Added raw dataset

.gitattributes

@@ -57,3 +57,21 @@ saved_model/**/* filter=lfs diff=lfs merge=lfs -text
 # Video files - compressed
 *.mp4 filter=lfs diff=lfs merge=lfs -text
 *.webm filter=lfs diff=lfs merge=lfs -text
+GeoCoq/eval/*.json filter=lfs diff=lfs merge=lfs -text
+GeoCoq/test/*.json filter=lfs diff=lfs merge=lfs -text
+multilingual/eval/*.json filter=lfs diff=lfs merge=lfs -text
+multilingual/test/*.json filter=lfs diff=lfs merge=lfs -text
+multilingual/train/*.json filter=lfs diff=lfs merge=lfs -text
+lean/eval/*.json filter=lfs diff=lfs merge=lfs -text
+lean/test/*.json filter=lfs diff=lfs merge=lfs -text
+lean/train/*.json filter=lfs diff=lfs merge=lfs -text
+coq/eval/*.json filter=lfs diff=lfs merge=lfs -text
+coq/test/*.json filter=lfs diff=lfs merge=lfs -text
+coq/train/*.json filter=lfs diff=lfs merge=lfs -text
+GeoCoq/train/*.json filter=lfs diff=lfs merge=lfs -text
+math-comp/eval/*.json filter=lfs diff=lfs merge=lfs -text
+math-comp/test/*.json filter=lfs diff=lfs merge=lfs -text
+math-comp/train/*.json filter=lfs diff=lfs merge=lfs -text
+category-theory/eval/*.json filter=lfs diff=lfs merge=lfs -text
+category-theory/test/*.json filter=lfs diff=lfs merge=lfs -text
+category-theory/train/*.json filter=lfs diff=lfs merge=lfs -text

GeoCoq/eval/GeoCoq_eval.yaml

@@ -0,0 +1,403 @@
+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

GeoCoq/eval/local.meta.json

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+oid sha256:ff7b268c4284b95fd0df83e54c6d2c4502727a0d23f513cd555096497a94e646
+size 388

GeoCoq/eval/local_data_0000004928.json

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+version https://git-lfs.github.com/spec/v1
+oid sha256:172135036cf1e0a9657bb6088150e25ebf1ab8e6e68d417017bd4d5d01ae257b
+size 18886874

GeoCoq/eval/local_lemma_0000000000.json

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:d45d1bb11ab18584e9c29bd2b628f2d845f4693962929973a89245afba9ab131
+size 24

GeoCoq/test/GeoCoq_test.yaml

@@ -0,0 +1,788 @@
+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

GeoCoq/test/local.meta.json

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GeoCoq/test/local_data_0000010000.json

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category-theory/eval/category-theory_eval.yaml

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+name: category-theory_eval
+num_files: 31
+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: 43
+datasets:
+- project: <path-to-repo>/category-theory/
+  files:
+  - path: Lib/MapDecide.v
+    theorems:
+    - map_expr_substitution_eq
+    - formula_denote_subst_formula
+  - path: Theory/Isomorphism.v
+    theorems:
+    - from_equiv_implies_iso_equiv
+  - path: Theory/Category.v
+    theorems:
+    - cod_id
+  - path: Instance/Lambda/Step.v
+    theorems:
+    - Value_cannot_start
+  - path: Instance/Lambda/Sem.v
+    theorems:
+    - RenSem_inil
+  - path: Instance/Two/Discrete.v
+    theorems:
+    - TwoDHom_Y_X_absurd
+  - path: Construction/Free/Quiver.v
+    theorems:
+    - tlistDA_morDA
+    - morDA_tlistDA
+    - QuiverHomomorphismEquivalence_Symmetric
+  - path: Structure/Cartesian.v
+    theorems:
+    - fork_comp
+    - exr_split
+    - exr_fork_assoc
+  - path: Construction/Free.v
+    theorems:
+    - morD_sound
+  - path: Structure/Monoidal/Semicartesian/Proofs.v
+    theorems:
+    - proj_right_natural
+  - path: Instance/Fun.v
+    theorems:
+    - nat_id_right
+    - whisker_right_id
+    - whisker_flip
+  - path: Theory/Metacategory/ArrowsOnly.v
+    theorems:
+    - mapsto_inv
+  - path: Construction/Comma/Adjunction.v
+    theorems:
+    - lawvere_from_morph_iso_functorial
+    - lawvere_to_morph_iso_functorial
+    - surjective_tripleF
+  - path: Instance/Lambda/Ren.v
+    theorems:
+    - RenExp_DropAll
+    - Keep_idRen
+  - path: Construction/Product.v
+    theorems:
+    - Product_Opposite
+  - path: Theory/Coq/Map.v
+    theorems:
+    - lookup_delete
+  - path: Theory/Natural/Transformation.v
+    theorems:
+    - fun_id_left
+  - path: Theory/Adjunction.v
+    theorems:
+    - Build_Adjunction'
+  - path: Structure/UniversalProperty/Universal/Arrow.v
+    theorems:
+    - fmap_respects'
+  - path: Tools/Abstraction.v
+    theorems:
+    - ccc_curry
+  - path: Lib/FMapExt.v
+    theorems:
+    - filter_empty
+    - filter_idempotent
+  - path: Structure/Group/Proofs.v
+    theorems:
+    - left_inverse_unique
+  - path: Structure/Monoidal/Proofs.v
+    theorems:
+    - bimap_triangle_left
+    - bimap_triangle_right
+  - path: Instance/Lambda/Multi.v
+    theorems:
+    - values_final
+  - path: Theory/Metacategory/DecideExample.v
+    theorems:
+    - formula_backward_example
+  - path: Structure/Cocartesian.v
+    theorems:
+    - left_comp
+  - path: Instance/Lambda/Norm.v
+    theorems:
+    - step_preserves_SN'
+  - path: Instance/Lambda.v
+    theorems:
+    - composition_assoc_sym
+  - path: Theory/Morphisms.v
+    theorems:
+    - epi_compose
+  - path: Functor/Bifunctor.v
+    theorems:
+    - bimap_id_left_right
+  - path: Instance/Comp.v
+    theorems:
+    - from_free_unique

