| name: math-comp_test | |
| num_files: 65 | |
| 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: 536 | |
| datasets: | |
| - project: <path-to-repo>/math-comp/ | |
| files: | |
| - path: mathcomp/algebra/ssralg.v | |
| theorems: | |
| - telescope_prodf_eq | |
| - opp_fun_is_additive | |
| - scalerK | |
| - iter_mulr_1 | |
| - prodf_seq_eq0 | |
| - invr0 | |
| - exprSr | |
| - mulC_unitP | |
| - invrZ | |
| - mulVKr | |
| - scalerDr | |
| - in_alg_is_rmorphism | |
| - fst_is_multiplicative | |
| - prodrXl | |
| - natrX | |
| - rmorph_sum | |
| - addUC | |
| - opp_fun_is_scalable | |
| - rmorphMNn | |
| - exprDn_comm | |
| - eqr_opp | |
| - expfB_cond | |
| - rmorphN1 | |
| - exprM | |
| - fpredMr | |
| - pair_scaleA | |
| - scalerN | |
| - path: mathcomp/algebra/matrix.v | |
| theorems: | |
| - adj1 | |
| - mxrowEblock | |
| - cormen_lup_detL | |
| - mul_col_mx | |
| - map2_row' | |
| - eq_mx | |
| - thinmxOver | |
| - mxtrace_mxdiag | |
| - invmxK | |
| - map_xrow | |
| - row_dsubmx | |
| - mulmxr_is_linear | |
| - block_mxA | |
| - col_ind | |
| - tr_submxcol | |
| - scalar_mx_is_semi_additive | |
| - row'Ku | |
| - trmx_ursub | |
| - mul_mx_diag | |
| - lift0_mx_is_perm | |
| - row_perm_key | |
| - map_castmx | |
| - mxblockB | |
| - submxcolD | |
| - path: mathcomp/algebra/ssrnum.v | |
| theorems: | |
| - deg2_poly_gt0 | |
| - ltr_pdivrMr | |
| - lt0r | |
| - sqr_norm_eq1 | |
| - lerXn2r | |
| - minr_pMl | |
| - le_total | |
| - Nreal_leF | |
| - real_lteif_distl | |
| - ler_nM2r | |
| - mulr_sign_lt0 | |
| - ler_ndivlMr | |
| - ring_display | |
| - ler_wiXn2l | |
| - lern1 | |
| - sqrtr_sqr | |
| - ltrP | |
| - le_def' | |
| - mulr_ile1 | |
| - aNge0 | |
| - real_exprn_odd_le0 | |
| - gtrDr | |
| - pnatr_eq0 | |
| - ler_pMn2l | |
| - bigmax_real | |
| - sqrtr_eq0 | |
| - real_ltr_normlW | |
| - ltr_nMn2l | |
| - mulr_ilt1 | |
| - psumr_neq0P | |
| - deg2_poly_root2 | |
| - exprn_odd_ge0 | |
| - real_ltr_distl | |
| - real_lteifNE | |
| - ler_rootCl | |
| - real_neqr_lt | |
| - normr_ge0 | |
| - le_def' | |
| - ler01 | |
| - real_ltrNnormlW | |
| - ge0_def | |
| - normrN1 | |
| - sgrN1 | |
| - natr_indexg_gt0 | |
| - sgr_odd | |
| - agt0 | |
| - ieexprIn | |
| - path: mathcomp/ssreflect/ssrnat.v | |
| theorems: | |
| - mul2n | |
| - odd_gt2 | |
| - leqif_geq | |
| - subn2 | |
| - leq_pmulr | |
| - homo_leq_in | |
| - gtn_min | |
| - contra_ltnT | |
| - half_gt0 | |
| - sqrnD | |
| - mulE | |
| - subnA | |
| - doubleMr | |
| - uphalfK | |
| - predn_sub | |
| - iterD | |
| - mul_expE | |
| - mulnSr | |
| - leqif_add | |
| - path: mathcomp/ssreflect/bigop.v | |
| theorems: | |
| - big_tnth | |
| - eq_big_idem | |
| - dvdn_biggcdP | |
| - big_ord1_cond_eq | |
| - addmA | |
| - big_all_cond | |
| - big_uniq | |
| - opm1 | |
| - eq_bigl | |
| - eq_bigmax | |
| - big_rcons | |
| - bigA_distr_bigA | |
