Perm 📖 | CompOp | 990 mathmath: Perm.decomposeFin_symm_of_refl, Polynomial.Gal.galActionHom_restrict, Perm.support_closure_subset_union, 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, Perm.subtypePerm_mul, 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, Perm.exists_fixed_point_of_prime, 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, AntivaryOn.sum_smul_lt_sum_comp_perm_smul_iff, Perm.smul_def, Perm.Basis.injective, Perm.SameCycle.exists_nat_pow_eq, Perm.support_prod_of_pairwise_disjoint, Perm.cycleType_eq', Perm.Basis.toCentralizer_equivariant, alternatingGroup.commutator_perm_eq, Cycle.formPerm_subsingleton, MonovaryOn.sum_mul_comp_perm_le_sum_mul, 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, Perm.prod_comp, alternatingGroup.isPreprimitive_of_three_le_card, 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.cycleType_eq, Perm.support_eq_empty_iff, Set.powersetCard.isPretransitive, Perm.disjoint_of_disjoint_support, Perm.subtypePerm_ofSubtype, AntivaryOn.sum_mul_eq_sum_mul_comp_perm_iff, ExteriorAlgebra.basis_mul_of_disjoint, 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.isThreeCycle_subset_alternatingGroup, Perm.next_toList_eq_apply, Perm.SameCycle.apply_left, Perm.disjoint_ofSubtype_noncommPiCoprod, Perm.closure_isSwap, MonovaryOn.sum_smul_comp_perm_le_sum_smul, 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, MonovaryOn.sum_smul_comp_perm_lt_sum_smul_iff, Perm.cycleType_mul_inv_mem_cycleFactorsFinset_eq_sub, swap_mul_self, Perm.eq_on_support_mem_disjoint, DomMulAct.mem_stabilizer_iff, Fintype.card_perm, Perm.IsCycleOn.exists_pow_eq', Perm.symm_mul, alternatingGroup.kleinFour_card_of_card_eq_four, Perm.sign_subtypePerm, Perm.set_support_zpow_subset, Perm.IsCycle.pow_eq_one_iff', Perm.disjoint_inv_right_iff, Perm.cycleFactorsFinset_mul_inv_mem_eq_sdiff, Perm.set_support_mul_subset, Matrix.permanent_permute_rows, AntivaryOn.sum_comp_perm_smul_eq_sum_smul_iff, Perm.closure_cycleType_eq_two_two_eq_alternatingGroup, Perm.Disjoint.zpow_disjoint_zpow, Perm.Basis.mem_support_self', Perm.IsCycle.pow_iff, Perm.subtypePerm_inv, Perm.disjoint_one_left, Perm.Basis.sameCycle, 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, Monovary.sum_comp_perm_mul_le_sum_mul, Perm.OnCycleFactors.kerParam_injective, Perm.mem_support_iff_of_commute, AnalyticOn.iteratedFDerivWithin_comp_perm, Perm.mem_support_ofSubtype, MonoidHom.toHomPerm_apply_symm_apply, comap_inv_leftUniformSpace, Perm.support_one, MonovaryOn.sum_comp_perm_smul_le_sum_smul, Tuple.sort_perm, Perm.one_def, Perm.sign_trans_trans_symm, SubmonoidClass.swap_mem_trans, swap_smul_involutive, Perm.mclosure_swap_castSucc_succ, List.formPerm_singleton, Perm.sum_comp', EuclideanGeometry.Sphere.isDiameter_iff_right_mem_and_pointReflection_center_right, Perm.Disjoint.commute, Perm.IsThreeCycle.support_eq_iff_mem_support, Perm.viaFintypeEmbedding_sign, Perm.IsCycle.eq_swap_of_apply_apply_eq_self, AlternatingGroup.isPreprimitive_of_three_le_card, Perm.card_support_eq_zero, Perm.ofSubtype_apply_mem_iff_mem, Matrix.cons_swap, Perm.sign_symm, Matrix.permMatrixHom_apply, Perm.IsCycle.commute_iff', Perm.cycleFactorsFinset_noncommProd, altCongrHom_apply_coe, Perm.disjoint_closure_of_disjoint_support, Fin.cycleIcc_of_last, Perm.congr_arg, Fin.cycleIcc_of_gt, Perm.alternatingGroup_le_of_index_le_two, 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, Function.IsFixedPt.perm_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, Perm.pow_eq_on_of_mem_support, 