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+name: category-theory_test
+num_files: 56
+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: 101
+datasets:
+- project: <path-to-repo>/category-theory/
+  files:
+  - path: Tools/Abstraction.v
+    theorems:
+    - forall_distribute
+    - ccc_apply_pair
+  - path: Instance/Fun.v
+    theorems:
+    - "nat_\u03C1"
+    - "nat_\u03BB"
+  - path: Structure/Cartesian.v
+    theorems:
+    - second_id
+    - second_split
+    - exl_second
+    - split_first
+  - path: Instance/Lambda/Full.v
+    theorems:
+    - Plug_injective
+  - path: Construction/Free/Quiver.v
+    theorems:
+    - tlist'_equiv_lengths
+    - transport_comp
+    - tlist_quiver_equiv
+    - Forgetful
+    - transport_quiver_cod
+  - path: Structure/Cartesian/Closed.v
+    theorems:
+    - uncurry_comp
+    - uncurry_inj
+    - eval_first
+  - path: Structure/Monoidal/Braided.v
+    theorems:
+    - Yang_Baxter_equation
+  - path: Instance/Lambda.v
+    theorems:
+    - composition_identity_left
+  - path: Lib/MapDecide.v
+    theorems:
+    - term_denote_subst_term
+    - formula_sound
+  - path: Structure/Bicartesian.v
+    theorems:
+    - fork_merge
+  - path: Functor/Diagonal.v
+    theorems:
+    - Diagonal_Product_Two
+  - path: Instance/Roof.v
+    theorems:
+    - RPos_RNeg_absurd
+    - RPos_RZero_absurd
+  - path: Lib/FMapExt.v
+    theorems:
+    - add_mapsto_iffT
+    - for_all_remove_inv_2
+    - add_equal_iff
+  - path: Theory/Coq/Map.v
+    theorems:
+    - pneq_dec
+    - size_delete
+    - delete_comm
+    - delete_idem
+  - path: Theory/Adjunction.v
+    theorems:
+    - from_adj_unit
+    - counit_fmap_unit
+    - adj_univ
+    - left_adjoint_iso
+  - path: Structure/UniversalProperty.v
+    theorems:
+    - preyoneda
+    - univ_property_unique_up_to_unique_iso
+  - path: Theory/Metacategory/ArrowsOnly.v
+    theorems:
+    - Two_2_object
+    - composition_right
+  - path: Solver/Normal.v
+    theorems:
+    - exprAD_sound'
+    - ex_normalize
+    - from_morphism_to_morphism_r
+  - path: Theory/Coq/Monad/Proofs.v
+    theorems:
+    - arrow_IsMonad
+  - path: Instance/Lambda/Multi.v
+    theorems:
+    - multistep_Fst1
+  - path: Structure/Binoidal.v
+    theorems:
+    - inj_left_right
+  - path: Solver/Decide.v
+    theorems:
+    - expr_sound
+    - ex_categorical
+  - path: Structure/Cocartesian.v
+    theorems:
+    - left_fork
+    - left_right
+  - path: Lib/NETList.v
+    theorems:
+    - netlist_app_length
+    - netlist_concat_app
+  - path: Structure/Monoidal/Semicartesian/Proofs.v
+    theorems:
+    - proj_left_left
+    - proj_right_tensor_id