| - big_sumType | |
| - eq_big | |
| - big_tuple | |
| - path: mathcomp/fingroup/morphism.v | |
| theorems: | |
| - morphim_normal | |
| - kerE | |
| - morphimEdom | |
| - sgvalmK | |
| - isog_symr | |
| - morphpre_sub | |
| - isogEcard | |
| - path: mathcomp/algebra/polydiv.v | |
| theorems: | |
| - dvdp_XsubCl | |
| - gcd1p | |
| - rdvdpp | |
| - rdvd0p | |
| - divpp | |
| - coprimepP | |
| - dvdp_mull | |
| - polyXsubCP | |
| - leq_trunc_divp | |
| - rmodp_eq0P | |
| - rmodpX | |
| - dvdpp | |
| - dvdpN0 | |
| - gcdp_modr | |
| - coprimepZr | |
| - dvdp_gdco | |
| - rmodp_sum | |
| - coprimep_expr | |
| - rdvdp_eqP | |
| - eqp_scale | |
| - coprimepp | |
| - gcdp_addl_mul | |
| - dvdp_exp | |
| - gcdp_map | |
| - edivpP | |
| - rmodp_id | |
| - edivp_eq | |
| - path: mathcomp/field/galois.v | |
| theorems: | |
| - fixedField_galois | |
| - comp_kHom | |
| - normal_field_splitting | |
| - gal_adjoin_eq | |
| - regular_splittingAxiom | |
| - kAutfE | |
| - galNormM | |
| - splitting_normalField | |
| - comp_AEndA | |
| - kAut_to_gal | |
| - kHomExtend_additive_subproof | |
| - gal_fixedField | |
| - path: mathcomp/character/vcharacter.v | |
| theorems: | |
| - mem_zchar | |
| - vchar_norm2 | |
| - cfnorm_dchi | |
| - zchar_subset | |
| - cfun1_vchar | |
| - path: mathcomp/solvable/cyclic.v | |
| theorems: | |
| - injm_Zp_unitm | |
| - orderXdiv | |
| - path: mathcomp/algebra/ring_quotient.v | |
| theorems: | |
| - mulqA | |
| - equiv_is_equiv | |
| - path: mathcomp/fingroup/quotient.v | |
| theorems: | |
| - cosetpre1 | |
| - index_morphim_ker | |
| - morphpre_quotm | |
| - quotient_normal | |
| - path: mathcomp/solvable/maximal.v | |
| theorems: | |
| - subcent1_extraspecial_maximal | |
| - min_card_extraspecial | |
| - isog_special | |
| - path: mathcomp/algebra/mxalgebra.v | |
| theorems: | |
| - addsmxA | |
| - mxrank_compl | |
| - mulmx_ker | |
| - col_ebase_unit | |
| - rank_leq_col | |
| - LUP_card_GL | |
| - row_leq_rank | |
| - mulmx_base | |
| - pinvmxE | |
| - mxrank_sum_cap | |
| - map_ltmx | |
| - capmxS | |
| - genmx_muls | |
| - mxrank_eq0 | |
| - col_base_full | |
| - path: mathcomp/solvable/extremal.v | |
| theorems: | |
| - extremal_generators_facts | |
| - def2 | |
| - path: mathcomp/fingroup/action.v | |
| theorems: | |
| - actKVin | |
| - astab1R | |
| - afixP | |
| - actperm_Aut | |
| - acts_qact_dom_norm | |
| - astabs_ract | |
| - astab1JG | |
| - afixYin | |
| - gacent1E | |
| - acts_actby | |
| - mem_orbit | |
| - path: mathcomp/algebra/poly.v | |
| theorems: | |
| - prim_order_exists | |
| - size_XaddC | |
| - size_scale | |
| - poly_alg_initial | |
| - map_monic | |
| - coef_comp_poly | |
| - size_addl | |
| - poly_ind | |
| - size_odd_poly_eq | |
| - derivN | |
| - take_poly_is_linear | |
| - map_Poly_id0 | |
| - polyCB | |
| - rootC | |
| - add_poly_key | |
