Documentation Verification Report

Map

📁 Source: Mathlib/Algebra/Group/Subgroup/Map.lean

Statistics

MetricCount
DefinitionsaddSubgroupCongr, addSubgroupMap, comapAddSubgroup, mapAddSubgroup, addSubgroupComap, addSubgroupMap, addSubgroupOf, addSubgroupOfEquivOfLe, comap, equivMapOfInjective, map, subgroupComap, subgroupMap, comapSubgroup, mapSubgroup, subgroupCongr, subgroupMap, comap, equivMapOfInjective, map, subgroupOf, subgroupOfEquivOfLe
22
TheoremsaddSubgroupCongr_apply, addSubgroupCongr_symm_apply, addSubgroupMap_symm_apply, coe_addSubgroupMap_apply, coe_comapAddSubgroup, coe_mapAddSubgroup, comapAddSubgroup_apply, comapAddSubgroup_symm_apply, mapAddSubgroup_apply, mapAddSubgroup_symm_apply, symm_comapAddSubgroup, symm_mapAddSubgroup, addSubgroupComap_apply_coe, addSubgroupComap_surjective_of_surjective, addSubgroupMap_apply_coe, addSubgroupMap_surjective, closure_preimage_le, map_closure, addSubgroupOfEquivOfLe_apply_coe, addSubgroupOfEquivOfLe_symm_apply_coe_coe, addSubgroupOf_bot_eq_bot, addSubgroupOf_bot_eq_top, addSubgroupOf_eq_bot, addSubgroupOf_eq_top, addSubgroupOf_inj, addSubgroupOf_isAddCommutative, addSubgroupOf_map_subtype, addSubgroupOf_self, apply_coe_mem_map, bot_addSubgroupOf, codisjoint_map, coe_addSubgroupOf, coe_comap, coe_equivMapOfInjective_apply, coe_map, comap_comap, comap_equiv_eq_map_symm, comap_equiv_eq_map_symm', comap_iInf, comap_id, comap_inclusion_addSubgroupOf, comap_inf, comap_injective_isAddCommutative, comap_mono, comap_subtype, comap_sup_comap_le, comap_toAddSubmonoid, comap_top, disjoint_map, equivMapOfInjective_coe_addEquiv, gc_map_comap, iSup_comap_le, inf_addSubgroupOf_left, inf_addSubgroupOf_right, le_comap_map, map_addSubgroupOf_eq_of_le, map_bot, map_comap_le, map_eq_comap_of_inverse, map_equiv_eq_comap_symm, map_equiv_eq_comap_symm', map_equiv_top, map_iInf, map_iSup, map_id, map_inf, map_inf_eq, map_inf_le, map_isAddCommutative, map_le_iff_le_comap, map_map, map_mono, map_sup, map_symm_eq_iff_map_eq, map_toAddSubmonoid, map_top_of_surjective, map_zero_eq_bot, mem_addSubgroupOf, mem_comap, mem_map, mem_map_equiv, mem_map_iff_mem, mem_map_of_mem, surjOn_iff_le_map, toSubgroup_comap, top_addSubgroupOf, closure_preimage_le, map_closure, subgroupComap_apply_coe, subgroupComap_surjective_of_surjective, subgroupMap_apply_coe, subgroupMap_surjective, coe_comapSubgroup, coe_mapSubgroup, coe_subgroupMap_apply, comapSubgroup_apply, comapSubgroup_symm_apply, mapSubgroup_apply, mapSubgroup_symm_apply, subgroupCongr_apply, subgroupCongr_symm_apply, subgroupMap_symm_apply, symm_comapSubgroup, symm_mapSubgroup, apply_coe_mem_map, bot_subgroupOf, codisjoint_map, coe_comap, coe_equivMapOfInjective_apply, coe_map, coe_subgroupOf, comap_comap, comap_equiv_eq_map_symm, comap_equiv_eq_map_symm', comap_iInf, comap_id, comap_inclusion_subgroupOf, comap_inf, comap_injective_isMulCommutative, comap_mono, comap_subtype, comap_sup_comap_le, comap_toSubmonoid, comap_top, disjoint_map, equivMapOfInjective_coe_mulEquiv, gc_map_comap, iSup_comap_le, inf_subgroupOf_left, inf_subgroupOf_right, le_comap_map, map_bot, map_comap_le, map_eq_comap_of_inverse, map_equiv_eq_comap_symm, map_equiv_eq_comap_symm', map_equiv_top, map_iInf, map_iSup, map_id, map_inf, map_inf_eq, map_inf_le, map_isMulCommutative, map_le_iff_le_comap, map_map, map_mono, map_one_eq_bot, map_subgroupOf_eq_of_le, map_sup, map_symm_eq_iff_map_eq, map_toSubmonoid, map_top_of_surjective, mem_comap, mem_map, mem_map_equiv, mem_map_iff_mem, mem_map_of_mem, mem_subgroupOf, subgroupOfEquivOfLe_apply_coe, subgroupOfEquivOfLe_symm_apply_coe_coe, subgroupOf_bot_eq_bot, subgroupOf_bot_eq_top, subgroupOf_eq_bot, subgroupOf_eq_top, subgroupOf_inj, subgroupOf_isMulCommutative, subgroupOf_map_subtype, subgroupOf_self, surjOn_iff_le_map, toAddSubgroup_comap, top_subgroupOf
172
Total194

AddEquiv

Definitions

NameCategoryTheorems
addSubgroupCongr 📖CompOp
4 mathmath: addSubgroupCongr_apply, SubAddAction.ofFixingAddSubgroup_of_eq_bijective, SubAddAction.ofFixingAddSubgroup_of_eq_apply, addSubgroupCongr_symm_apply
addSubgroupMap 📖CompOp
3 mathmath: addSubgroupMap_symm_apply, coe_addSubgroupMap_apply, AddSubgroup.equivMapOfInjective_coe_addEquiv
comapAddSubgroup 📖CompOp
4 mathmath: coe_comapAddSubgroup, comapAddSubgroup_apply, symm_comapAddSubgroup, comapAddSubgroup_symm_apply
mapAddSubgroup 📖CompOp
4 mathmath: symm_mapAddSubgroup, mapAddSubgroup_symm_apply, coe_mapAddSubgroup, mapAddSubgroup_apply