+  - path: Theory/Functor.v
+    theorems:
+    - ToAFunctor_FromAFunctor
+    - transport_relation_exchange
+    - transport_adjunction
+    - proper_transport_r
+    - fun_equiv_comp_assoc
+    - fun_strict_equiv_id_left
+  - path: Instance/Coq/Monad.v
+    theorems:
+    - join_fmap_fmap_x
+    - join_fmap_ret_x
+  - path: Theory/Morphisms.v
+    theorems:
+    - id_monic
+    - id_epic
+    - id_invol
+  - path: Theory/Coq/Tuple/Proofs.v
+    theorems:
+    - unsplit
+  - path: Theory/Isomorphism.v
+    theorems:
+    - to_equiv_implies_iso_equiv
+  - path: Construction/Free.v
+    theorems:
+    - composition_tapp
+  - path: Instance/Shapes.v
+    theorems:
+    - sized_resized
+    - sized
+  - path: Instance/Lambda/Step.v
+    theorems:
+    - Step_deterministic
+  - path: Instance/Lambda/Ren.v
+    theorems:
+    - RenExp_ValueP
+    - RenVar_idRen
+  - path: Functor/Bifunctor.v
+    theorems:
+    - bimap_id_right_left
+  - path: Instance/Comp.v
+    theorems:
+    - Project
+  - path: Theory/Natural/Transformation.v
+    theorems:
+    - fun_id_right
+  - path: Theory/Coq/List/Proofs.v
+    theorems:
+    - Permutation_insert
+    - Permutation_Forall
+  - path: Monad/Adjunction.v
+    theorems:
+    - Adjunction_Nat_Monad
+  - path: Construction/Comma/Adjunction.v
+    theorems:
+    - lawvere_eqv_counit_fmap_unit
+    - lawvere_to_functorial
+  - path: Adjunction/Hom.v
+    theorems:
+    - hom_unit_naturality_consequence
+  - path: Instance/Lambda/Norm.v
+    theorems:
+    - Exp_SN
+  - path: Instance/Fun/Cartesian.v
+    theorems:
+    - ump_product_auto3
+    - ump_product_auto1
+    - ump_product'
+  - path: Lib/Datatypes.v
+    theorems:
+    - match_last
+    - last_rcons
+    - map_inj
+  - path: Instance/Lambda/Sem.v
+    theorems:
+    - SubSem_idSub
+  - path: Functor/Construction/Product/Monoidal.v
+    theorems:
+    - ProductFunctor_LaxMonoidal_ap_functor_nat
+  - path: Theory/Metacategory/DecideExample.v
+    theorems:
+    - problem3
+  - path: Functor/Hom.v
+    theorems:
+    - Curried_Hom
+  - path: Instance/Parallel.v
+    theorems:
+    - ParHom_Id_false_absurd
+  - path: Structure/Monoidal/Cartesian/Proofs.v
+    theorems:
+    - proj_left_braid
+  - path: Solver/Reify.v
+    theorems:
+    - test_lookup
+  - path: Construction/Cayley.v
+    theorems:
+    - Cayley_Right
+  - path: Theory/Coq/Applicative/Proofs.v
+    theorems:
+    - pure_comp
+  - path: Construction/Comma.v
+    theorems:
+    - comma_proj_com_iso
+  - path: Structure/Terminal.v
+    theorems:
+    - one_comp
+  - path: Structure/Monoidal/Proofs.v
+    theorems:
+    - tensor_id_left_inj