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, Perm.commute_iff_of_mem_cycleFactorsFinset, neg_addLeft, Perm.IsThreeCycle.mem_commutator_alternatingGroup, Perm.coe_support_eq_set_support, Set.Countable.exists_cycleOn, PEquiv.toMatrix_toPEquiv_eq, optionCongr_one, Perm.IsCycle.cycleFactorsFinset_eq_singleton, permCongrHom_coe, alternatingGroup.closure_isThreeCycles_eq_top, Perm.cycleFactorsFinset_eq_singleton_self_iff, midpoint_pointReflection_left, Perm.SameCycle.zpow_right, Perm.sumCongrHom.card_range, Set.BijOn.perm_zpow, Perm.decomposeFin.symm_sign, swap_eq_one_iff, Perm.mem_support_cycle_of_cycle, Perm.sameCycle_apply_right, pointReflection_vsub_right, MonovaryOn.sum_comp_perm_mul_le_sum_mul, Perm.cycleType_ofSubtype, pointReflection_midpoint_right, Perm.subtypeCongr.right_apply_subtype, Perm.mem_list_cycles_iff, alternatingGroup.characteristic_kleinFour, Tuple.unique_monotone, Perm.cycleOf_apply_apply_pow_self, Perm.inv_eq_iff_eq, Perm.extendDomain_apply_subtype, mem_closure_isSwap, AlternatingMap.map_congr_perm, Perm.mem_range_ofSubtype_iff, Perm.prodExtendRight_apply_ne, instInfinitePerm, Perm.zpow_apply_eq_of_apply_apply_eq_self, Set.powersetCard.isPretransitive_alternatingGroup, Perm.closure_isCycle, alternatingGroup.kleinFour_isKleinFour, Perm.extendDomain_inv, AlternatingGroup.card_of_cycleType_singleton, alternatingGroup.mem_range_ofSubtype_iff, extendSubtype_not_mem, 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.isCycle_swap_mul_aux₁, Perm.card_of_cycleType_eq_zero_iff, Function.IsFixedPt.perm_zpow, List.formPerm_apply_mem_of_mem, Perm.self_mem_cycle_factors_commute, 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, Perm.list_cycles_perm_list_cycles, 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.nodup_of_pairwise_disjoint, Perm.IsCycleOn.exists_pow_eq, Perm.zpow_apply_eq_self_of_apply_eq_self, 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, alternatingGroup.closure_cycleType_eq_two_two_eq_top, Function.Embedding.swap_apply, Perm.swap_mem_stabilizer, Perm.cycleFactorsFinset_one, List.formPerm_apply_getElem, Perm.cycleType_prime_order, AntivaryOn.sum_smul_le_sum_comp_perm_smul, Perm.card_isConj_eq, finRotate_apply_zero, swap_mul_involutive, Matrix.det_permutation, List.formPerm_apply_getElem_length, Perm.support_noncommProd, Perm.extendDomain_pow, MonovaryOn.sum_mul_comp_perm_eq_sum_mul_iff, Perm.subtypePermOfFintype_apply, 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.sameCycle_apply_left, alternatingGroup.map_ofSubtype, Perm.IsCycleOn.inv, Tuple.self_comp_sort, Perm.cycleOf_apply_of_not_sameCycle, mul_swap_eq_swap_mul, Perm.card_of_cycleType, RegularWreathProduct.toPermInj, Set.LeftInvOn.extendDomain, Perm.Basis.ofPermHom_mem_centralizer, Function.IsFixedPt.perm_pow, Fin.cons_apply_cycleRange, Tuple.bubble_sort_induction', Perm.mem_cycleType_iff, MulAction.toPermHom_apply, Perm.subtypeEquivSubtypePerm_apply_of_mem, Matrix.permanent_permute_cols, Perm.sign_bij, Perm.coe_one, Perm.trans_one, Perm.Disjoint.pow_disjoint_pow, Perm.set_support_inv_eq, 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.eq_top_of_isPreprimitive_of_isSwap_mem, Perm.isConj_swap, Perm.support_zpow_le, Perm.sign_of_pow_two_eq_one, AntivaryOn.sum_mul_le_sum_mul_comp_perm, Antivary.sum_mul_eq_sum_mul_comp_perm_iff, coe_addRight, Monovary.sum_comp_perm_smul_lt_sum_smul_iff, inv_mulRight, alternatingGroup.isConj_of, 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, AntivaryOn.sum_smul_lt_sum_smul_comp_perm_iff, 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.ofSubtype_subtypePerm_of_mem, Perm.support_mul_le, coe_finRotate, Perm.perm_symm_mapsTo_iff_mapsTo, Perm.card_support_prod_list_of_pairwise_disjoint, Perm.lcm_cycleType, card_derangements_fin_add_two, length_permsOfList, Perm.one_trans, swap_mem_closure_isSwap, mul_swap_involutive, Perm.mul_def, Perm.commute_of_mem_cycleFactorsFinset_commute, 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, Set.BijOn.perm_pow, ContinuousMultilinearMap.iteratedFDeriv_comp_diagonal, Perm.sumCongr_swap_one, Perm.subgroup_eq_top_of_isPreprimitive_of_isSwap_mem, 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, Set.SurjOn.extendDomain, 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, Matrix.cons_cons_comp_swap_zero_one, Perm.card_fixedPoints, Perm.toList_pow_apply_eq_rotate, permCongr_apply, Perm.mem_sumCongrHom_range_of_perm_mapsTo_inl, Set.MapsTo.perm_pow, Perm.refl_mul, AntivaryOn.sum_mul_lt_sum_comp_perm_mul_iff, 