Theorems

NameKindAssumesProvesValidatesDepends On
addSubgroupCongr_apply 📖mathematicalAddSubgroup
SetLike.instMembership
AddSubgroup.instSetLike
DFunLike.coe
AddEquiv
AddSubgroup.add
EquivLike.toFunLike
instEquivLike
addSubgroupCongr
addSubgroupCongr_symm_apply 📖mathematicalAddSubgroup
SetLike.instMembership
AddSubgroup.instSetLike
DFunLike.coe
AddEquiv
AddSubgroup.add
EquivLike.toFunLike
instEquivLike
symm
addSubgroupCongr
addSubgroupMap_symm_apply 📖mathematicalDFunLike.coe
AddEquiv
AddSubgroup
SetLike.instMembership
AddSubgroup.instSetLike
AddSubgroup.map
AddMonoidHomClass.toAddMonoidHom
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
EquivLike.toFunLike
instEquivLike
AddEquivClass.instAddMonoidHomClass
instAddEquivClass
AddSubgroup.add
symm
addSubgroupMap
Set
Set.instMembership
SetLike.coe
SetLike.mem_coe
Set.image
Equiv
Equiv.instEquivLike
toEquiv
Equiv.symm
Set.mem_image_equiv
AddEquivClass.instAddMonoidHomClass
instAddEquivClass
coe_addSubgroupMap_apply 📖mathematicalAddSubgroup
SetLike.instMembership
AddSubgroup.instSetLike
AddSubgroup.map
AddMonoidHomClass.toAddMonoidHom
AddEquiv
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
EquivLike.toFunLike
instEquivLike
AddEquivClass.instAddMonoidHomClass
instAddEquivClass
DFunLike.coe
AddSubgroup.add
addSubgroupMap
AddEquivClass.instAddMonoidHomClass
instAddEquivClass
coe_comapAddSubgroup 📖mathematicalDFunLike.coe
OrderIso
AddSubgroup
Preorder.toLE
PartialOrder.toPreorder
AddSubgroup.instPartialOrder
instFunLikeOrderIso
comapAddSubgroup
AddSubgroup.comap
toAddMonoidHom
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
coe_mapAddSubgroup 📖mathematicalDFunLike.coe
OrderIso
AddSubgroup
Preorder.toLE
PartialOrder.toPreorder
AddSubgroup.instPartialOrder
instFunLikeOrderIso
mapAddSubgroup
AddSubgroup.map
toAddMonoidHom
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
comapAddSubgroup_apply 📖mathematicalDFunLike.coe
RelIso
AddSubgroup
Preorder.toLE
PartialOrder.toPreorder
AddSubgroup.instPartialOrder
RelIso.instFunLike
comapAddSubgroup
AddSubgroup.comap
AddMonoidHomClass.toAddMonoidHom
AddEquiv
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
EquivLike.toFunLike
instEquivLike
comapAddSubgroup_symm_apply 📖mathematicalDFunLike.coe
RelIso
AddSubgroup
Preorder.toLE
PartialOrder.toPreorder
AddSubgroup.instPartialOrder
RelIso.instFunLike
RelIso.symm
comapAddSubgroup
AddSubgroup.comap
AddMonoidHomClass.toAddMonoidHom
AddEquiv
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
EquivLike.toFunLike
instEquivLike
symm
mapAddSubgroup_apply 📖mathematicalDFunLike.coe
RelIso
AddSubgroup
Preorder.toLE
PartialOrder.toPreorder
AddSubgroup.instPartialOrder
RelIso.instFunLike
mapAddSubgroup
AddSubgroup.map
AddMonoidHomClass.toAddMonoidHom
AddEquiv
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
EquivLike.toFunLike
instEquivLike
mapAddSubgroup_symm_apply 📖mathematicalDFunLike.coe
RelIso
AddSubgroup
Preorder.toLE
PartialOrder.toPreorder
AddSubgroup.instPartialOrder
RelIso.instFunLike
RelIso.symm
mapAddSubgroup
AddSubgroup.map
AddMonoidHomClass.toAddMonoidHom
AddEquiv
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
EquivLike.toFunLike
instEquivLike
symm
symm_comapAddSubgroup 📖mathematicalOrderIso.symm
AddSubgroup
Preorder.toLE
PartialOrder.toPreorder
AddSubgroup.instPartialOrder
comapAddSubgroup
symm
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
symm_mapAddSubgroup 📖mathematicalOrderIso.symm
AddSubgroup
Preorder.toLE
PartialOrder.toPreorder
AddSubgroup.instPartialOrder
mapAddSubgroup
symm
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid

AddMonoidHom

Definitions

NameCategoryTheorems
addSubgroupComap 📖CompOp
2 mathmath: addSubgroupComap_surjective_of_surjective, addSubgroupComap_apply_coe
addSubgroupMap 📖CompOp
3 mathmath: addSubgroupMap_apply_coe, AddSubgroup.ker_addSubgroupMap, addSubgroupMap_surjective

Theorems

NameKindAssumesProvesValidatesDepends On
addSubgroupComap_apply_coe 📖mathematicalAddSubmonoid
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
SetLike.instMembership
AddSubmonoid.instSetLike
AddSubgroup.toAddSubmonoid
DFunLike.coe
AddMonoidHom
AddSubgroup
AddSubgroup.instSetLike
AddSubgroup.comap
AddZeroClass.toAddZero
AddSubgroup.toAddGroup
instFunLike
addSubgroupComap
AddSubmonoid.comap
addSubgroupComap_surjective_of_surjective 📖mathematicalDFunLike.coe
AddMonoidHom
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
instFunLike
AddSubgroup
SetLike.instMembership
AddSubgroup.instSetLike
AddSubgroup.comap
AddSubgroup.toAddGroup
addSubgroupComap
addSubmonoidComap_surjective_of_surjective
addSubgroupMap_apply_coe 📖mathematicalAddSubmonoid
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
SetLike.instMembership
AddSubmonoid.instSetLike
AddSubmonoid.map
AddMonoidHom
AddZeroClass.toAddZero
instFunLike
AddSubgroup.toAddSubmonoid
DFunLike.coe
AddSubgroup
AddSubgroup.instSetLike
AddSubgroup.map
AddSubgroup.toAddGroup
addSubgroupMap
addSubgroupMap_surjective 📖mathematicalAddSubgroup
SetLike.instMembership
AddSubgroup.instSetLike
AddSubgroup.map
DFunLike.coe
AddMonoidHom
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddSubgroup.toAddGroup
instFunLike
addSubgroupMap
addSubmonoidMap_surjective
closure_preimage_le 📖mathematicalAddSubgroup
Preorder.toLE
PartialOrder.toPreorder
AddSubgroup.instPartialOrder
AddSubgroup.closure
Set.preimage
DFunLike.coe
AddMonoidHom
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
instFunLike
AddSubgroup.comap
AddSubgroup.closure_le
SetLike.mem_coe
AddSubgroup.mem_comap
AddSubgroup.subset_closure
map_closure 📖mathematicalAddSubgroup.map
AddSubgroup.closure
Set.image
DFunLike.coe
AddMonoidHom
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
instFunLike
GaloisConnection.l_comm_of_u_comm
Set.image_preimage
AddSubgroup.gc_map_comap
GaloisInsertion.gc