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category-theory/train/category-theory_train.yaml

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+name: category-theory_train
+num_files: 107
+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: 573
+datasets:
+- project: <path-to-repo>/category-theory/
+  files:
+  - path: Structure/Cartesian.v
+    theorems:
+    - exr_first
+    - swap_second
+    - swap_inj_l
+    - exl_fork_comp
+    - first_comp
+    - exl_split
+    - exr_fork
+    - fork_exl_exr
+    - exl'_fork
+    - second_fork
+    - swap_fork
+    - first_id
+    - exr_second
+    - split_comp
+    - first_split
+    - swap_inj_r
+    - split_id
+    - exl_fork
+    - fork'_natural
+    - swap_first
+    - split_second
+    - exr'_fork
+    - first_second
+    - fork_inv
+    - swap_invol
+    - exr_fork_comp
+    - exl_fork_assoc
+    - exl_first
+    - second_comp
+    - split_fork
+    - first_fork
+  - path: Lib/FMapExt.v
+    theorems:
+    - filter_not_in
+    - update_empty_r
+    - MapsTo_singleton
+    - update_add
+    - for_all_remove_inv
+    - Oeq_neq_sym
+    - filter_add_false
+    - for_all_empty
+    - update_empty_l
+    - take_first_None
+    - for_all_impl
+    - remove_add
+    - add_associative
+    - in_mapsto_iff
+    - mapsto_dec
+    - update_find_l
+    - filter_add_false_r
+    - filter_add_true_r
+    - filter_add_true
+    - for_all_add_true
+    - in_mapsto_iffT
+    - for_all_remove
+    - filter_Empty
+    - update_find_r
+    - not_in_mapsto_iff
+    - Proper_Oeq_negb
+  - path: Instance/Parallel.v
+    theorems:
+    - ParHom_inv_t
+    - ParHom_Y_X_absurd
+    - ParHom_inv
+  - path: Structure/Monoidal/Proofs.v
+    theorems:
+    - tensor_id_right_inj
+    - unit_identity
+    - id_unit_left
+    - triangle_identity_right
+    - bimap_id_unit_left
+    - id_unit_right
+    - inverse_pentagon_identity
+    - triangle_identity_left
+    - bimap_unit_right_id
+    - inverse_triangle_identity
+  - path: Structure/Cone.v
+    theorems:
+    - Cocone
+  - path: Tools/Abstraction.v
+    theorems:
+    - ccc_terminal
+    - convert_fork
+    - ccc_apply
+    - ccc_id
+    - distribute_forall
+  - path: Structure/Cocartesian.v
+    theorems:
+    - cover_inl
+    - cover_inr
+    - inr_right
+    - inr_left
+    - inl_right
+    - right_id
+    - paws_invol
+    - right_cover
+    - left_cover
+    - cover_right
+    - inr_merge
+    - paws_left
+    - left_id
+    - right_comp
+    - merge_comp
+    - cover_left
+    - merge_inl_inr
+    - cover_id
+    - right_fork
+    - inl_left
+    - paws_fork
+    - cover_comp
+    - paws_right
+    - inl_merge
+    - merge_inv
+  - path: Construction/Free/Quiver.v
+    theorems:
+    - QuiverComp
+    - transport_comp_mid
+    - tlist'_quiver_equiv_transitive
+    - transport_quiver_dom
+    - tlist'_quiver_equiv_symmetric
+    - QuiverHomomorphismEquivalence_Transitive
+    - QuiverComp
+    - tlist'_quiver_equiv_reflexive
+    - InducedFunctor
+    - transport_id
+    - inductive_implies_fixpoint
+    - fixpoint_implies_inductive
+    - QuiverHomomorphismEquivalence_Reflexive
+    - QuiverHomomorphismOfFunctor
+    - UniversalArrowQuiverCat
+    - UnitQuiverCatAdjunction
+    - transport_r_comp
+  - path: Structure/Monoidal/Closed.v
+    theorems:
+    - curry_inj
+    - curry_uncurry
+    - curry_eval
+    - uncurry_curry
+    - uncurry_inj
+  - path: Theory/Coq/Map.v
+    theorems:
+    - fromList_toList
+    - compress_delete
+    - lookup_insert
+    - insert_delete
+    - MapsTo_lookup
+    - toList_fromList
+    - compress_equiv
+    - size_compress
+  - path: Functor/Structure/Monoidal.v
+    theorems:
+    - ap_iso_to_from
+    - ap_iso_from_to
+  - path: Instance/Lambda/Norm.v
+    theorems:
+    - SubExp_SN
+    - step_preserves_SN
+    - step_preserves_halting
+    - value_halts
