Perm 📖 | CompOp | 840 mathmath: Perm.decomposeFin_symm_of_refl, Polynomial.Gal.galActionHom_restrict, GrpCat.SurjectiveOfEpiAuxs.τ_apply_fromCoset, Fin.sign_cycleIcc_of_eq, Perm.SameCycle.exists_pow_eq_of_mem_support, extendSubtype_mem, DilationEquiv.toPerm_apply, Perm.sameCycle_conj, right_vsub_pointReflection, AlternatingMap.domCoprod.summand_mk'', Monovary.sum_mul_comp_perm_eq_sum_mul_iff, Matrix.det_apply, Fin.cycleIcc_ge, Fin.cycleRange_succAbove, Perm.SameCycle.exists_pow_eq, Perm.cycleOf_inv, Fin.cycleIcc.trans_right_one, image_swap_of_mem_of_notMem, Polynomial.Gal.galActionHom_bijective_of_prime_degree', Perm.mem_cycleFactorsFinset_conj, alternatingGroup.eq_bot_of_card_le_two, List.form_perm_zpow_apply_mem_imp_mem, Finset.product_self_eq_disjiUnion_perm_aux, Perm.smul_def, Perm.Basis.injective, Perm.SameCycle.exists_nat_pow_eq, Perm.Basis.toCentralizer_equivariant, alternatingGroup.commutator_perm_eq, Cycle.formPerm_subsingleton, Matrix.transpose_permMatrix, Perm.disjoint_refl_iff, Perm.card_support_swap_mul, Perm.IsCycle.exists_pow_eq, apply_swap_eq_self, ContinuousMultilinearMap.alternatization_apply_apply, zsmul_addLeft, alternatingGroup.isPreprimitive_of_three_le_card, Perm.apply_inv_self, map_equiv_removeNone, AlternatingMap.map_perm, Perm.sign_of_cycleType, Polynomial.Gal.galActionHom_injective, Perm.cycleFactorsFinset_eq_empty_iff, Matrix.det_permute, Perm.card_support_le_one, Perm.card_of_cycleType_mul_eq, mem_derangements_iff_fixedPoints_eq_empty, Pi.colex_asc, constVAdd_zero, Perm.support_eq_empty_iff, Set.powersetCard.isPretransitive, Perm.disjoint_of_disjoint_support, Perm.subtypePerm_ofSubtype, Perm.Basis.toCentralizer_apply, swap_apply_apply, Perm.notMem_support, addRight_add, Monovary.sum_smul_comp_perm_le_sum_smul, Perm.ofFn_comp_perm, comp_swap_eq_update, swap_apply_self, Perm.subtypeCongrHom_injective, Perm.cycleOf_self_apply_zpow, Perm.iterate_eq_pow, Perm.next_toList_eq_apply, Perm.SameCycle.apply_left, Perm.disjoint_ofSubtype_noncommPiCoprod, Perm.closure_isSwap, Perm.exists_mem_stabilizer_smul_eq, Perm.OnCycleFactors.mem_range_toPermHom_iff', Perm.val_equivUnitsEnd_apply, alternatingGroup.card_two_sylow_of_card_eq_four, Perm.subtypeCongr.apply, AlternatingMap.domCoprod_coe, permCongr_symm_apply, swap_mul_self, DomMulAct.mem_stabilizer_iff, Fintype.card_perm, Perm.IsCycleOn.exists_pow_eq', Perm.symm_mul, alternatingGroup.kleinFour_card_of_card_eq_four, Perm.set_support_zpow_subset, Perm.IsCycle.pow_eq_one_iff', Perm.disjoint_inv_right_iff, Perm.set_support_mul_subset, Matrix.permanent_permute_rows, Perm.Disjoint.zpow_disjoint_zpow, Perm.Basis.mem_support_self', Perm.IsCycle.pow_iff, Perm.disjoint_one_left, Perm.OnCycleFactors.kerParam_range_card, Matrix.adjp_apply, Perm.cycleOf_eq_one_iff, GrpCat.SurjectiveOfEpiAuxs.