AddSubgroup

Definitions

NameCategoryTheorems
addSubgroupOf 📖CompOp
59 mathmath: inf_addSubgroupOf_inf_normal_of_left, IsFiniteRelIndex.to_finiteIndex_addSubgroupOf, quotientEquivProdOfLE_symm_apply, addSubgroupOf_eq_top, quotientiInfAddSubgroupOfEmbedding_apply_mk, coe_addSubgroupOf, addSubgroupOfContinuousAddEquivOfLe_apply, top_addSubgroupOf, inf_addSubgroupOf_left, inf_addSubgroupOf_right, addSubgroupOf_self, AddMonoidHom.addSubgroupOf_range_eq_of_le, AddMonoidHom.ker_restrict, prod_addSubgroupOf_prod_normal, addSubgroupOf_normalizer_eq, ker_addSubgroupMap, addSubgroupOfEquivOfLe_apply_coe, addSubgroupOf_map_subtype, Normal.addSubgroupOf, quotientAddSubgroupOfMapOfLE_apply_mk, instFiniteIndex_addSubgroupOf, addSubgroupOfEquivOfLe_symm_apply_coe_coe, addSubgroupOf_isAddCommutative, codisjoint_addSubgroupOf_sup, QuotientAddGroup.quotientMapAddSubgroupOfOfLe_mk, addSubgroupOf_bot_eq_top, normal_addSubgroupOf_iff, bot_addSubgroupOf, relIndex_addSubgroupOf, MapSubtype.orderIso_symm_apply, addSubgroupOf_inj, normal_addSubgroupOf, comap_subtype, map_addSubgroupOf_eq_of_le, normal_addSubgroupOf_of_le_normalizer, normal_addSubgroupOf_iff_le_normalizer, quotientiInfAddSubgroupOfEmbedding_apply, addSubgroupOf_bot_eq_bot, quotientEquivProdOfLE'_apply, mem_addSubgroupOf, quotientEquivProdOfLE'_symm_apply, addSubgroupOfContinuousAddEquivOfLe_symm_apply, quotientEquivProdOfLE_apply, IsSubnormal.iff_eq_top_or_exists, exists_leftTransversal_of_FiniteIndex, inclusion_range, addSubgroupOfContinuousAddEquivOfLe_toAddEquiv, inf_addSubgroupOf_inf_normal_of_right, forall, comap_inclusion_addSubgroupOf, addSubgroupOf_eq_bot, quotientAddSubgroupOfEmbeddingOfLE_apply_mk, addSubgroupOf_isOpen, addSubgroupOf_sup, AddAction.orbitRel_addSubgroupOf, normal_addSubgroupOf_iff_le_normalizer_inf, normal_addSubgroupOf_sup_of_le_normalizer, normal_in_normalizer, IsSubnormal.isSubnormal_iff
addSubgroupOfEquivOfLe 📖CompOp
4 mathmath: addSubgroupOfContinuousAddEquivOfLe_apply, addSubgroupOfEquivOfLe_apply_coe, addSubgroupOfEquivOfLe_symm_apply_coe_coe, addSubgroupOfContinuousAddEquivOfLe_toAddEquiv
comap 📖CompOp
78 mathmath: DFinsupp.range_mapRangeAddMonoidHom, index_comap_of_surjective, characteristic_iff_comap_le, coe_comap, card_comap_dvd_of_injective, comap_equiv_eq_map_symm, comap_map_eq, AddEquiv.coe_comapAddSubgroup, ZLattice.comap_toAddSubgroup, comap_map_eq_self, comap_inf, AddMonoidHom.addSubgroupComap_surjective_of_surjective, ker_le_comap, comap_normalizer_eq_of_surjective, QuotientAddGroup.strictMono_comap_prod_image, AddMonoidHom.comap_ker, map_equiv_eq_comap_symm, comap_normalizer_eq_of_le_range, AddMonoidHom.addSubgroupComap_apply_coe, prod_top, comap_sup_eq_of_le_range, QuotientAddGroup.strictMono_comap_prod_map, Characteristic.comap_quotient_mk, map_comap_eq_self, map_comap_eq, QuotientAddGroup.comap_map_mk', AddEquiv.comapAddSubgroup_apply, comap_mono, index_comap, comap_toAddSubmonoid, DFinsupp.ker_mapRangeAddMonoidHom, map_le_iff_le_comap, comap_le_comap_of_surjective, AddMonoidHom.prodMap_comap_prod, map_equiv_eq_comap_symm', DirectSum.ker_map, comap_id, DirectSum.range_map, mem_comap, comap_injective, characteristic_iff_le_comap, Normal.comap, top_prod, gc_map_comap, comap_lt_comap_of_surjective, comap_iInf, Characteristic.fixed, le_pi_iff, QuotientAddGroup.comap_comap_center, FiniteIndexNormalAddSubgroup.toAddSubgroup_comap, comap_subtype, Subgroup.toAddSubgroup_comap, map_comap_eq_self_of_surjective, Submodule.AddMonoidHom.coe_toIntLinearMap_comap, map_eq_comap_of_inverse, AddMonoidHom.closure_preimage_le, comap_top, OpenAddSubgroup.toAddSubgroup_comap, le_comap_map, map_comap_le, comap_sup_eq, AddMonoidHom.comap_bot, comap_equiv_eq_map_symm', iSup_comap_le, comap_comap, comap_inclusion_addSubgroupOf, comap_sup_comap_le, goursat, relIndex_comap, comap_injective_isAddCommutative, comap_map_eq_self_of_injective, le_normalizer_comap, toSubgroup_comap, characteristic_iff_comap_eq, comap_le_comap_of_le_range, AddEquiv.comapAddSubgroup_symm_apply, QuotientAddGroup.le_comap_mk', normal_comap
equivMapOfInjective 📖CompOp
2 mathmath: coe_equivMapOfInjective_apply, equivMapOfInjective_coe_addEquiv
map 📖CompOp
123 mathmath: mem_map_iff_mem, map_toAddSubmonoid, map_eq_map_iff, AddEquiv.addSubgroupMap_symm_apply, AddMonoidHom.range_comp, AddMonoidHom.ker_comp_addEquiv, index_map_equiv, map_inf_le, le_prod_iff, card_map_of_injective, comap_equiv_eq_map_symm, map_eq_range_iff, comap_map_eq, AddAction.stabilizer_vadd_eq_stabilizer_map_conj, map_map, QuotientAddGroup.ker_map, AddAction.map_stabilizer_le, map_zero_eq_bot, index_map_eq, coe_equivMapOfInjective_apply, AddMonoidHom.range_eq_map, characteristic_iff_le_map, relIndex_map_map, card_subtype, mem_map_of_mem, AddMonoidHom.addSubgroupMap_apply_coe, comap_map_eq_self, NumberField.Units.span_basisOfIsMaxRank, ker_addSubgroupMap, map_top_of_surjective, map_inf_eq, map_subtype_le, map_equiv_top, AddMonoidHom.map_range, AddMonoidHom.map_closure, dvd_index_map, map_le_map_iff, NumberField.Units.dirichletUnitTheorem.map_logEmbedding_sup_torsion, index_map, Normal.map, map_equiv_eq_comap_symm, addSubgroupOf_map_subtype, MonoidHom.coe_toAdditive_map, map_subtype_lt_map_subtype, pi_le_iff, map_normalizer_eq_of_bijective, index_map_dvd, AddEquiv.mapAddSubgroup_symm_apply, QuotientAddGroup.strictMono_comap_prod_map, map_equiv_normalizer_eq, map_comap_eq_self, characteristic_iff_map_eq, map_eq_bot_iff, map_comap_eq, QuotientAddGroup.comap_map_mk', SubAddAction.fixingAddSubgroup_vadd_eq_fixingAddSubgroup_map_conj, map_eq_bot_iff_of_injective, map_le_map_iff_of_injective, map_le_iff_le_comap, apply_coe_mem_map, IsSubnormal.trans', NormedAddGroupHom.comp_range, QuotientAddGroup.ker_lift, le_normalizer_map, map_equiv_eq_comap_symm', AddAction.IsBlock.of_addSubgroup_of_conjugate, AddMonoidHom.addSubgroupMap_surjective, AddEquiv.coe_addSubgroupMap_apply, index_map_of_injective, relIndex_map_map_of_injective, map_isAddCommutative, AddMonoidHom.restrict_range, map_bot, AddEquiv.coe_mapAddSubgroup, MapSubtype.orderIso_apply_coe, map_injective, AddMonoidHom.map_zmultiples, index_map_subtype, card_map_dvd, map_mono, gc_map_comap, map_subtype_le_map_subtype, AddEquiv.mapAddSubgroup_apply, disjoint_map, mem_map_equiv, map_id, map_lt_map_iff_of_injective, AddMonoidHom.coe_toIntLinearMap_map, prod_le_iff, map_addSubgroupOf_eq_of_le, AddMonoidHom.coe_toMultiplicative_map, SubAddAction.fixingAddSubgroup_of_insert, map_comap_eq_self_of_surjective, map_iInf, coe_map, map_eq_comap_of_inverse, index_map_of_bijective, QuotientAddGroup.map_normal, le_comap_map, map_comap_le, map_inf, map_symm_eq_iff_map_eq, QuotientAddGroup.quotientQuotientEquivQuotientAux_mk, surjOn_iff_le_map, comap_equiv_eq_map_symm', mem_map, QuotientAddGroup.map_mk'_self, Submodule.map_toAddSubgroup, SubAddAction.fixingAddSubgroup_map_conj_eq, goursat, relIndex_comap, pointwise_smul_def, relIndex_ker, map_iSup, DenseRange.topologicalClosure_map_addSubgroup, comap_map_eq_self_of_injective, map_sup, codisjoint_map, QuotientAddGroup.quotientQuotientEquivQuotientAux_mk_mk, map_le_map_iff', characteristic_iff_map_le, map_le_range, map_centralizer_le_centralizer_image