+    - strong_normalization
+    - multistep_preserves_SN
+    - normal_forms_unique
+    - multistep_preserves_SN'
+  - path: Structure/Monoidal/Cartesian/Proofs.v
+    theorems:
+    - proj_right_braid
+    - eliminate_left_diagonal
+    - proj_right_left_diagonal
+    - proj_left_id_diagonal
+    - proj_right_id_diagonal
+    - unit_right_eliminate
+    - unit_left_eliminate
+    - proj_left_right_diagonal
+    - eliminate_right_diagonal
+  - path: Lib/MapDecide.v
+    theorems:
+    - formula_substitution_eq
+    - map_expr_size_subst_all_map_expr
+    - find_mapsto_iff_ex
+    - formula_size_subst_formula
+    - term_substitution_eq
+    - term_denote_substitution
+    - formula_size_subst_all_formula
+    - map_expr_denote_subst_map_expr
+    - map_contains_MapsTo
+    - term_beq_sound
+    - map_expr_size_subst_map_expr
+    - terms_not_conflicted
+  - path: Instance/Shapes.v
+    theorems:
+    - Trie_case0
+    - trie_vec
+    - vec_Trie_left
+    - resized_sized
+    - size_unsize
+    - vec_trie
+    - vec_Trie_right
+    - Trie_map_flatten
+    - resized
+    - map_id
+    - map_concat
+    - Trie_right
+    - Trie_left
+    - map_map
+    - map_append
+  - path: Construction/Subcategory.v
+    theorems:
+    - Full_Implies_Full_Functor
+  - path: Instance/Lambda/Full.v
+    theorems:
+    - AppR_LAM
+    - Ctxt_id_left
+    - Ctxt_id_right
+    - strong_progress
+    - Ctxt_comp_assoc
+    - AppL_LAM
+    - Redex_deterministic
+    - Plug_functional
+  - path: Adjunction/Hom.v
+    theorems:
+    - hom_fmap_counit_unit
+    - hom_counit_fmap_unit
+    - hom_counit_naturality_consequence
+  - path: Instance/Sets/Par.v
+    theorems:
+    - from_to_impossible
+    - to_from_impossible
+    - from_to
+    - to_from
+  - path: Theory/Adjunction.v
+    theorems:
+    - fmap_counit_unit
+    - to_adj_unit
+    - to_adj_comp_law
+    - right_adjoint_iso
+    - unit_comp
+    - to_adj_counit
+    - fmap_from_adj_unit
+    - from_adj_respects
+    - from_adj_comp_law
+    - counit_comp
+    - from_adj_counit
+    - adj_univ_impl
+    - fmap_to_adj_counit
+    - adj_monic
+    - to_adj_respects
+  - path: Solver/Normal.v
+    theorems:
+    - exprAD_sound
+    - from_morphism_to_morphism
+    - from_morphism_app_r
+    - append_assoc
+    - from_morphism_app
+    - exprSD_enough
+  - path: Theory/Metacategory/ArrowsOnly.v
+    theorems:
+    - composition_identity_left
+    - Two_2_morphism
+    - composable_pairs_step_disjoint
+    - Two_2_object
+    - composition_respects
+    - composition_associative
+    - peano_rect'
+    - composition_identity_right
+    - composable_pairs_step_find
+    - composable_pairs_succ
+    - composition_left
+    - peano_rect'
+    - find_add_inv
+  - path: Structure/Monoidal/Semicartesian.v
+    theorems:
+    - eliminate_comp
+  - path: Functor/Construction/Product/Monoidal.v
+    theorems:
+    - ProductFunctor_fst_LaxMonoidal_ap_functor_nat
+    - ProductFunctor_Monoidal_proj2_ap_functor_iso
+    - ProductFunctor_LaxMonoidal_proj2_ap_functor_nat
+    - ProductFunctor_proj_LaxMonoidal
+    - ProductFunctor_snd_LaxMonoidal_ap_functor_nat
+    - ProductFunctor_LaxMonoidal_proj1_ap_functor_nat
+  - path: Natural/Transformation/Opposite.v
+    theorems:
+    - Opposite_Transform_invol
+  - path: Structure/BiCCC.v
+    theorems:
+    - unmerge_uncurry
+    - uncurry_merge
+  - path: Instance/Two/Discrete.v
+    theorems:
+    - TwoDHom_inv_t
+    - TwoDHom_inv
+    - TwoDHom_X_Y_absurd
+  - path: Lib/NETList.v
+    theorems:
+    - netlist_find_sublist_app
+    - netlist_rev_length
+    - netlist_concat_tadd
+    - netlist_rev_unit
+    - netlist_rev_involutive
+    - netlist_find_sublist_nat_ex1
+    - netlist_app_assoc
+    - netlist_cons_uncons
+    - netlist_app_comm_cons
+    - netlist_rev_app_distr
+  - path: Theory/Coq/Monad/Proofs.v
+    theorems:
+    - Identity_IsMonad
+    - Compose_IsMonad
+  - path: Theory/Coq/List/Proofs.v
+    theorems:
+    - olast_spec
+    - olast_last
+    - sortBy_sorted
+    - olast_cons
+    - Forall_insert
+    - Permutation_sortBy
+    - StronglySorted_insert
+    - Forall_append
+    - StronglySorted_cat
+    - Forall_ordered
+  - path: Theory/Isomorphism.v
+    theorems:
+    - iso_sym_right_inverse
+    - iso_sym_left_inverse
+    - to_equiv_implies_iso_equiv
+    - to_equiv_implies_iso_equiv
+  - path: Structure/Monoidal/Relevance.v
+    theorems:
+    - braid2_natural
+  - path: Theory/Coq/Maybe/Proofs.v
+    theorems:
+    - ap_endo_nothing
+    - fmap_endo_nothing
+    - alt_endo_nothing
+    - bind_endo_just
+    - fmap_endo_just
+    - Maybe_choose_spec
+    - bind_endo_nothing
+    - alt_endo_just
+    - ap_endo_just
+  - path: Lib/TList.v
+    theorems:
+    - tlist_concat_tnil
+    - tlist_rev_length
+    - tlist_app_assoc
+    - tlist_app_cons
+    - tlist_app_length
+    - tlist_app_tnil_r
+    - tlist_rev_involutive
+    - tlist_rev_unit
+    - tlist_rev_app_distr
+    - tlist_concat_app
+    - tlist_app_comm_cons
+    - tlist_concat_tcons
+    - tlist_app_tnil_l
+  - path: Lib/Datatypes.v
+    theorems:
+    - Forall_app
+    - let_projT1
+    - last_app_cons
+    - length_remove
+    - last_Forall
+    - Acc_symprod2
+    - let_snd
+    - list_rect2
+    - last_cons
+    - let_projT2
+    - let_fst
+    - wf_symprod2
+  - path: Structure/Cartesian/Closed.v
+    theorems:
+    - curry_comp
+    - curry_inj
+    - uncurry_comp_r
+    - curry_unfork
+    - curry_id
+    - uncurry_curry
+    - curry_uncurry
+    - curry_fork
+    - eval_curry
+    - curry_eval
+    - curry_comp_l
+  - path: Theory/Morphisms.v
+    theorems:
+    - sections_are_monic
+    - flip_Retraction
+    - retractions_are_epic
+    - flip_invol
+    - id_idem
+    - flip_Section
+    - monic_compose
+  - path: Instance/Lambda/Sem.v
+    theorems:
+    - SubSem_ScR
+    - RenSem_idRen
+    - SemExp_wk
+    - SubSem_ScS
+    - SemVar_SubSem
+    - SemExp_RenSem
+    - ScR_idRen
+    - SubSem_RcS
+    - SubSem_inil
+    - SemExp_SubSem
+    - RenSem_RcR
+    - RenSem_skip1
+    - SemVar_RenSem
+  - path: Theory/Universal/Arrow.v
+    theorems:
+    - AdjunctionFromUniversalArrows
+    - ump_universal_arrows
+    - universal_arrow_from_UMP
+    - LeftAdjointFunctorFromUniversalArrows
+  - path: Instance/Lambda/Multi.v
+    theorems:
+    - multi_trans
+    - multi_R
+    - multistep_Snd1
+    - multistep_Pair
+    - multistep_Pair2
+    - multistep_AppR
+    - multistep_Pair1
+  - path: Theory/Functor.v
+    theorems:
+    - fun_equiv_id_left
+    - fun_equiv_id_right
+    - fun_equiv_fmap_from
+    - fun_strict_equiv_comp_assoc
+    - transport_functorial_dom
+    - proper_transport_r
+    - transport_trans
+    - FullyFaithful
+    - transport_f_equal
+    - transport_functorial_cod
+    - FromAFunctor_ToAFunctor
+    - proper_transport_r
+    - proper_transport
+    - fun_equiv_to_fmap
+    - fun_strict_equiv_id_right
+    - fobj_Compose
+    - transport_r_trans
+  - path: Instance/Comp.v
+    theorems:
+    - Bool
+    - Product
+    - component_compose
+    - component_compose
+    - component_compose
+    - component_compose
+    - GroupEq
+    - induced_hom
+  - path: Functor/Structure/Cartesian/Closed.v
+    theorems:
+    - exp_out_inj
+    - exp_out_in
+    - exp_in_inj
+    - fmap_eval
+    - exp_in_out
+  - path: Theory/Coq/Tuple/Proofs.v
+    theorems:
+    - fst_snd
+    - uncurry_works
+  - path: Solver/Reify.v
+    theorems:
+    - test_reifyExpr
+    - test_addToObjList
+    - test_allObjs
+    - test_addToCatList
+    - test_catLists
+    - test_reifyTerm
+    - test_toList
+    - ex_find_vars
+    - ex_reify_and_change
+    - test_lookupObj
+    - test_listSize
+    - test_updateCat