| - polyseq1 | |
| - char_prim_root | |
| - comp_polyCr | |
| - monicMr | |
| - size_comp_poly_leq | |
| - derivX | |
| - horner_evalE | |
| - map_polyXsubC | |
| - coef1 | |
| - scale_polyDl | |
| - size_XnaddC | |
| - path: mathcomp/ssreflect/order.v | |
| theorems: | |
| - comp_is_top_morphism | |
| - lexi_cons | |
| - rcomplPjoin | |
| - meetBI | |
| - joinCA | |
| - comparable_bigr | |
| - meetUr | |
| - enum1 | |
| - incomparable_leF | |
| - ltEsig | |
| - meetEseq | |
| - joinKUC | |
| - complEdiff | |
| - le_refl | |
| - joins_sup | |
| - lteif_orb | |
| - le_refl | |
| - le_enum_rank_in | |
| - contraTlt | |
| - meetCA | |
| - nonincn_inP | |
| - le_nmono_in | |
| - joinC | |
| - lt_path_min | |
| - idfun_is_meet_morphism | |
| - meetC | |
| - comparable_contra_ltn_lt | |
| - minEle | |
| - comparable_gt_max | |
| - lt_le_asym | |
| - ltEprodlexi | |
| - le_def | |
| - opredI | |
| - joinIB | |
| - leBl | |
| - joinACA | |
| - botEseq | |
| - bigmin_mkcondr | |
| - leUidl | |
| - comparable_gt_min | |
| - idfun_is_nondecreasing | |
| - decn_inP | |
| - ltW_homo | |
| - max_idPr | |
| - botEsig | |
| - le_nmono | |
| - meetAC | |
| - ge_max | |
| - anti | |
| - leBx | |
| - neqhead_lexiE | |
| - contraNle | |
| - meetA | |
| - comparable_maxCA | |
| - path: mathcomp/character/mxabelem.v | |
| theorems: | |
| - mx_repr_action_faithful | |
| - astabs_rowg_repr | |
| - path: mathcomp/character/mxrepresentation.v | |
| theorems: | |
| - mx_abs_irr_cent_scalar | |
| - map_reprJ | |
| - bigcapmx_module | |
| - map_gring_row | |
| - component_mx_module | |
| - repr_mxM | |
| - rcenter_normal | |
| - mx_second_rsim | |
| - kquo_repr_coset | |
| - in_factmod_addsK | |
| - mx_Jacobson_density | |
| - card_irr | |
| - genmx_Socle | |
| - gring_opJ | |
| - val_factmodJ | |
| - val_submod_eq0 | |
| - irr_modeV | |
| - gen_is_multiplicative | |
| - mxmodule1 | |
| - mxsimple_isoP | |
| - mxmodule_eigenvector | |
| - mxsemisimpleS | |
| - Wedderburn_ideal | |
| - hom_cyclic_mx | |
| - socle_rsimP | |
| - path: mathcomp/solvable/abelian.v | |
| theorems: | |
| - rank_cycle | |
| - primes_exponent | |
| - exponent_Zgroup | |
| - Ohm1 | |
| - exponent2_abelem | |
| - p_rank_abelem | |
| - TIp1ElemP | |
| - path: mathcomp/field/finfield.v | |
| theorems: | |
| - finRing_nontrivial | |
| - path: mathcomp/ssreflect/prime.v | |
| theorems: | |
| - Euclid_dvd_prod | |
| - trunc_log_ltn | |
| - up_log2_double | |
| - trunc_log_up_log | |
| - totient_prime | |
| - trunc_logP | |
| - lognM | |
| - primesX | |
| - pdiv_id | |
| - pdiv_pfactor | |
| - path: mathcomp/algebra/polyXY.v | |
| theorems: | |
| - sizeYE | |
| - swapXY_is_scalable | |
| - max_size_coefXY | |
| - poly_XaY0 | |
| - path: mathcomp/algebra/vector.v | |
| theorems: | |
| - dimv0 | |
| - lfun_addC | |
| - sumv_sup | |
| - comp_lfun0l | |
| - memvK | |