Theorems

NameKindAssumesProvesValidatesDepends On
addSubgroupOfEquivOfLe_apply_coe 📖mathematicalAddSubgroup
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
SetLike.instMembership
instSetLike
DFunLike.coe
AddEquiv
toAddGroup
addSubgroupOf
add
EquivLike.toFunLike
AddEquiv.instEquivLike
addSubgroupOfEquivOfLe
addSubgroupOfEquivOfLe_symm_apply_coe_coe 📖mathematicalAddSubgroup
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
SetLike.instMembership
instSetLike
toAddGroup
addSubgroupOf
DFunLike.coe
AddEquiv
add
EquivLike.toFunLike
AddEquiv.instEquivLike
AddEquiv.symm
addSubgroupOfEquivOfLe
addSubgroupOf_bot_eq_bot 📖mathematicaladdSubgroupOf
Bot.bot
AddSubgroup
instBot
SetLike.instMembership
instSetLike
toAddGroup
Unique.instSubsingleton
addSubgroupOf_bot_eq_top 📖mathematicaladdSubgroupOf
Bot.bot
AddSubgroup
instBot
Top.top
SetLike.instMembership
instSetLike
toAddGroup
instTop
Unique.instSubsingleton
addSubgroupOf_eq_bot 📖mathematicaladdSubgroupOf
Bot.bot
AddSubgroup
SetLike.instMembership
instSetLike
toAddGroup
instBot
Disjoint
instPartialOrder
BoundedOrder.toOrderBot
Preorder.toLE
PartialOrder.toPreorder
CompleteLattice.toBoundedOrder
instCompleteLattice
disjoint_iff
bot_addSubgroupOf
bot_inf_eq
addSubgroupOf_eq_top 📖mathematicaladdSubgroupOf
Top.top
AddSubgroup
SetLike.instMembership
instSetLike
toAddGroup
instTop
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
top_addSubgroupOf
top_inf_eq
inf_eq_right
addSubgroupOf_inj 📖mathematicaladdSubgroupOf
AddSubgroup
instMin
SetLike.ext_iff
mem_addSubgroupOf
mem_inf
addSubgroupOf_isAddCommutative 📖mathematicalIsAddCommutative
AddSubgroup
SetLike.instMembership
instSetLike
toAddGroup
addSubgroupOf
add
comap_injective_isAddCommutative
Subtype.coe_injective
addSubgroupOf_map_subtype 📖mathematicalmap
AddSubgroup
SetLike.instMembership
instSetLike
toAddGroup
subtype
addSubgroupOf
instMin
SetLike.ext'
Subtype.image_preimage_coe
Set.inter_comm
addSubgroupOf_self 📖mathematicaladdSubgroupOf
Top.top
AddSubgroup
SetLike.instMembership
instSetLike
toAddGroup
instTop
top_unique
apply_coe_mem_map 📖mathematicalAddSubgroup
SetLike.instMembership
instSetLike
map
DFunLike.coe
AddMonoidHom
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddMonoidHom.instFunLike
mem_map_of_mem
Subtype.prop
bot_addSubgroupOf 📖mathematicaladdSubgroupOf
Bot.bot
AddSubgroup
instBot
SetLike.instMembership
instSetLike
toAddGroup
ext
codisjoint_map 📖mathematicalDFunLike.coe
AddMonoidHom
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddMonoidHom.instFunLike
Codisjoint
AddSubgroup
instPartialOrder
BoundedOrder.toOrderTop
Preorder.toLE
PartialOrder.toPreorder
CompleteLattice.toBoundedOrder
instCompleteLattice
mapcodisjoint_iff
map_sup
map_top_of_surjective
coe_addSubgroupOf 📖mathematicalSetLike.coe
AddSubgroup
SetLike.instMembership
instSetLike
toAddGroup
addSubgroupOf
Set.preimage
DFunLike.coe
AddMonoidHom
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddMonoidHom.instFunLike
subtype
coe_comap 📖mathematicalSetLike.coe
AddSubgroup
instSetLike
comap
Set.preimage
DFunLike.coe
AddMonoidHom
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddMonoidHom.instFunLike
coe_equivMapOfInjective_apply 📖mathematicalDFunLike.coe
AddMonoidHom
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddMonoidHom.instFunLike
AddSubgroup
SetLike.instMembership
instSetLike
map
AddEquiv
add
EquivLike.toFunLike
AddEquiv.instEquivLike
equivMapOfInjective
coe_map 📖mathematicalSetLike.coe
AddSubgroup
instSetLike
map
Set.image
DFunLike.coe
AddMonoidHom
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddMonoidHom.instFunLike
comap_comap 📖mathematicalcomap
AddMonoidHom.comp
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
comap_equiv_eq_map_symm 📖mathematicalcomap
AddMonoidHomClass.toAddMonoidHom
AddEquiv
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
EquivLike.toFunLike
AddEquiv.instEquivLike
AddEquivClass.instAddMonoidHomClass
AddEquiv.instAddEquivClass
map
AddEquiv.symm
AddEquivClass.instAddMonoidHomClass
AddEquiv.instAddEquivClass
map_equiv_eq_comap_symm
comap_equiv_eq_map_symm' 📖mathematicalcomap
AddEquiv.toAddMonoidHom
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
map
AddEquiv.symm
AddZero.toAdd
AddZeroClass.toAddZero
AddEquivClass.instAddMonoidHomClass
AddEquiv.instAddEquivClass
map_equiv_eq_comap_symm
comap_iInf 📖mathematicalcomap
iInf
AddSubgroup
instInfSet
GaloisConnection.u_iInf
gc_map_comap
comap_id 📖mathematicalcomap
AddMonoidHom.id
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
ext
comap_inclusion_addSubgroupOf 📖mathematicalAddSubgroup
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
comap
SetLike.instMembership
instSetLike
toAddGroup
inclusion
addSubgroupOf
comap_inf 📖mathematicalcomap
AddSubgroup
instMin
GaloisConnection.u_inf
gc_map_comap
comap_injective_isAddCommutative 📖mathematicalDFunLike.coe
AddMonoidHom
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddMonoidHom.instFunLike
IsAddCommutative
AddSubgroup
SetLike.instMembership
instSetLike
comap
add
add_comm
map_add
AddMonoidHomClass.toAddHomClass
AddMonoidHom.instAddMonoidHomClass
coe_add
comap_mono 📖mathematicalAddSubgroup
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
comapSet.preimage_mono
comap_subtype 📖mathematicalcomap
AddSubgroup
SetLike.instMembership
instSetLike
toAddGroup
subtype
addSubgroupOf
comap_sup_comap_le 📖mathematicalAddSubgroup
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
SemilatticeSup.toMax
Lattice.toSemilatticeSup
CompleteLattice.toLattice
instCompleteLattice
comap
Monotone.le_map_sup
comap_mono
comap_toAddSubmonoid 📖mathematicaltoAddSubmonoid
comap
AddMonoidHomClass.toAddMonoidHom
AddEquiv
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
EquivLike.toFunLike
AddEquiv.instEquivLike
AddEquivClass.instAddMonoidHomClass
AddEquiv.instAddEquivClass
AddSubmonoid.comap
AddMonoidHom
AddMonoidHom.instFunLike
AddMonoidHom.instAddMonoidHomClass
AddEquiv.toAddMonoidHom
AddEquivClass.instAddMonoidHomClass
AddEquiv.instAddEquivClass
comap_top 📖mathematicalcomap
Top.top
AddSubgroup
instTop
GaloisConnection.u_top
gc_map_comap
disjoint_map 📖mathematicalDFunLike.coe
AddMonoidHom
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddMonoidHom.instFunLike
Disjoint
AddSubgroup
instPartialOrder
BoundedOrder.toOrderBot
Preorder.toLE
PartialOrder.toPreorder
CompleteLattice.toBoundedOrder
instCompleteLattice
mapdisjoint_iff
map_inf
map_bot
equivMapOfInjective_coe_addEquiv 📖mathematicalequivMapOfInjective
AddMonoidHomClass.toAddMonoidHom
AddEquiv
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
EquivLike.toFunLike
AddEquiv.instEquivLike
AddEquivClass.instAddMonoidHomClass
AddEquiv.instAddEquivClass
EquivLike.injective
AddEquiv.addSubgroupMap
AddEquiv.ext
AddEquivClass.instAddMonoidHomClass
AddEquiv.instAddEquivClass
EquivLike.injective
gc_map_comap 📖mathematicalGaloisConnection
AddSubgroup
PartialOrder.toPreorder
instPartialOrder
