater | |
| - path: theories/Main/Meta_theory/Parallel_postulates/rah_existential_saccheri.v | |
| theorems: | |
| - rah__existential_saccheri | |
| - path: theories/Main/Tarski_dev/Ch07_midpoint.v | |
| theorems: | |
| - Mid_cases | |
| - col_bet2_cong2 | |
| - bet2_lt2__lt | |
| - midpoint_distinct_1 | |
| - midpoint_out_1 | |
| - path: theories/Algebraic/Counter_models/counter_model_bet_identity.v | |
| theorems: | |
| - cong_aux_2 | |
| - path: theories/Algebraic/Counter_models/nD/counter_model_bet_symmetry.v | |
| theorems: | |
| - onemx_neq0 | |
| - path: theories/Elements/OriginalProofs/proposition_05b.v | |
| theorems: | |
| - proposition_05b | |
| - path: theories/Main/Meta_theory/Models/tarski_to_gupta_inspired.v | |
| theorems: | |
| - T_euclidean_to_TG_euclidean | |
| - path: theories/Main/Tactics/CoincR_for_concy.v | |
| theorems: | |
| - st_ok_empty_for_concy | |
| - path: theories/Main/Meta_theory/Continuity/dedekind_completeness.v | |
| theorems: | |
| - extension_image_density | |
| - path: theories/Algebraic/Counter_models/nD/independent_version_to_beeson.v | |
| theorems: | |
| - ITbetween_inner_transitivity | |
| - path: theories/Coinc/Utils/arity.v | |
| theorems: | |
| - nthCircPerm1Eq | |
| - pred_conj_aux | |
| - path: theories/Algebraic/Counter_models/nD/bet_identity.v | |
| theorems: | |
| - g2_2 | |
| - g2_6_2 | |
| - path: theories/Main/Meta_theory/Models/tarski_to_coinc_theory_for_cop.v | |
| theorems: | |
| - not_col_perm_1 | |
| - path: theories/Coinc/CoincR.v | |
| theorems: | |
| - interp_CPHdOK | |
| - path: theories/Main/Highschool/incenter.v | |
| theorems: | |
| - incenter_permut213 | |
| - path: theories/Algebraic/Counter_models/Planar/counter_model_bet_symmetry.v | |
| theorems: | |
| - parP | |
| - path: theories/Elements/OriginalProofs/lemma_samesidereflexive.v | |
| theorems: | |
| - lemma_samesidereflexive | |
| - path: theories/Main/Meta_theory/Continuity/elementary_continuity_props.v | |
| theorems: | |
| - segment_circle__one_point_line_circle | |
| - path: theories/Elements/OriginalProofs/proposition_31short.v | |
| theorems: | |
| - proposition_31short | |
| - path: theories/Main/Tarski_dev/Ch13_6_Desargues_Hessenberg.v | |
| theorems: | |
| - l13_19 | |
| - path: theories/Main/Meta_theory/Continuity/angle_archimedes.v | |
| theorems: | |
| - archi_in_acute_angles | |
| - angles_archi_aux | |
| - path: theories/Main/Highschool/orientation.v | |
| theorems: | |
| - symmetry_preserves_bet | |
| - path: theories/Main/Annexes/inscribed_angle.v | |
| theorems: | |
| - suma__suppa | |
| - path: theories/Elements/OriginalProofs/proposition_23C.v | |
| theorems: | |
| - proposition_23C | |
| - path: theories/Elements/OriginalProofs/lemma_collinearbetween.v | |
| theorems: | |
| - lemma_collinearbetween | |
| - path: theories/Elements/OriginalProofs/lemma_RTsymmetric.v | |
| theorems: | |
| - lemma_RTsymmetric | |
| - path: theories/Main/Highschool/SegmTrisect.v | |
| theorems: | |
| - SegmTrisectSecondThirdExistence | |
| - path: theories/Main/Annexes/defect.v | |
| theorems: | |
| - defect_perm_312 | |
| - path: theories/Elements/OriginalProofs/lemma_3_6b.v | |
| theorems: | |
| - lemma_3_6b | |
| - path: theories/Algebraic/Counter_models/Planar/counter_model_upper_dim.v | |
| theorems: | |
| - bc_neq | |
| - path: theories/Elements/OriginalProofs/lemma_TCreflexive.v | |
| theorems: | |
| - lemma_TCreflexive | |