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