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, alternatingGroup.subgroup_eq_top_of_isPreprimitive, permCongr_mul, Perm.cycleFactorsFinset_pairwise_disjoint, Perm.sameCycle_pow_right, Perm.decomposeFin_symm_apply_succ, AntivaryOn.sum_smul_comp_perm_eq_sum_smul_iff, Perm.sign_symm_trans_trans, swap_inv, card_perms_of_finset, List.zipWith_swap_prod_support', Perm.pairwise_commute_of_mem_zpowers, Perm.isCycle_swap_mul_aux₂, Tuple.comp_sort_eq_comp_iff_monotone, Perm.mem_ofSign, permCongr_symm, Perm.ofSubtype_subtypePerm, 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, Perm.cycleType_eq_two_two_subset_alternatingGroup, alternatingGroup.two_sylow_eq_kleinFour_of_card_eq_four, alternatingGroup.nontrivial_of_three_le_card, DomMulAct.stabilizer_card', Perm.exists_fixed_point_of_prime', Perm.support_inv, List.formPerm_mem_iff_mem, Perm.subtypePerm_apply_pow_of_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, Perm.alternatingGroup_le_of_isPreprimitive_of_isThreeCycle_mem, Set.image_perm, swap_apply_eq_iff, AlternatingGroup.isMultiplyPretransitive, Perm.IsCycle.support_pow_of_pos_of_lt_orderOf, 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, Perm.mem_cycleFactorsFinset_support, Perm.pow_apply_eq_self_of_apply_eq_self, AddConstEquiv.toPerm_apply, Perm.subtypeCongrHom_apply, Tuple.unique_antitone, EuclideanGeometry.Sphere.IsTangent.eq_orthRadius_or_eq_orthRadius_pointReflection_of_parallel_orthRadius, Perm.cycleType_eq_zero, MulAction.toPerm_injective, Perm.inv_subtypePerm, Finset.univ_perm_fin_succ, swap_eq_update, EuclideanGeometry.Sphere.IsDiameter.pointReflection_center_right, Perm.pow_apply_mem_support, Perm.pow_apply_eq_of_apply_apply_eq_self, Function.Involutive.toPerm_involutive, Tuple.eq_sort_iff, AntivaryOn.sum_mul_lt_sum_mul_comp_perm_iff, Perm.support_conj_eq_smul_support, Perm.viaEmbedding_apply, permCongr_def, Monovary.sum_comp_perm_mul_eq_sum_mul_iff, Perm.fst_prodExtendRight, Perm.isPretransitive_of_isCycle_mem, AddAction.toPermHom_apply_symm_apply, Perm.OnCycleFactors.coe_toPermHom, Tuple.antitone_pair_of_not_sorted', coe_constVAdd, Perm.exists_mem_stabilizer_isThreeCycle, Set.BijOn.extendDomain, 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, Set.BijOn.perm_inv, Perm.cycleOf_apply, Perm.Disjoint.inv_left, swap_mul_swap_mul_swap, MonovaryOn.sum_smul_comp_perm_eq_sum_smul_iff, Perm.sigmaCongrRightHom.card_range, Perm.subgroup_eq_top_of_swap_mem, 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, MonovaryOn.sum_comp_perm_smul_lt_sum_smul_iff, Set.powersetCard.addAction_faithful, Fin.cycleRange_of_lt, Perm.swap_mul_swap_same_mem_closure_three_cycles, alternatingGroup.range_ofSubtype, List.formPerm_pow_length_eq_one_of_nodup, AlternatingGroup.isPretransitive_of_three_le_card, Perm.OnCycleFactors.Subgroup.Centralizer.toConjAct_smul_mem_cycleFactorsFinset, 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, MonovaryOn.sum_comp_perm_mul_eq_sum_mul_iff, Set.InvOn.extendDomain, 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.isConj_of_support_equiv, Perm.apply_mem_support, LinearMap.IsSymmetric.eigenvalues_def, mem_closure_isSwap', DomMulAct.stabilizerMulEquiv_apply, GrpCat.SurjectiveOfEpiAuxs.h_apply_fromCoset, Perm.disjoint_one_right, Perm.apply_mem_fixedPoints_iff_mem_of_mem_centralizer, surjective_of_isSwap_of_isPretransitive, 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.support_pow_coprime, 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', Perm.ofSubtype_eq_iff, Polynomial.Gal.galActionHom_bijective_of_prime_degree, Perm.OnCycleFactors.kerParam_range_eq_centralizer_of_count_le_one, Perm.cycleOf_mem_cycleFactorsFinset_iff, Perm.subtypePerm_zpow, Perm.ofSubtype_swap_eq, Perm.prod_comp', Perm.extendDomain_one, finRotate_apply, 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, Set.MapsTo.extendDomain, 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, Perm.disjoint_prod_perm, 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.Basis.ofPermHomFun_apply_of_cycleOf_mem, 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, ExteriorAlgebra.