map
comap
map_le_iff_le_comap
iSup_comap_le 📖mathematicalAddSubgroup
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
iSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
instCompleteLattice
comap
Monotone.le_map_iSup
comap_mono
inf_addSubgroupOf_left 📖mathematicaladdSubgroupOf
AddSubgroup
instMin
inf_comm
inf_addSubgroupOf_right
inf_addSubgroupOf_right 📖mathematicaladdSubgroupOf
AddSubgroup
instMin
inf_right_idem
le_comap_map 📖mathematicalAddSubgroup
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
comap
map
GaloisConnection.le_u_l
gc_map_comap
map_addSubgroupOf_eq_of_le 📖mathematicalAddSubgroup
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
map
SetLike.instMembership
instSetLike
toAddGroup
subtype
addSubgroupOf
addSubgroupOf_map_subtype
inf_eq_left
map_bot 📖mathematicalmap
Bot.bot
AddSubgroup
instBot
GaloisConnection.l_bot
gc_map_comap
map_comap_le 📖mathematicalAddSubgroup
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
map
comap
GaloisConnection.l_u_le
gc_map_comap
map_eq_comap_of_inverse 📖mathematicalDFunLike.coe
AddMonoidHom
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddMonoidHom.instFunLike
map
comap
SetLike.ext'
coe_map
coe_comap
Set.image_eq_preimage_of_inverse
map_equiv_eq_comap_symm 📖mathematicalmap
AddMonoidHomClass.toAddMonoidHom
AddEquiv
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
EquivLike.toFunLike
AddEquiv.instEquivLike
AddEquivClass.instAddMonoidHomClass
AddEquiv.instAddEquivClass
comap
AddEquiv.symm
map_equiv_eq_comap_symm'
map_equiv_eq_comap_symm' 📖mathematicalmap
AddEquiv.toAddMonoidHom
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
comap
AddEquiv.symm
AddZero.toAdd
AddZeroClass.toAddZero
SetLike.coe_injective
Equiv.image_eq_preimage_symm
map_equiv_top 📖mathematicalmap
AddMonoidHomClass.toAddMonoidHom
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
EquivLike.toFunLike
AddEquivClass.instAddMonoidHomClass
Top.top
AddSubgroup
instTop
map_top_of_surjective
AddEquivClass.instAddMonoidHomClass
EquivLike.surjective
map_iInf 📖mathematicalDFunLike.coe
AddMonoidHom
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddMonoidHom.instFunLike
map
iInf
AddSubgroup
instInfSet
SetLike.coe_injective
coe_iInf
Set.InjOn.image_iInter_eq
Set.injOn_of_injective
map_iSup 📖mathematicalmap
iSup
AddSubgroup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
instCompleteLattice
GaloisConnection.l_iSup
gc_map_comap
map_id 📖mathematicalmap
AddMonoidHom.id
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
SetLike.coe_injective
Set.image_id
map_inf 📖mathematicalDFunLike.coe
AddMonoidHom
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddMonoidHom.instFunLike
map
AddSubgroup
instMin
SetLike.coe_injective
Set.image_inter
map_inf_eq 📖mathematicalDFunLike.coe
AddMonoidHom
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddMonoidHom.instFunLike
map
AddSubgroup
instMin
SetLike.coe_set_eq
Set.image_inter
map_inf_le 📖mathematicalAddSubgroup
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
map
instMin
le_inf
map_mono
inf_le_left
inf_le_right
map_isAddCommutative 📖mathematicalIsAddCommutative
AddSubgroup
SetLike.instMembership
instSetLike
map
add
coe_add
map_add
AddMonoidHomClass.toAddHomClass
AddMonoidHom.instAddMonoidHomClass
add_comm
map_le_iff_le_comap 📖mathematicalAddSubgroup
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
map
comap
Set.image_subset_iff
map_map 📖mathematicalmap
AddMonoidHom.comp
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
SetLike.coe_injective
Set.image_image
map_mono 📖mathematicalAddSubgroup
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
mapSet.image_mono
map_sup 📖mathematicalmap
AddSubgroup
SemilatticeSup.toMax
Lattice.toSemilatticeSup
CompleteLattice.toLattice
instCompleteLattice
GaloisConnection.l_sup
gc_map_comap
map_symm_eq_iff_map_eq 📖mathematicalmap
AddMonoidHomClass.toAddMonoidHom
AddEquiv
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
EquivLike.toFunLike
AddEquiv.instEquivLike
AddEquivClass.instAddMonoidHomClass
AddEquiv.instAddEquivClass
AddEquiv.symm
AddEquivClass.instAddMonoidHomClass
AddEquiv.instAddEquivClass
map_map
AddEquiv.coe_addMonoidHom_trans
AddEquiv.symm_trans_self
AddEquiv.coe_addMonoidHom_refl
map_id
AddEquiv.self_trans_symm
map_toAddSubmonoid 📖mathematicaltoAddSubmonoid
map
AddSubmonoid.map
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddMonoidHom
AddZeroClass.toAddZero
AddMonoidHom.instFunLike
AddMonoidHom.instAddMonoidHomClass
map_top_of_surjective 📖mathematicalDFunLike.coe
AddMonoidHom
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddMonoidHom.instFunLike
map
Top.top
AddSubgroup
instTop
eq_top_iff
map_zero_eq_bot 📖mathematicalmap
AddMonoidHom
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
instZeroAddMonoidHom
Bot.bot
AddSubgroup
instBot
eq_bot_iff
ZeroMemClass.zero_mem
AddSubmonoidClass.toZeroMemClass
AddSubgroupClass.toAddSubmonoidClass
instAddSubgroupClass
mem_addSubgroupOf 📖mathematicalAddSubgroup
SetLike.instMembership
instSetLike
toAddGroup
addSubgroupOf
mem_comap 📖mathematicalAddSubgroup
SetLike.instMembership
instSetLike
comap
DFunLike.coe
AddMonoidHom
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddMonoidHom.instFunLike
mem_map 📖mathematicalAddSubgroup
SetLike.instMembership
instSetLike
map
DFunLike.coe
AddMonoidHom
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddMonoidHom.instFunLike
mem_map_equiv 📖mathematicalAddSubgroup
SetLike.instMembership
instSetLike
map
AddEquiv.toAddMonoidHom
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
DFunLike.coe
AddEquiv
AddZero.toAdd
AddZeroClass.toAddZero
EquivLike.toFunLike
AddEquiv.instEquivLike
AddEquiv.symm
Set.mem_image_equiv
mem_map_iff_mem 📖mathematicalDFunLike.coe
AddMonoidHom
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddMonoidHom.instFunLike
AddSubgroup
SetLike.instMembership
instSetLike
map
Function.Injective.mem_set_image
mem_map_of_mem 📖mathematicalAddSubgroup
SetLike.instMembership
instSetLike
map
DFunLike.coe
AddMonoidHom
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddMonoidHom.instFunLike
Set.mem_image_of_mem
surjOn_iff_le_map 📖mathematicalSet.SurjOn
DFunLike.coe
AddMonoidHom
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddMonoidHom.instFunLike
SetLike.coe
AddSubgroup
instSetLike
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
map
toSubgroup_comap 📖mathematicalSubgroup.comap
Multiplicative
Multiplicative.group
DFunLike.coe
Equiv
AddMonoidHom
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
MonoidHom
MulOneClass.toMulOne
Multiplicative.mulOneClass
EquivLike.toFunLike
Equiv.instEquivLike
AddMonoidHom.toMultiplicative
OrderIso
AddSubgroup
Subgroup
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
Subgroup.instPartialOrder
instFunLikeOrderIso
toSubgroup
comap
top_addSubgroupOf 📖mathematicaladdSubgroupOf
Top.top
AddSubgroup
instTop
SetLike.instMembership
instSetLike
toAddGroup