τ_apply_infinity, Perm.disjoint_ofSubtype_of_memFixedPoints_self, Fin.cycleRange_apply, Perm.exists_mem_stabilizer_isThreeCycle_of_two_lt_ncard, Perm.permCongr_eq_mul, Monovary.sum_comp_perm_mul_le_sum_mul, Perm.OnCycleFactors.kerParam_injective, Perm.Disjoint.cycleType, AnalyticOn.iteratedFDerivWithin_comp_perm, MonoidHom.toHomPerm_apply_symm_apply, comap_inv_leftUniformSpace, Perm.support_one, Tuple.sort_perm, Perm.one_def, Perm.sign_trans_trans_symm, swap_smul_involutive, Perm.mclosure_swap_castSucc_succ, List.formPerm_singleton, EuclideanGeometry.Sphere.isDiameter_iff_right_mem_and_pointReflection_center_right, Perm.Disjoint.commute, Perm.IsThreeCycle.support_eq_iff_mem_support, Perm.viaFintypeEmbedding_sign, AlternatingGroup.isPreprimitive_of_three_le_card, Perm.card_support_eq_zero, Perm.ofSubtype_apply_mem_iff_mem, Perm.sign_symm, Matrix.permMatrixHom_apply, Perm.IsCycle.commute_iff', altCongrHom_apply_coe, Perm.disjoint_closure_of_disjoint_support, Fin.cycleIcc_of_last, Perm.congr_arg, Fin.cycleIcc_of_gt, zpow_mulRight, Perm.cycleOf_one, Fin.sign_cycleRange, Perm.sign_eq_prod_prod_Ioi, Perm.coe_mul, Perm.support_pow_le, Perm.decomposeFin_symm_apply_one, Perm.prod_Ioi_comp_eq_sign_mul_prod, Antivary.sum_mul_le_sum_comp_perm_mul, Perm.OnCycleFactors.nat_card_range_toPermHom, Fin.cycleIcc.trans_left_one, Perm.IsCycle.conj, alternatingGroup.normalClosure_swap_mul_swap_five, Perm.support_swap_mul_eq, Fin.coe_cycleRange_of_lt, Perm.sumCongr_inv, injective_pointReflection_left_of_injective_two_nsmul, Perm.zpow_apply_mem_support_of_mem_cycleFactorsFinset_iff, Nat.card_perm, alternatingGroup.subsingleton_two_sylow, Perm.support_swap_mul_swap, Perm.mul_mem_alternatingGroup_of_isSwap, dist_left_pointReflection, Perm.cycleFactorsFinset_eq_finset, Matrix.conjTranspose_permMatrix, Perm.cycleType_swap_mul_swap_of_nodup, alternatingGroup.isCoatom_stabilizer_singleton, Perm.sign_of_cycleType_eq_replicate, Perm.Disjoint.card_support_mul, neg_addLeft, Perm.coe_support_eq_set_support, Set.Countable.exists_cycleOn, PEquiv.toMatrix_toPEquiv_eq, optionCongr_one, Perm.IsCycle.cycleFactorsFinset_eq_singleton, permCongrHom_coe, Perm.cycleFactorsFinset_eq_singleton_self_iff, midpoint_pointReflection_left, Perm.SameCycle.zpow_right, Perm.sumCongrHom.card_range, Perm.decomposeFin.symm_sign, swap_eq_one_iff, Perm.sameCycle_apply_right, pointReflection_vsub_right, Perm.cycleType_ofSubtype, pointReflection_midpoint_right, Perm.subtypeCongr.right_apply_subtype, alternatingGroup.characteristic_kleinFour, Perm.cycleOf_apply_apply_pow_self, Perm.inv_eq_iff_eq, Perm.extendDomain_apply_subtype, mem_closure_isSwap, AlternatingMap.map_congr_perm, Perm.prodExtendRight_apply_ne, instInfinitePerm, Set.powersetCard.isPretransitive_alternatingGroup, Perm.closure_isCycle, alternatingGroup.kleinFour_isKleinFour, Perm.extendDomain_inv, AlternatingGroup.card_of_cycleType_singleton, extendSubtype_not_mem, Perm.image_inv, Perm.fixed_point_card_lt_of_ne_one, finRotate_succ_eq_decomposeFin, Antivary.sum_mul_le_sum_mul_comp_perm, Perm.SameCycle.exists_pow_eq', Fin.cycleRange_zero, alternatingGroup.normalClosure_finRotate_five, card_derangements_invariant, Matrix.permMatrix_mul, Perm.isCycle_inv, Perm.isConj_of_cycleType_eq, Perm.sign_prodExtendRight, AddAction.toPerm_zero, Perm.cycleOf_pow_apply_self, Perm.card_of_cycleType_eq_zero_iff, List.formPerm_apply_mem_of_mem, Fin.coe_cycleRange_of_le, alternatingGroup.kleinFour_eq_commutator, Perm.subtypeEquivSubtypePerm_apply_coe, Perm.Disjoint.disjoint_cycleFactorsFinset, lt_finRotate_iff_ne_last, Perm.Disjoint.inv_right, Perm.sign_abs, Perm.SameCycle.exists_fin_pow_eq, Fin.sign_cycleIcc_of_ge, Perm.default_eq, Perm.subtypeCongr.left_apply_subtype, GrpCat.SurjectiveOfEpiAuxs.g_apply_infinity, GrpCat.SurjectiveOfEpiAuxs.comp_eq, nsmul_addLeft, Perm.SameCycle.pow_right, Perm.Basis.card_ofPermHom_support, List.formPerm_apply_getElem_zero, Perm.sumCongr_apply, Perm.signAux_inv, addLeft_add, alternatingGroup.center_eq_bot, alternatingGroup.stabilizer.surjective_toPerm, finCycle_eq_finRotate_iterate, comap_neg_leftUniformSpace, Tuple.graphEquiv₂_apply, finite_compl_fixedBy_swap, Perm.Basis.ofPermHom_apply, Perm.IsCycleOn.exists_pow_eq, MultilinearMap.domCoprod_alternization_coe, Function.Injective.map_swap, Perm.instSymmDisjoint, Perm.mem_support_iff_mem_support_of_mem_cycleFactorsFinset, midpoint_pointReflection_right, swap_comp_apply, finRotate_of_lt, EuclideanGeometry.Sphere.IsDiameter.pointReflection_center_left, Perm.Disjoint.support_mul, Set.prod_self_eq_iUnion_perm, Perm.sign_trans, pow_mulLeft, Perm.perm_mapsTo_inl_iff_mapsTo_inr, Perm.sameCycle_zpow_right, Perm.signAux_one, Perm.OnCycleFactors.mem_range_toPermHom'_iff, Perm.extendDomain_apply_image, Perm.extendDomain_mul, pointReflection_involutive, Perm.IsCycle.pow_eq_one_iff, Perm.sign_sumCongr, Perm.sign_eq_prod_prod_Iio, Function.Embedding.swap_apply, Perm.swap_mem_stabilizer, Perm.cycleFactorsFinset_one, List.formPerm_apply_getElem, Perm.card_isConj_eq, finRotate_apply_zero, swap_mul_involutive, Matrix.det_permutation, List.formPerm_apply_getElem_length, Perm.support_noncommProd, Perm.extendDomain_pow, Perm.viaFintypeEmbedding_apply_image, Perm.disjoint_prod_right, NumberField.InfinitePlace.ComplexEmbedding.conjugate_sign, Perm.IsCycle.existsUnique_cycle_nontrivial_subtype, Perm.closure_cycle_coprime_swap, Perm.Disjoint.mul_apply_eq_iff, Perm.prodExtendRight_apply_eq, Perm.not_solvable, permCongr_trans, Finset.univ_perm_option, Perm.isThreeCycle_sq_of_three_mem_cycleType_five, Fin.cycleIcc_to_cycleRange, Perm.IsSwap.finite_compl_fixedBy, alternatingGroup.coe_kleinFour_of_card_eq_four, Perm.subtypeCongrHom.card_range, derangements.Equiv.RemoveNone.mem_fiber, mulLeft_one, Fin.snoc_eq_cons_rotate, Perm.cycleOf_apply_apply_self, Perm.cycleOf_self_apply_pow, Pi.lex_desc, Perm.viaEmbeddingHom_apply, Perm.sigmaCongrRight_one, swap_apply_def, Perm.cycleOf_apply_apply_zpow_self, Antivary.sum_smul_lt_sum_comp_perm_smul_iff, Perm.sameCycle_inv, Perm.ext_iff, dist_right_pointReflection, Perm.IsSwap.orderOf, GrpCat.SurjectiveOfEpiAuxs.agree, Antivary.sum_smul_le_sum_smul_comp_perm, Perm.preimage_inv, Perm.sameCycle_apply_left, Perm.IsCycleOn.inv, Tuple.self_comp_sort, Perm.cycleOf_apply_of_not_sameCycle, mul_swap_eq_swap_mul, Perm.card_of_cycleType, RegularWreathProduct.toPermInj, Perm.Basis.ofPermHom_mem_centralizer, Fin.cons_apply_cycleRange, Perm.mem_cycleType_iff, MulAction.toPermHom_apply, Perm.subtypeEquivSubtypePerm_apply_of_mem, Matrix.permanent_permute_cols, Perm.coe_one, Perm.trans_one, Perm.Disjoint.pow_disjoint_pow, Perm.set_support_inv_eq, Perm.inv_apply_self, Perm.support_zpowers_of_mem_cycleFactorsFinset_le, Fin.sign_cycleIcc_of_le, Cardinal.mk_perm_eq_two_power, neg_addRight, addRight_zero, Perm.stabilizer_isPreprimitive, Perm.applyFaithfulSMul, Perm.support_ofSubtype, swap_mul_eq_iff, Perm.IsThreeCycle.inv_iff, Matrix.permMatrix_one, Perm.mem_alternatingGroup, Perm.IsCycle.support_pow_eq_iff, Perm.SameCycle.apply_right, Perm.ofSign_disjoint, Matrix.det_reindex, Perm.isConj_swap, Perm.support_zpow_le, Antivary.sum_mul_eq_sum_mul_comp_perm_iff, coe_addRight, Monovary.sum_comp_perm_smul_lt_sum_smul_iff, inv_mulRight, Perm.SameCycle.zpow_left, Fin.cycleRange_of_eq, Perm.Basis.mem_support_self, Perm.decomposeOption_symm_of_none_apply, Perm.OnCycleFactors.val_centralizer_smul, Perm.isCycleOn_inv, zpow_mulLeft, Perm.IsCycleOn.pow_card_apply, nsmul_addRight, Perm.IsCycle.pow_eq_pow_iff, Perm.sign_refl, Fin.succAbove_cycleRange, coe_mulLeft, List.formPerm_pow_apply_head, Perm.IsCycle.orderOf, Fin.cycleRange_of_le, Perm.support_mul_le, coe_finRotate, Perm.perm_symm_mapsTo_iff_mapsTo, Perm.lcm_cycleType, card_derangements_fin_add_two, length_permsOfList, Perm.one_trans, swap_mem_closure_isSwap, mul_swap_involutive, Perm.mul_def, Perm.disjoint_conj, Perm.IsCycleOn.range_pow, Perm.sigmaCongrRight_inv, instCharacteristicPermAlternatingGroup, AlternatingGroup.card_of_cycleType, Perm.zpow_apply_mem_support, Perm.coe_inv, Perm.cycleFactorsFinset_eq_singleton_iff, Perm.Basis.toPermHom_apply_toCentralizer, Perm.apply_pow_apply_eq_iff, Perm.IsCycle.cycleOf, Perm.SameCycle.inv, Perm.IsCycleOn.apply_mem_iff, Perm.ofSubtype_apply_of_mem, Perm.sign_mul, ContinuousMultilinearMap.iteratedFDeriv_comp_diagonal, Perm.sumCongr_swap_one, Perm.finRotate_bit1_mem_alternatingGroup, Perm.centralizer_le_alternating_iff, Monovary.sum_mul_comp_perm_le_sum_mul, swap_mul_eq_mul_swap, Perm.OnCycleFactors.mem_ker_toPermHom_iff, Perm.Basis.ofPermHom_support, swap_apply_of_ne_of_ne, Perm.one_symm, Perm.IsThreeCycle.eq_swap_mul_swap_iff_mem_support, Perm.getElem_toList, Antivary.sum_smul_lt_sum_smul_comp_perm_iff, List.formPerm_pow_apply_getElem, Fin.cycleIcc_of_ge_of_lt, Perm.mul_symm, midpoint_eq_iff', Perm.IsThreeCycle.inv, AddAction.toPerm_injective, Perm.card_fixedPoints, Perm.toList_pow_apply_eq_rotate, permCongr_apply, Perm.refl_mul, alternatingGroup.index_eq_one, Perm.IsCycle.exists_zpow_eq, Perm.Basis.ofPermHomFun_commute_zpow_apply, Perm.subtypeEquivSubtypePerm_apply_of_not_mem, AffineEquiv.pointReflection_apply_eq_equivPointReflection_apply, Perm.signAux3_mul_and_swap, Perm.SameCycle.apply_eq_self_iff, permCongr_mul, Perm.cycleFactorsFinset_pairwise_disjoint, Perm.sameCycle_pow_right, Perm.decomposeFin_symm_apply_succ, Perm.sign_symm_trans_trans, swap_inv, card_perms_of_finset, List.zipWith_swap_prod_support', Perm.pairwise_commute_of_mem_zpowers, Tuple.comp_sort_eq_comp_iff_monotone, Perm.mem_ofSign, permCongr_symm, Perm.sumCongr_one_swap, Perm.support_swap_mul_ge_support_diff, permCongrHom_symm, Perm.Basis.ofPermHomFun_apply_mem_support_cycle_iff, Perm.mem_cycleFactorsFinset_conj', Perm.sigmaCongrRightHom_injective, alternatingGroup.two_sylow_eq_kleinFour_of_card_eq_four, alternatingGroup.nontrivial_of_three_le_card, DomMulAct.stabilizer_card', Perm.support_inv, List.formPerm_mem_iff_mem, Perm.IsCycle.existsUnique_cycle_subtype, List.formPerm_apply_mem_eq_self_iff, Fin.cycleIcc_def_gt, Perm.extendDomain_apply_not_subtype, Perm.ofSubtype_apply_coe, coe_addLeft, Perm.zpow_eq_zpow_on_iff, mul_swap_mul_self, swap_mem_stabilizer, AnalyticOn.iteratedFDeriv_comp_perm, Perm.IsCycle.zpowersEquivSupport_apply, permCongr_refl, left_vsub_pointReflection, GrpCat.SurjectiveOfEpiAuxs.h_apply_fromCoset', Perm.sumCongr_one, Perm.Disjoint.symmetric, MultilinearMap.alternatization_apply, Perm.disjoint_inv_left_iff, Perm.sumCongr_mul, coe_finRotate_of_ne_last, Perm.OnCycleFactors.cycleType_kerParam_apply_apply, doublyStochastic_eq_convexHull_permMatrix, swap_apply_eq_iff, AlternatingGroup.isMultiplyPretransitive, GrpCat.SurjectiveOfEpiAuxs.h_apply_infinity, alternatingGroup.exists_mem_stabilizer_smul_eq, Perm.decomposeOption_symm_sign, mul_swap_eq_iff, alternatingGroup.coe_two_sylow_of_card_eq_four, AddConstEquiv.toPerm_apply, Perm.subtypeCongrHom_apply, EuclideanGeometry.Sphere.IsTangent.eq_orthRadius_or_eq_orthRadius_pointReflection_of_parallel_orthRadius, Perm.cycleType_eq_zero, MulAction.toPerm_injective, Finset.univ_perm_fin_succ, swap_eq_update, EuclideanGeometry.Sphere.IsDiameter.pointReflection_center_right, Perm.pow_apply_mem_support, Function.Involutive.toPerm_involutive, Tuple.eq_sort_iff, Perm.viaEmbedding_apply, permCongr_def, Monovary.sum_comp_perm_mul_eq_sum_mul_iff, Perm.fst_prodExtendRight, AddAction.toPermHom_apply_symm_apply, Perm.OnCycleFactors.coe_toPermHom, Tuple.antitone_pair_of_not_sorted', coe_constVAdd, Perm.exists_mem_stabilizer_isThreeCycle, Perm.IsThreeCycle.nodup_iff_mem_support, Perm.sign_permCongr, Perm.eq_top_of_isMultiplyPretransitive, Perm.IsCycleOn.pow_apply_eq_pow_apply, two_mul_card_alternatingGroup, List.support_formPerm_le', Perm.card_cycleType_eq_zero, bijOn_swap, commutator_alternatingGroup_eq_top, Perm.cycleOf_self_apply, dist_pointReflection_right, Perm.cycleOf_apply, Perm.Disjoint.inv_left, swap_mul_swap_mul_swap, Perm.sigmaCongrRightHom.card_range, ContinuousMultilinearMap.alternatization_apply_toContinuousMultilinearMap, Perm.coe_subsingleton, Perm.instIsPreprimitive, Perm.SameCycle.conj, Perm.sumCongrHom_injective, List.formPerm_apply_of_notMem, List.formPerm_apply_head, Monovary.sum_smul_comp_perm_lt_sum_smul_iff, Set.powersetCard.addAction_faithful, Fin.cycleRange_of_lt, Perm.swap_mul_swap_same_mem_closure_three_cycles, List.formPerm_pow_length_eq_one_of_nodup, AlternatingGroup.isPretransitive_of_three_le_card, closure_of_isSwap_of_isPretransitive, Perm.toList_one, Perm.support_prod_le, card_alternatingGroup, alternatingGroup.stabilizer_isPreprimitive, Perm.inv_def, Perm.cycleType_conj, Perm.prod_list_swap_mem_alternatingGroup_iff_even_length, Matrix.swap_mulVec, Perm.support_conj, Cycle.formPerm_apply_mem_eq_next, Matrix.permMatrix_mulVec, Perm.dvd_of_mem_cycleType, two_mul_nat_card_alternatingGroup, Perm.pow_mod_card_support_cycleOf_self_apply, extremePoints_doublyStochastic, Monovary.sum_comp_perm_mul_lt_sum_mul_iff, Perm.fin_5_not_solvable, ContDiffAt.iteratedFDeriv_comp_perm, Perm.cycleType_one, Perm.IsSwap.mul_mem_closure_three_cycles, Perm.pow_apply_mem_toList_iff_mem_support, Cardinal.mk_perm_eq_self_power, Perm.sigmaCongrRightHom_apply, Perm.IsThreeCycle.alternating_normalClosure, Perm.IsCycleOn.range_zpow, Perm.cycleFactorsFinset_conj_eq, Perm.decomposeFin_symm_