ιMulti_family_mul_of_disjoint, Perm.subtypePerm_apply_zpow_of_mem, Perm.IsCycle.isCycle_pow_pos_of_lt_prime_order, permCongrHom_coe_equiv, AntivaryOn.sum_comp_perm_mul_eq_sum_mul_iff, Set.SurjOn.perm_pow, 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, Perm.cycleFactorsFinset_eq_list_toFinset, 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, MonovaryOn.sum_comp_perm_smul_eq_sum_smul_iff, Perm.Basis.ofPermHomFun_mul, Perm.instIsPretransitive, Perm.IsThreeCycle.mem_commutatorSet_alternatingGroup, 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.exists_with_cycleType_iff, 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, alternatingGroup.isConj_swap_mul_swap_of_cycleType_two, AlternatingMap.map_swap_add, Perm.exists_mem_support_of_mem_support_prod, 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_eq_sign_of_equiv, Tuple.bubble_sort_induction, 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, AntivaryOn.sum_smul_le_sum_smul_comp_perm, 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.cycleOf_mul_of_apply_right_eq_self, 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.Disjoint.isConj_mul, surjective_of_isSwap_of_isPretransitive', Perm.sign_prod_list_swap, Perm.mclosure_isSwap, Perm.not_isCycle_one, derangements.Equiv.RemoveNone.fiber_none, Perm.cycleFactorsFinset_mem_commute', Perm.pow_mod_orderOf_cycleOf_apply, Perm.cycle_zpow_mem_support_iff, Set.RightInvOn.extendDomain, Perm.moves_in, Perm.Disjoint.cycleType_noncommProd, Perm.IsSwap.of_subtype_isSwap, Perm.subtypePerm_apply, List.zipWith_swap_prod_support, Perm.alternatingGroup_le_of_isPreprimitive, 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.nodup_of_pairwise_disjoint_cycles, Perm.sign_prodCongrLeft, alternatingGroup.card_of_card_eq_four, finRotate_succ_apply, Perm.card_of_cycleType_singleton, Perm.monotone_iff, alternatingGroup.isThreeCycle_isConj, List.formPerm_apply_mem_eq_next, Perm.mem_conj_support, Perm.disjoint_noncommProd_right, Perm.perm_inv_mapsTo_iff_mapsTo, AlternatingGroup.map_subtype_of_cycleType, Perm.disjoint_mul_inv_of_mem_cycleFactorsFinset, 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, Perm.subtypePerm_pow, lt_finRotate_iff_ne_neg_one, Perm.isInvariant_of_support_le, Perm.subtypePerm_one, 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, Perm.support_le_prod_of_mem, 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, AntivaryOn.sum_mul_le_sum_comp_perm_mul, Perm.val_inv_equivUnitsEnd_apply, HasFPowerSeriesWithinOnBall.iteratedFDerivWithin_eq_sum, alternatingGroup.index_eq_two, Perm.Basis.ofPermHomFun_one, Perm.support_subtypePerm, inv_mulLeft, Perm.ofSubtype_subtypePerm_of_not_mem, derangements.Equiv.RemoveNone.fiber_some, Perm.subtypePermOfFintype_one, 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, alternatingGroup.stabilizer_subgroup_isPreprimitive, 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.has_swap_mem_of_lt_stabilizer, 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, Finset.exists_cycleOn, 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.sum_comp, MonovaryOn.sum_mul_comp_perm_lt_sum_mul_iff, 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.zpow_eq_ofSubtype_subtypePerm_iff, Perm.decomposeFin_symm_apply_zero, MultilinearMap.alternatization_def, Perm.OnCycleFactors.range_toPermHom_eq_range_toPermHom', Perm.OnCycleFactors.centralizer_smul_def, Tuple.monotone_sort, alternatingGroup.conj_smul_range_ofSubtype, Perm.inv_trans_self, Perm.conj_smul_range_ofSubtype, 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.ofSubtype_comp_subtype, alternatingGroup.isCoatom_stabilizer_of_ncard_lt_ncard_compl, MonovaryOn.sum_comp_perm_mul_lt_sum_mul_iff, 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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