MonoidHom

Definitions

NameCategoryTheorems
subgroupComap 📖CompOp
2 mathmath: subgroupComap_apply_coe, subgroupComap_surjective_of_surjective
subgroupMap 📖CompOp
3 mathmath: Subgroup.ker_subgroupMap, subgroupMap_surjective, subgroupMap_apply_coe

Theorems

NameKindAssumesProvesValidatesDepends On
closure_preimage_le 📖mathematicalSubgroup
Preorder.toLE
PartialOrder.toPreorder
Subgroup.instPartialOrder
Subgroup.closure
Set.preimage
DFunLike.coe
MonoidHom
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
instFunLike
Subgroup.comap
Subgroup.closure_le
SetLike.mem_coe
Subgroup.mem_comap
Subgroup.subset_closure
map_closure 📖mathematicalSubgroup.map
Subgroup.closure
Set.image
DFunLike.coe
MonoidHom
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
instFunLike
GaloisConnection.l_comm_of_u_comm
Set.image_preimage
Subgroup.gc_map_comap
GaloisInsertion.gc
subgroupComap_apply_coe 📖mathematicalSubmonoid
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
SetLike.instMembership
Submonoid.instSetLike
Subgroup.toSubmonoid
DFunLike.coe
MonoidHom
Subgroup
Subgroup.instSetLike
Subgroup.comap
MulOneClass.toMulOne
Subgroup.toGroup
instFunLike
subgroupComap
Submonoid.comap
subgroupComap_surjective_of_surjective 📖mathematicalDFunLike.coe
MonoidHom
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
instFunLike
Subgroup
SetLike.instMembership
Subgroup.instSetLike
Subgroup.comap
Subgroup.toGroup
subgroupComap
submonoidComap_surjective_of_surjective
subgroupMap_apply_coe 📖mathematicalSubmonoid
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
SetLike.instMembership
Submonoid.instSetLike
Submonoid.map
MonoidHom
MulOneClass.toMulOne
instFunLike
Subgroup.toSubmonoid
DFunLike.coe
Subgroup
Subgroup.instSetLike
Subgroup.map
Subgroup.toGroup
subgroupMap
subgroupMap_surjective 📖mathematicalSubgroup
SetLike.instMembership
Subgroup.instSetLike
Subgroup.map
DFunLike.coe
MonoidHom
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
Subgroup.toGroup
instFunLike
subgroupMap
submonoidMap_surjective

MulEquiv

Definitions

NameCategoryTheorems
comapSubgroup 📖CompOp
4 mathmath: comapSubgroup_symm_apply, coe_comapSubgroup, comapSubgroup_apply, symm_comapSubgroup
mapSubgroup 📖CompOp
4 mathmath: mapSubgroup_apply, coe_mapSubgroup, mapSubgroup_symm_apply, symm_mapSubgroup
subgroupCongr 📖CompOp
6 mathmath: subgroupCongr_apply, SubMulAction.ofFixingSubgroup_of_eq_apply, Submodule.unitsQuotEquivRelPic_symm_apply, ClassGroup.equivPic_symm_apply, SubMulAction.ofFixingSubgroup_of_eq_bijective, subgroupCongr_symm_apply
subgroupMap 📖CompOp
3 mathmath: Subgroup.equivMapOfInjective_coe_mulEquiv, coe_subgroupMap_apply, subgroupMap_symm_apply