+    - test_lookupCat
+    - test_lookupArr
+    - test_reifyObj
+    - test_addToList
+    - test_addToArrList
+    - test_allVars
+  - path: Instance/Cat.v
+    theorems:
+    - Cat_Iso_from_Full
+  - path: Structure/UniversalProperty/Universal/Arrow.v
+    theorems:
+    - UniversalArrowIsUniversalProperty
+  - path: Instance/Sets.v
+    theorems:
+    - surjectivity_is_epic
+    - bijective_is_iso
+    - injectivity_is_monic
+    - setoid_morphism_compose_respects
+  - path: Theory/Coq/Functor/Proofs.v
+    theorems:
+    - compose_fmap
+  - path: Theory/Natural/Transformation.v
+    theorems:
+    - fun_id_right_and_sym
+    - fun_id_right_sym_and
+    - fun_comp_assoc
+    - fun_id_left_sym
+    - fun_id_right_sym
+    - fun_comp_assoc_and_sym
+    - Build_Transform'
+    - nat_compose_respects
+    - fun_comp_assoc_sym
+    - fun_comp_assoc_sym_and
+    - fun_id_left_and_sym
+    - fun_id_left_sym_and
+  - path: Instance/Roof.v
+    theorems:
+    - RZero_RPos_id
+    - RNeg_RZero_absurd
+    - RNeg_RNeg_id
+    - RoofHom_inv
+    - RNeg_RPos_absurd
+    - RoofHom_inv_t
+  - path: Instance/Lambda.v
+    theorems:
+    - composition_assoc
+    - composition_identity_right
+    - SemExp_identity
+    - SemExp_composition
+  - path: Instance/Two.v
+    theorems:
+    - TwoHom_inv_t
+    - TwoHom_Y_X_absurd
+    - TwoHom_inv
+  - path: Instance/Fun.v
+    theorems:
+    - "nat_\u03B1"
+    - "nat_\u03B1_whisker_assoc"
+    - whisker_right_dist
+    - whisker_left_dist
+    - "nat_\u03B1_whisker_right_comp"
+    - "nat_\u03B1_whisker_left_comp"
+    - nat_id_left
+    - whisker_left_id
+    - nat_comp_assoc
+    - "nat_\u03B1_nat_\u03B1"
+    - Functor_Setoid_Nat_Iso
+    - whisker_left_right
+  - path: Instance/Cones/Comma.v
+    theorems:
+    - Cones_Comma
+    - Cones_to_Comma
+    - Cones_from_Comma
+  - path: Construction/Product.v
+    theorems:
+    - fst_comp
+    - snd_comp
+  - path: Theory/Coq/Applicative/Proofs.v
+    theorems:
+    - Compose_IsApplicative
+    - compose_ap
+    - Identity_IsApplicative
+    - ap_comp
+    - arrow_IsApplicative
+  - path: Instance/One/Diagonal.v
+    theorems:
+    - Diagonal_Unique
+  - path: Structure/Monoidal/Naturality.v
+    theorems:
+    - monoidal_naturality
+  - path: Instance/Lambda/Step.v
+    theorems:
+    - AppR_LAM
+    - strong_progress
+    - AppL_LAM
+    - value_is_nf
+    - Value_irreducible
+  - path: Functor/Bifunctor.v
+    theorems:
+    - bimap_id_id
+    - bimap_comp
+    - bimap_fmap
+    - bimap_comp_id_left
+    - bimap_comp_id_right
+  - path: Instance/Fun/Cartesian.v
+    theorems:
+    - ump_product_auto4
+    - ump_product_auto4
+    - fmap_respects'
+    - ump_product_auto2
+  - path: Structure/Group/Proofs.v
+    theorems:
+    - mappend_inverse
+    - mempty_left_diagonal
+    - mempty_right_diagonal
+  - path: Structure/Initial.v
+    theorems:
+    - zero_comp
+  - path: Adjunction/Natural/Transformation/Opposite.v
+    theorems:
+    - Opposite_Adjunction_Transform_invol
+  - path: Instance/Lambda/Ren.v
+    theorems:
+    - DropAll_nil_idRen
+    - RenExp_idRen
+    - RenExp_preserves_size
+    - NoRen_idRen
+    - Keep_RcR
+    - RcR_idRen_right
+    - RcR_idRen_left
+    - RenVar_RcR
+    - RcR_assoc
+    - RenVar_skip1
+    - RenExp_RcR
+  - path: Structure/UniversalProperty.v
+    theorems:
+    - univ_property_respects_iso
+    - univ_property_unique
+    - representability_by_yoneda
+  - path: Theory/Metacategory/DecideExample.v
+    theorems:
+    - map_decide_test
+    - problem4
+    - problem5
+    - problem100
+  - path: Construction/Comma/Adjunction.v
+    theorems:
+    - lawvere_iso_to_from
+    - Left_Functoriality
+    - lawvere_from_to
+    - "\u03BC_\u03BA_\u03B8"
+    - "\u03C6_\u03C8_equiv"
+    - lawvere_iso_from
+    - lawvere_iso_from_to
+    - "\u03C8_\u03C6_equiv"