| - span_basis | |
| - comp_lfunNl | |
| - free_span | |
| - fun_of_lfunK | |
| - memv_capP | |
| - vs2mxP | |
| - capvSl | |
| - hommx1 | |
| - sub_span | |
| - dim_span | |
| - path: mathcomp/fingroup/perm.v | |
| theorems: | |
| - perm_mulP | |
| - out_perm | |
| - cast_perm_inj | |
| - porbit_id | |
| - porbit_perm | |
| - odd_tperm | |
| - tpermKg | |
| - inj_tperm | |
| - path: mathcomp/algebra/ssrint.v | |
| theorems: | |
| - addSz | |
| - ler_pMz2r | |
| - ltr_pMz2l | |
| - ler_wnMz2l | |
| - exprSz | |
| - exprz_out | |
| - sqrn_dist | |
| - mulrN1z | |
| - sgzN1 | |
| - distnEr | |
| - path: mathcomp/algebra/intdiv.v | |
| theorems: | |
| - divzN | |
| - coprimez_dvdr | |
| - gcdzMl | |
| - modzz | |
| - coprimezMl | |
| - path: mathcomp/ssreflect/choice.v | |
| theorems: | |
| - pickle_taggedK | |
| - sig2W | |
| - choose_id | |
| - path: mathcomp/field/fieldext.v | |
| theorems: | |
| - minPoly_dvdp | |
| - vsval_multiplicative | |
| - subfx_inj_is_multiplicative | |
| - dim_refBaseField | |
| - path: mathcomp/ssreflect/fintype.v | |
| theorems: | |
| - val_seq_sub_enum | |
| - predT_subset | |
| - eq_forallb | |
| - nth_enum_ord | |
| - bumpC | |
| - image_pre | |
| - disjointWl | |
| - enum_rank_in_inj | |
| - card_geqP | |
| - forall_inP | |
| - fintype1 | |
| - cardID | |
| - neq_lift | |
| - path: mathcomp/algebra/zmodp.v | |
| theorems: | |
| - unit_Zp_mulgC | |
| - sub_Zp_1 | |
| - Zp_abelian | |
| - Fp_cast | |
| - path: mathcomp/character/character.v | |
| theorems: | |
| - cfRepr_prod | |
| - irr_inj | |
| - xcfunZl | |
| - xcfun_r_is_additive | |
| - cfRepr_muln | |
| - constt_charP | |
| - cfRes_irr_irr | |
| - irr_classK | |
| - cfker_repr | |
| - lin_Res_IirrE | |
| - cfRes_eq0 | |
| - cfAut_char | |
| - lin_charV | |
| - irr_consttE | |
| - char1_gt0 | |
| - path: mathcomp/solvable/sylow.v | |
| theorems: | |
| - Sylow_superset | |
| - ZgroupS | |
| - path: mathcomp/field/falgebra.v | |
| theorems: | |
| - adjoin_cons | |
| - expv0 | |
| - lfun_invE | |
| - expv1n | |
| - agenv_sub_modl | |
| - lfun_mulrRV | |
| - path: mathcomp/field/algC.v | |
| theorems: | |
| - truncC0 | |
| - truncCM | |
| - Cnat_prod_eq1 | |
| - posP | |
| - eqCmod_addl_mul | |
| - eqCmodMl | |
| - eqCmodD | |
| - eqCmod_trans | |
| - CtoL_is_multiplicative | |
| - path: mathcomp/ssreflect/path.v | |
| theorems: | |
| - mem2E | |
| - splitP2r | |
| - rotr_ucycle | |
| - mem_merge | |
| - rotr_cycle | |
| - mem2r_cat | |
| - sorted_eq_in | |
| - cycle_relI | |
| - drop_sorted | |
| - splitPr | |
| - path: mathcomp/algebra/mxpoly.v | |
| theorems: | |
| - map_mx_companion | |
| - map_char_poly | |
| - rVpoly_is_linear | |
| - horner_rVpoly_inj | |
| - path: mathcomp/algebra/fraction.v | |
| theorems: | |
| - tofrac0 | |
| - equivf_trans | |
| - path: mathcomp/ssreflect/div.v | |
| theorems: | |
| - eqn_div | |