of_one, alternatingGroup.normal, Fin.cycleRange_mk_zero, alternatingGroup.normal_kleinFour, Function.Injective.swap_apply, Perm.subgroup_eq_top_of_nontrivial, Perm.apply_mem_support, LinearMap.IsSymmetric.eigenvalues_def, mem_closure_isSwap', DomMulAct.stabilizerMulEquiv_apply, GrpCat.SurjectiveOfEpiAuxs.h_apply_fromCoset, Perm.disjoint_one_right, Matrix.det_mul_aux, Finset.sum_smul_sum_eq_sum_perm, Perm.Disjoint.mul_eq_one_iff, HasFPowerSeriesWithinOnBall.iteratedFDerivWithin_eq_sum_of_completeSpace, Perm.IsThreeCycle.orderOf, alternatingGroup.isSimpleGroup_five, AffineSubspace.mem_perpBisector_iff_inner_pointReflection_vsub_eq_zero, Finset.sum_mul_sum_eq_sum_perm, Perm.OnCycleFactors.mem_range_toPermHom_iff, Perm.IsCycle.pow_eq_one_iff'', Perm.IsCycle.inv, Perm.toCycle_next, alternatingGroup.isCoatom_stabilizer, zsmul_addRight, Monovary.sum_comp_perm_smul_eq_sum_smul_iff, Monovary.sum_comp_perm_smul_le_sum_smul, Matrix.det_permute', Polynomial.Gal.galActionHom_bijective_of_prime_degree, Perm.OnCycleFactors.kerParam_range_eq_centralizer_of_count_le_one, Perm.cycleOf_mem_cycleFactorsFinset_iff, Perm.ofSubtype_swap_eq, Perm.extendDomain_one, Perm.Disjoint.mul_right, Perm.IsCycle.zpowersEquivSupport_symm_apply, Perm.card_support_conj, Perm.IsCycle.isCycleOn, Set.powersetCard.isPreprimitive_perm, Perm.IsThreeCycle.isThreeCycle_sq, swap_mul_self_mul, Perm.one_apply, List.formPerm_apply_lt_getElem, Perm.mem_cycleFactorsFinset_iff, Perm.sameCycle_zpow_left, permCongr_eq_mul, alternatingGroup.exponent_kleinFour_of_card_eq_four, coe_mulRight, Perm.IsCycle.swap_mul, Fin.cycleIcc_eq, Perm.IsCycleOn.zpow_apply_eq, MultilinearMap.alternatization_coe, finRotate_last', Perm.Basis.mem_fixedPoints_or_exists_zpow_eq, Perm.IsCycleOn.zpow_apply_eq_zpow_apply, Perm.ofSubtype_apply_of_not_mem, Set.Subsingleton.isCycleOn_one, Antivary.sum_mul_lt_sum_comp_perm_mul_iff, Perm.Disjoint.conj, Perm.cycleFactorsFinset_mem_commute, Perm.OnCycleFactors.toPermHom_apply, Perm.isConj_iff_cycleType_eq, Perm.isCoatom_stabilizer, Set.powersetCard.isPreprimitive_alternatingGroup, Perm.Disjoint.mul_left, alternatingGroup.instNontrivialSubtypePermFinHAddNatOfNatMemSubgroup, iteratedWreathToPermHomInj, Perm.closure_cycle_adjacent_swap, Matrix.trace_permutation, Perm.ofSubtype_injective, swap_injective_of_left, Perm.equivUnitsEnd_symm_apply_symm_apply, Subgroup.normalCore_eq_ker, List.formPerm_eq_one_iff, DomMulAct.stabilizerEquiv_invFun_eq, swap_smul_self_smul, permCongrHom_coe_equiv, mem_perms_of_finset_iff, GrpCat.SurjectiveOfEpiAuxs.h_apply_fromCoset_nin_range, Perm.SameCycle.cycleOf_apply, Fin.cycleRange_of_gt, card_derangements_eq_numDerangements, card_derangements_fin_eq_numDerangements, Perm.sign_extendDomain, alternatingGroup.commutator_perm_le, Monovary.sum_mul_comp_perm_lt_sum_mul_iff, HasFPowerSeriesOnBall.iteratedFDeriv_eq_sum_of_completeSpace, Perm.cycleFactorsFinset_conj, AddAction.toPermHom_apply_apply, Cycle.formPerm_reverse, Perm.cycleType_inv, mem_permsOfList_of_mem, alternatingGroup.isPretransitive_of_three_le_card, Antivary.sum_smul_comp_perm_eq_sum_smul_iff, MultilinearMap.domDomCongr_mul, List.formPerm_cons_cons, Perm.mul_apply, List.formPerm_eq_head_iff_eq_getLast, Perm.Basis