+    - "\u03B7_\u03B8_\u03BA"
+    - "expand_\u03C6_\u03C8"
+    - lawvere_iso_to
+    - Adjunction_Comma
+    - lawvere_eqv_fmap_counit_unit
+    - surjective_tripleG
+    - lawvere_to_from
+    - Right_Functoriality
+    - "expand_\u03C8_\u03C6"
+    - lawvere_from_functorial
+  - path: Instance/Lambda/Log.v
+    theorems:
+    - ExpP_P
+    - ExpR_R
+  - path: Functor/Hom.v
+    theorems:
+    - Yoneda_Embedding'
+    - Curried_Hom
+  - path: Theory/Category.v
+    theorems:
+    - dom_id
+    - cod_comp
+    - dom_comp
+    - Build_Category'_Coq
+  - path: Construction/Free.v
+    theorems:
+    - morDA_tlistDA
+    - tlistDA_morDA
+    - composition_tnil
+  - path: Construction/Enriched.v
+    theorems:
+    - Functor_is_Enriched_over_Set
+    - Category_is_Enriched_over_Set
+  - path: Instance/Lambda/Value.v
+    theorems:
+    - ValueP_dec
+    - ValueP_irrelevance
+  - path: Monad/Kleisli.v
+    theorems:
+    - monad_id_right
+    - monad_comp_assoc
+    - monad_id_left
+  - path: Structure/UniversalProperty/Limit.v
+    theorems:
+    - LimitIsUniversalProperty
+    - ump_limit_construct_proper
+    - cone_coherence_auto1
+    - cone_equiv_to_morphism_equiv
+    - ump_limit_construct_recover
+    - ump_limit_construct_recover'
+    - ump_limit_construct
+  - path: Construction/Cayley.v
+    theorems:
+    - Cayley_Left
+  - path: Functor/Diagonal.v
+    theorems:
+    - Diagonal_Product_Two
+  - path: Functor/Structure/Cartesian.v
+    theorems:
+    - prod_out_in
+    - prod_out_inj
+    - prod_in_inj
+    - prod_in_out
+  - path: Construction/Opposite.v
+    theorems:
+    - op_invol
+  - path: Theory/Kan/Extension.v
+    theorems:
+    - left_adjoint_impl
+    - left_adjoints_preserve
+  - path: Adjunction/Opposite.v
+    theorems:
+    - Opposite_Adjunction_invol
+  - path: Lib/IList.v
+    theorems:
+    - ith
+    - ith_exact
+  - path: Structure/Limit/Cartesian.v
+    theorems:
+    - Cartesian_Limit
+  - path: Structure/Monoid.v
+    theorems:
+    - uncurry_exl_fork_exr
+    - mappend_assoc_sym
+  - path: Instance/Lambda/Sound.v
+    theorems:
+    - soundness
+  - path: Theory/Coq/List.v
+    theorems:
+    - oends
+  - path: Structure/Cone/Const.v
+    theorems:
+    - Cone_Comma
+    - Cone_Natural_Transform
+  - path: Functor/Structure/Monoidal/Pure.v
+    theorems:
+    - pure_natural
+    - fmap_pure
+  - path: Structure/Monoidal/Symmetric.v
+    theorems:
+    - bimap_braid
+    - braid_bimap_braid
+    - hexagon_rotated
+  - path: Instance/Poset.v
+    theorems:
+    - eq_equiv
+  - path: Monad/Monoid.v
+    theorems:
+    - Monoid_Monad
+  - path: Solver/Decide.v
+    theorems:
+    - expr_tauto
+  - path: Functor/Traversable/Product.v
+    theorems:
+    - ProductFunctor_Traversable_ap_functor_nat
+  - path: Instance/Coq/Monad.v
+    theorems:
+    - join_fmap_join_x
+    - join_ret_x
+  - path: Structure/UniversalProperty/Cartesian.v
+    theorems:
+    - CartesianProductIsUniversalProperty
+  - path: Instance/Lambda/Exp.v
+    theorems:
+    - Exp_size_preserved
+  - path: Functor/Opposite.v
+    theorems:
+    - Opposite_Functor_invol
+  - path: Construction/Product/Comma.v
+    theorems:
+    - Comma_Product
+  - path: Structure/Monoidal/Semicartesian/Proofs.v
+    theorems:
+    - proj_right_right
+    - proj_left_tensor_id
+    - proj_left_natural
+  - path: Construction/Comma.v
+    theorems:
+    - comma_proj_mor_iso
+  - path: Structure/Limit/Kan/Extension.v
+    theorems:
+    - Kan_Limit
+  - path: Structure/Monoidal/Internal/Product.v
+    theorems:
+    - exl_swap
+    - exr_swap
+  - path: Structure/Limit/Terminal.v
+    theorems:
+    - Terminal_Limit
+  - path: Structure/Monoidal/Semicocartesian.v
+    theorems:
+    - generate_comp
+  - path: Monad/Adjunction.v
+    theorems:
+    - Adjunction_Monad

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