| - eqn_modDl | |
| - dvdn_eq | |
| - modnMmr | |
| - dvdn0 | |
| - dvdn_lcmr | |
| - path: mathcomp/solvable/frobenius.v | |
| theorems: | |
| - Frobenius_kerS | |
| - FrobeniusJgroup | |
| - path: mathcomp/solvable/alt.v | |
| theorems: | |
| - simple_Alt_3 | |
| - path: mathcomp/solvable/jordanholder.v | |
| theorems: | |
| - JordanHolderUniqueness | |
| - gactsI | |
| - gastabsP | |
| - gactsP | |
| - path: mathcomp/solvable/burnside_app.v | |
| theorems: | |
| - S23_inv | |
| - S05_inj | |
| - eqperm_map2 | |
| - path: mathcomp/algebra/rat.v | |
| theorems: | |
| - scalqE | |
| - fracq0 | |
| - normqE | |
| - numq_le0 | |
| - natq_div | |
| - addqC | |
| - path: mathcomp/algebra/qpoly.v | |
| theorems: | |
| - size_mk_monic_gt1 | |
| - npolyXE | |
| - qpoly_mulVz | |
| - big_coef_npoly | |
| - path: mathcomp/character/inertia.v | |
| theorems: | |
| - inertia_isom | |
| - im_cfclass_Iirr | |
| - nNG | |
| - path: mathcomp/fingroup/gproduct.v | |
| theorems: | |
| - complP | |
| - bigcprodW | |
| - sdprodg1 | |
| - injm_pairg1 | |
| - cprodP | |
| - perm_bigcprod | |
| - dprodJ | |
| - divgrMid | |
| - astabsEsd | |
| - sdprod_subr | |
| - xsdprodm_dom1 | |
| - bigcprodYP | |
| - cprodWpp | |
| - dprodWC | |
| - path: mathcomp/field/qfpoly.v | |
| theorems: | |
| - plogpD | |
| - path: mathcomp/solvable/gseries.v | |
| theorems: | |
| - morphpre_maximal | |
| - path: mathcomp/ssreflect/generic_quotient.v | |
| theorems: | |
| - right_trans | |
| - path: mathcomp/algebra/archimedean.v | |
| theorems: | |
| - aut_natr | |
| - floor_ge_int | |
| - ceil_def | |
| - path: mathcomp/algebra/interval.v | |
| theorems: | |
| - le_ninfty | |
| - oppr_itvco | |
| - le_bound_trans | |
| - path: mathcomp/solvable/nilpotent.v | |
| theorems: | |
| - solvableS | |
| - ucn1 | |
| - path: mathcomp/ssreflect/fingraph.v | |
| theorems: | |
| - eq_froots | |
| - order_id | |
| - relU_sym | |
| - order_set_finv | |
| - finv_eq_can | |
| - finv_f_cycle | |
| - path: mathcomp/solvable/center.v | |
| theorems: | |
| - center_dprod | |
| - center_sub | |
| - path: mathcomp/field/separable.v | |
| theorems: | |
| - Derivation_mul_poly | |
| - char0_PET | |
| - path: mathcomp/solvable/commutator.v | |
| theorems: | |
| - comm3G1P | |
| - der_subS | |
| - commgX | |
| - isog_der | |
| - path: mathcomp/solvable/gfunctor.v | |
| theorems: | |
| - gFsub | |
| - path: mathcomp/ssreflect/ssrAC.v | |
| theorems: | |
| - count_memE | |
| - path: mathcomp/field/closed_field.v | |
| theorems: | |
| - ex_elim_qf | |
| - path: mathcomp/algebra/finalg.v | |
| theorems: | |
| - zmod_abelian | |
| - path: mathcomp/fingroup/automorphism.v | |
| theorems: | |
| - ker_autm | |
| - path: mathcomp/ssreflect/binomial.v | |
| theorems: | |
| - ffactSS | |
| - path: mathcomp/solvable/hall.v | |
| theorems: | |
| - coprime_quotient_cent | |