.ofPermHomFun_mul, Perm.instIsPretransitive, Fin.cycleIcc_of_lt, Set.powersetCard.mulAction_faithful, AlternatingMap.map_swap, IsMultiplyPretransitive.alternatingGroup_le, Perm.map_finRange_perm, Perm.equivUnitsEnd_symm_apply_apply, pointReflection_self, Polynomial.Splits.toPermHom_apply_eq_one_or_isSwap_of_ncard_le_of_mem_inertia, Perm.viaFintypeEmbedding_apply_notMem_range, dist_pointReflection_left, AddAction.coe_toPermHom, Perm.isCycleOn_one, sign_finRotate, alternatingGroup.isMultiplyPretransitive, Perm.Disjoint.cycleType_mul, Perm.IsCycle.sign, Perm.sign_inv, Polynomial.Gal.card_complex_roots_eq_card_real_add_card_not_gal_inv, Perm.subtypeCongr.left_apply, Perm.IsThreeCycle.sign, pointReflection_midpoint_left, Perm.isCycleOn_singleton, SymmetricPower.tprod_equiv, Perm.IsCycle.existsUnique_cycle, AlternatingMap.domDomCongr_perm, Perm.IsCycle.forall_commute_iff, Perm.cycleType_def, AlternatingMap.map_swap_add, Perm.subtypeEquivSubtypePerm_symm_apply, Perm.IsSwap.sign_eq, ContDiffWithinAt.iteratedFDerivWithin_comp_perm, mulRight_mul, Perm.mul_refl, Perm.Basis.cycleOf_eq, Perm.stabilizer.surjective_toPerm, Polynomial.Splits.surjective_toPermHom_of_iSup_inertia_eq_top, mem_permsOfList_iff, finRotate_last, Tuple.comp_perm_comp_sort_eq_comp_sort, Perm.OnCycleFactors.kerParam_range_le_centralizer, Perm.sign_prodCongrRight, Perm.decomposeOption_symm_apply, swap_bijOn_exchange, List.formPerm_apply_getLast, AlternatingMap.map_add_swap, Perm.isCoatom_stabilizer_of_ncard_lt_ncard_compl, List.formPerm_reverse, Perm.Disjoint.orderOf, Perm.orderOf_cycleOf_dvd_orderOf, Perm.IsCycle.commute_iff, List.support_formPerm_of_nodup', Perm.sign_one, Perm.extendDomain_eq_one_iff, Perm.pairwise_disjoint_of_mem_zpowers, Perm.sameCycle_pow_left, Perm.viaFintypeEmbedding_apply_mem_range, Perm.eq_top_if_isMultiplyPretransitive, Perm.congr_fun, Perm.subtypeCongr.right_apply, Perm.CycleType.count_def, Perm.extendDomain_zpow, Cycle.formPerm_eq_self_of_notMem, Perm.closure_prime_cycle_swap, Perm.sumCongrHom_apply, Perm.prod_prodExtendRight, Perm.sameCycle_one, Perm.eq_inv_iff_eq, DomMulAct.stabilizer_ncard, List.formPerm_eq_self_of_notMem, MonoidHom.toHomPerm_apply_apply, Perm.set_support_apply_mem, Perm.extendDomainHom_apply, Perm.viaEmbedding_apply_of_notMem, Perm.ofSubtype_support_disjoint, Perm.pow_prime_eq_one_iff, instNontrivialPerm, Perm.decomposeOption_apply, Perm.Disjoint.cycleFactorsFinset_mul_eq_union, Perm.cycleFactorsFinset_injective, Matrix.det_apply', addLeft_zero, Antivary.sum_smul_le_sum_comp_perm_smul, Perm.sign_prod_list_swap, Perm.mclosure_isSwap, Perm.not_isCycle_one, derangements.Equiv.RemoveNone.fiber_none, Perm.pow_mod_orderOf_cycleOf_apply, Perm.cycle_zpow_mem_support_iff, Perm.moves_in, Perm.IsSwap.of_subtype_isSwap, List.zipWith_swap_prod_support, Perm.cycleOf_zpow_apply_self, swap_apply_right, Perm.partition_eq_of_isConj, List.formPerm_cons_concat_apply_last, Antivary.sum_comp_perm_mul_eq_sum_mul_iff, Perm.sign_prodCongrLeft, alternatingGroup.card_of_card_eq_four, finRotate_succ_apply, Perm.card_of_cycleType_singleton, Perm.monotone_iff, List.formPerm_apply_mem_eq_next, Perm.mem_conj_support, Perm.perm_inv_mapsTo_iff_mapsTo, AlternatingGroup.map_subtype_of_cycleType, Perm.sign_of_cycleType', nodup_permsOfList, Perm.sign_subtypeCongr, mulLeft_mul, GrpCat.SurjectiveOfEpiAuxs.g_apply_fromCoset, extendSubtype_apply_of_mem, Perm.cycleOf_apply_self, AlternatingMap.domCoprod_apply, Perm.SameCycle.pow_left, lt_finRotate_iff_ne_neg_one, Perm.isInvariant_of_support_le, Perm.OnCycleFactors.kerParam_range_eq, nat_card_alternatingGroup, Perm.ofSubtype_mem_stabilizer, Perm.closure_cycleType_eq_2_2_eq_alternatingGroup, Perm.coe_pow, Perm.ofSign_disjUnion, exteriorPower.toTensorPower_apply_ιMulti, Perm.prod_Iio_comp_eq_sign_mul_prod, AffineSubspace.mem_perpBisector_pointReflection_iff_inner_eq_zero, alternatingGroup_eq_sign_ker, mulRight_one, EuclideanGeometry.Sphere.isDiameter_iff_left_mem_and_pointReflection_center_left, swap_apply_left, Perm.SameCycle.exists_pow_eq'', optionCongr_sign, MulAction.coe_toPermHom, Finset.product_self_eq_disjiUnion_perm, Perm.IsCycleOn.conj, Fin.cycleIcc_of_le_of_le, DomMulAct.stabilizer_card, Perm.val_inv_equivUnitsEnd_apply, HasFPowerSeriesWithinOnBall.iteratedFDerivWithin_eq_sum, alternatingGroup.index_eq_two, Perm.Basis.ofPermHomFun_one, inv_mulLeft, derangements.Equiv.RemoveNone.fiber_some, Perm.zpow_apply_comm, Perm.IsCycleOn.pow_apply_eq, Antivary.sum_mul_lt_sum_mul_comp_perm_iff, swap_bijOn_self, extendSubtype_apply_of_not_mem, commutator_alternatingGroup_eq_self, Perm.sign_swap', Perm.apply_zpow_apply_eq_iff, exists_eq_sum_perm_of_mem_doublyStochastic, Fin.cycleIcc_def_gt', Function.Injective.swap_comp, MulAction.toPerm_one, Perm.IsThreeCycle.mem_alternatingGroup, Perm.OnCycleFactors.kerParam_apply, AlternatingGroup.card_of_cycleType_mul_eq, Perm.sign_swap, Fin.cons_comp_cycleRange, Perm.disjoint_iff_eq_or_eq, swap_injective_of_right, Perm.isThreeCycle_swap_mul_swap_same, Perm.closure_three_cycles_eq_alternating, constVAdd_add, Fin.cycleIcc.trans, GrpCat.SurjectiveOfEpiAuxs.τ_apply_fromCoset', Perm.card_isConj_mul_eq, Perm.sign_ofSubtype, permCongrHom_trans, Matrix.vecMul_swap, List.formPerm_append_pair, Perm.sigmaCongrRight_mul, Perm.nat_card_centralizer, HasFPowerSeriesOnBall.iteratedFDeriv_eq_sum, Perm.set_support_symm_eq, Perm.extendDomainHom_injective, pointReflection_vsub_left, Function.Involutive.coe_toPerm, Perm.Disjoint.cycleOf_mul_distrib, Perm.cycleOf_ne_one_iff_mem_cycleFactorsFinset, List.formPerm_nil, Perm.IsCycle.isConj_iff, Perm.decomposeFin_symm_apply_zero, MultilinearMap.alternatization_def, Perm.OnCycleFactors.range_toPermHom_eq_range_toPermHom', Perm.OnCycleFactors.centralizer_smul_def, Tuple.monotone_sort, Perm.inv_trans_self, Function.Embedding.swap_comp, Perm.signAux_mul, Antivary.sum_comp_perm_smul_eq_sum_smul_iff, Perm.sign_surjective, pow_mulRight, Perm.commute_ofSubtype_noncommPiCoprod, Fin.cycleRange_self, pointReflection_apply, alternatingGroup.isCoatom_stabilizer_of_ncard_lt_ncard_compl, Perm.OnCycleFactors.sign_kerParam_apply_apply, Perm.IsCycle.isConj, Monovary.sum_smul_comp_perm_eq_sum_smul_iff, AlternatingMap.domCoprod.summand_add_swap_smul_eq_zero, LinearMap.IsSymmetric.eigenvectorBasis_def, Perm.viaEmbeddingHom_injective, pointReflection_fixed_iff_of_injective_two_nsmul, Perm.isMultiplyPretransitive
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