Theorems

NameKindAssumesProvesValidatesDepends On
coe_comapSubgroup 📖mathematicalDFunLike.coe
OrderIso
Subgroup
Preorder.toLE
PartialOrder.toPreorder
Subgroup.instPartialOrder
instFunLikeOrderIso
comapSubgroup
Subgroup.comap
toMonoidHom
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
coe_mapSubgroup 📖mathematicalDFunLike.coe
OrderIso
Subgroup
Preorder.toLE
PartialOrder.toPreorder
Subgroup.instPartialOrder
instFunLikeOrderIso
mapSubgroup
Subgroup.map
toMonoidHom
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
coe_subgroupMap_apply 📖mathematicalSubgroup
SetLike.instMembership
Subgroup.instSetLike
Subgroup.map
MonoidHomClass.toMonoidHom
MulEquiv
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
EquivLike.toFunLike
instEquivLike
MulEquivClass.instMonoidHomClass
instMulEquivClass
DFunLike.coe
Subgroup.mul
subgroupMap
MulEquivClass.instMonoidHomClass
instMulEquivClass
comapSubgroup_apply 📖mathematicalDFunLike.coe
RelIso
Subgroup
Preorder.toLE
PartialOrder.toPreorder
Subgroup.instPartialOrder
RelIso.instFunLike
comapSubgroup
Subgroup.comap
MonoidHomClass.toMonoidHom
MulEquiv
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
EquivLike.toFunLike
instEquivLike
comapSubgroup_symm_apply 📖mathematicalDFunLike.coe
RelIso
Subgroup
Preorder.toLE
PartialOrder.toPreorder
Subgroup.instPartialOrder
RelIso.instFunLike
RelIso.symm
comapSubgroup
Subgroup.comap
MonoidHomClass.toMonoidHom
MulEquiv
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
EquivLike.toFunLike
instEquivLike
symm
mapSubgroup_apply 📖mathematicalDFunLike.coe
RelIso
Subgroup
Preorder.toLE
PartialOrder.toPreorder
Subgroup.instPartialOrder
RelIso.instFunLike
mapSubgroup
Subgroup.map
MonoidHomClass.toMonoidHom
MulEquiv
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
EquivLike.toFunLike
instEquivLike
mapSubgroup_symm_apply 📖mathematicalDFunLike.coe
RelIso
Subgroup
Preorder.toLE
PartialOrder.toPreorder
Subgroup.instPartialOrder
RelIso.instFunLike
RelIso.symm
mapSubgroup
Subgroup.map
MonoidHomClass.toMonoidHom
MulEquiv
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
EquivLike.toFunLike
instEquivLike
symm
subgroupCongr_apply 📖mathematicalSubgroup
SetLike.instMembership
Subgroup.instSetLike
DFunLike.coe
MulEquiv
Subgroup.mul
EquivLike.toFunLike
instEquivLike
subgroupCongr
subgroupCongr_symm_apply 📖mathematicalSubgroup
SetLike.instMembership
Subgroup.instSetLike
DFunLike.coe
MulEquiv
Subgroup.mul
EquivLike.toFunLike
instEquivLike
symm
subgroupCongr
subgroupMap_symm_apply 📖mathematicalDFunLike.coe
MulEquiv
Subgroup
SetLike.instMembership
Subgroup.instSetLike
Subgroup.map
MonoidHomClass.toMonoidHom
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
EquivLike.toFunLike
instEquivLike
MulEquivClass.instMonoidHomClass
instMulEquivClass
Subgroup.mul
symm
subgroupMap
Set
Set.instMembership
SetLike.coe
SetLike.mem_coe
Set.image
Equiv
Equiv.instEquivLike
toEquiv
Equiv.symm
Set.mem_image_equiv
MulEquivClass.instMonoidHomClass
instMulEquivClass
symm_comapSubgroup 📖mathematicalOrderIso.symm
Subgroup
Preorder.toLE
PartialOrder.toPreorder
Subgroup.instPartialOrder
comapSubgroup
symm
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
symm_mapSubgroup 📖mathematicalOrderIso.symm
Subgroup
Preorder.toLE
PartialOrder.toPreorder
Subgroup.instPartialOrder
mapSubgroup
symm
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid

Subgroup

Definitions

NameCategoryTheorems
comap 📖CompOp
97 mathmath: Sylow.coe_comapOfKerIsPGroup, MonoidHom.comap_bot, gc_map_comap, comap_equiv_eq_map_symm, Characteristic.fixed, comap_toSubmonoid, frattini_le_comap_frattini_of_surjective, MulEquiv.comapSubgroup_symm_apply, comap_equiv_eq_map_symm', map_comap_eq, normal_comap, comap_injective, le_normalizer_comap, IsPGroup.comap_of_ker_isPGroup, MonoidHom.closure_preimage_le, top_prod, comap_id, isCoatom_comap_of_surjective, characteristic_iff_comap_eq, comap_injective_isMulCommutative, IntermediateField.map_fixingSubgroup, comap_upperCentralSeries, characteristic_iff_comap_le, comap_lt_comap_of_surjective, comap_sup_eq, comap_normalizer_eq_of_surjective, Sylow.exists_comap_eq_of_injective, le_pi_iff, MulEquiv.coe_comapSubgroup, characteristic_iff_le_comap, iSup_comap_le, comap_inf, comap_map_eq_self_of_injective, comap_sup_comap_le, mem_comap, surjective_cosetToCuspOrbit, comap_map_eq, ker_le_comap, QuotientGroup.strictMono_comap_prod_image, MulEquiv.comapSubgroup_apply, comap_upperCentralSeries_quotient_center, comap_le_comap_of_surjective, map_eq_comap_of_inverse, Sylow.coe_comapOfInjective, map_comap_eq_self, le_comap_map, prod_top, comap_sup_eq_of_le_range, map_le_iff_le_comap, index_comap, QuotientGroup.comap_map_mk', cosetToCuspOrbit_apply_mk, map_equiv_eq_comap_symm', ValuationSubring.unitsModPrincipalUnitsEquivResidueFieldUnits_comp_quotientGroup_mk_apply, comap_inclusion_subgroupOf, toAddSubgroup_comap, map_comap_eq_self_of_surjective, comap_map_eq_self, map_comap_le, comap_mono, relIndex_comap, Sylow.card_quotient_normalizer_modEq_card_quotient, Sylow.exists_comap_subtype_eq, comap_comap, comap_top, comap_iInf, MonoidHom.prodMap_comap_prod, index_comap_of_surjective, IsPGroup.comap_subtype, IsPGroup.comap_of_injective, IsArithmetic.finiteIndex_comap, upperCentralSeriesStep_eq_comap_center, Sylow.prime_dvd_card_quotient_normalizer, FiniteIndexNormalSubgroup.toSubgroup_comap, comap_normalClosure, MonoidHom.subgroupComap_apply_coe, OpenSubgroup.toSubgroup_comap, ValuationSubring.ker_unitGroupToResidueFieldUnits, QuotientGroup.comap_comap_center, coe_comap, QuotientGroup.strictMono_comap_prod_map, Normal.comap, comap_normalizer_eq_of_le_range, comap_le_comap_of_le_range, QuotientGroup.le_comap_mk', AddSubgroup.toSubgroup_comap, ValuationSubring.unitsModPrincipalUnitsEquivResidueFieldUnits_comp_quotientGroup_mk, Characteristic.comap_quotient_mk, MonoidHom.subgroupComap_surjective_of_surjective, map_equiv_eq_comap_symm, Sylow.exists_comap_eq_of_ker_isPGroup, goursat, comap_subtype, MonoidHom.comap_ker, centralizer_eq_comap_stabilizer, card_comap_dvd_of_injective, isCoatom_comap
equivMapOfInjective 📖CompOp
2 mathmath: equivMapOfInjective_coe_mulEquiv, coe_equivMapOfInjective_apply
map 📖CompOp
179 mathmath: card_map_of_injective, Ideal.Quotient.map_ker_stabilizer_subtype, gc_map_comap, MapSubtype.orderIso_apply_coe, comap_equiv_eq_map_symm, DiscreteTiling.PlacedTile.ext_iff_of_preimage, instHasDetOneMapSpecialLinearGroupGeneralLinearGroupToGL, SubMulAction.fixingSubgroup_smul_eq_fixingSubgroup_map_conj, index_map_of_bijective, map_sup, CongruenceSubgroup.exists_Gamma_le_conj', map_eq_map_iff, isCoatom_map, map_le_range, map_injective, pi_le_iff, derivedSeries_le_map_derivedSeries, comap_equiv_eq_map_symm', map_one_eq_bot, CongruenceSubgroup.strictPeriods_Gamma0, apply_coe_mem_map, map_inf_eq, ModularForm.levelOne_neg_weight_rank_zero, map_comap_eq, map_iSup, CongruenceSubgroup.exists_Gamma_le_conj, DiscreteTiling.PlacedTile.ext_iff_of_exists, MulEquiv.mapSubgroup_apply, MonoidHom.map_range, coe_map, map_inf_le, instIsArithmeticMapSpecialLinearGroupFinOfNatNatIntGeneralLinearGroupRealMapGLOfFiniteIndex, coe_equivMapOfInjective_apply, map_le_map_iff_of_injective, upperCentralSeries.map, pointwise_smul_def, map_derivedSeries_eq, map_top_of_surjective, NumberField.Units.map_complexEmbedding_torsion, mem_map_equiv, map_equiv_top, MonoidHom.range_eq_map, DiscreteTiling.PlacedTile.smul_mk_mk, DiscreteTiling.PlacedTile.ext_iff, IsSubnormal.trans', MonoidHom.range_comp, SubMulAction.fixingSubgroup_of_insert, map_subgroupOf_eq_of_le, map_derivedSeries_le_derivedSeries, strictWidthInfty_eq_one_of_T_mem, map_symm_eq_iff_map_eq, mem_map_of_mem, ModularFormClass.one_mem_strictPeriods_SL2Z, characteristic_iff_map_le, QuotientGroup.quotientQuotientEquivQuotientAux_mk, MonoidHom.restrict_range, ModularForm.levelOne_weight_zero_rank_one, CongruenceSubgroup.strictWidthInfty_Gamma0, map_id, map_commutator_eq, relIndex_map_map, mem_map_iff_mem, strictPeriods_eq_zmultiples_one_of_T_mem, MonoidHom.coe_toAdditive_map, EisensteinSeries.q_expansion_riemannZeta, MulAction.stabilizer_smul_eq_stabilizer_map_conj, map_lt_map_iff_of_injective, index_map_of_injective, MulAction.IsBlock.of_subgroup_of_conjugate, map_subtype_le_map_subtype, codisjoint_map, DiscreteTiling.PlacedTile.coe_mk_mk, MulEquiv.coe_mapSubgroup, card_map_dvd, map_eq_bot_iff, map_normalizer_eq_of_bijective, QuotientGroup.ker_map, map_bot, map_centralizer_le_centralizer_image, MulEquiv.mapSubgroup_symm_apply, InfiniteGalois.restrict_fixedField, comap_map_eq_self_of_injective, isArithmetic_iff_finiteIndex, map_normalClosure, DiscreteTiling.PlacedTile.smul_mk_coe, map_toSubmonoid, EisensteinSeries.isBoundedAtImInfty_eisensteinSeries_SIF, MonoidHom.map_closure, le_prod_iff, map_subtype_lt_map_subtype, map_le_map_iff, CongruenceSubgroup.strictWidthInfty_Gamma1, QuotientGroup.quotientQuotientEquivQuotientAux_mk_mk, comap_map_eq, EisensteinSeries.eisensteinSeries_SIF_apply, subgroupOf_map_subtype, ConjAct.normal_of_characteristic_of_normal, Submodule.unitsQuotEquivRelPic_symm_apply, map_eq_bot_iff_of_injective, lowerCentralSeries.map, map_le_map_iff', QuotientGroup.ker_lift, disjoint_map, MulAction.map_stabilizer_le, QuotientGroup.map_normal, map_eq_comap_of_inverse, dvd_index_map, CongruenceSubgroup.strictPeriods_Gamma1, map_subtype_le, Normal.map, lowerCentralSeries_map_subtype_le, map_comap_eq_self, le_comap_map, ClassGroup.equivPic_symm_apply, index_map_equiv, CongruenceSubgroup.strictWidthInfty_Gamma, map_eq_range_iff, prod_le_iff, EisensteinSeries.q_expansion_bernoulli, map_le_iff_le_comap, SubMulAction.fixingSubgroup_map_conj_eq, ker_subgroupMap, relIndex_map_map_of_injective, MonoidHom.ker_comp_mulEquiv, QuotientGroup.comap_map_mk', CongruenceSubgroup.strictPeriods_Gamma, map_equiv_eq_comap_symm', DenseRange.topologicalClosure_map_subgroup, AddMonoidHom.coe_toMultiplicative_map, map_comap_eq_self_of_surjective, comap_map_eq_self, map_comap_le, relIndex_comap, Sylow.normalizer_sup_eq_top, mem_map, MulEquiv.coe_subgroupMap_apply, map_iInf, SlashInvariantForm.vAdd_width_periodic, index_map_eq, map_mono, EisensteinSeries.eisensteinSeriesSIF_apply, index_map_dvd, IsPGroup.map, MonoidHom.map_zpowers, EisensteinSeries.eisensteinSeries_tendstoLocallyUniformlyOn, MonoidHom.subgroupMap_surjective, characteristic_iff_map_eq, Sylow.coe_mapSurjective, DiscreteTiling.PlacedTile.coe_mk_coe, card_subtype, QuotientGroup.map_mk'_self, EisensteinSeries.eisensteinSeries_SIF_MDifferentiable, relIndex_ker, index_map, MulEquiv.subgroupMap_symm_apply, map_commutator, index_map_subtype, Equiv.Perm.OnCycleFactors.kerParam_range_eq, instHasDetOneMapSpecialLinearGroupGeneralLinearGroupMapGL, MonoidHom.subgroupMap_apply_coe, NumberField.IsCMField.map_unitsMulComplexConjInv_torsion, EisensteinSeries.eisensteinSeriesSIF_mdifferentiable, surjOn_iff_le_map, QuotientGroup.strictMono_comap_prod_map, AddSubgroup.inertia_map_subtype, map_rootsOfUnity, le_normalizer_map, map_equiv_eq_comap_symm, goursat, IsGaloisGroup.map_mulEquivAlgEquiv_fixingSubgroup, characteristic_iff_le_map, map_equiv_normalizer_eq, map_inf, map_isMulCommutative, map_map, IsPrimitiveRoot.map_rootsOfUnity, SlashInvariantForm.T_zpow_width_invariant, EisensteinSeries.isBoundedAtImInfty_eisensteinSeriesSIF, map_subtype_commutator
subgroupOf 📖CompOp
79 mathmath: prod_subgroupOf_prod_normal, subgroupOfContinuousMulEquivOfLe_toMulEquiv, subgroupOf_normalizer_eq, normal_subgroupOf_iff, AddSubgroup.subgroupOf_inertia, subgroupOf_inj, conj_smul_subgroupOf, SlashInvariantForm.quotientFunc_mk, subgroupOf_isMulCommutative, subgroupOf_eq_top, ModularForm.norm_eq_zero_iff, IsSubnormal.iff_eq_top_or_exists, quotientEquivProdOfLE_apply, subgroupOf_isOpen, SlashInvariantForm.quotientFunc_smul, MonoidHom.subgroupOf_range_eq_of_le, subgroupOf_self, CuspForm.coe_trace, normal_subgroupOf_sup_of_le_normalizer, quotientSubgroupOfEmbeddingOfLE_apply_mk, map_subgroupOf_eq_of_le, instFiniteIndex_subgroupOf, normal_subgroupOf_iff_le_normalizer_inf, relIndex_subgroupOf, normalizerMonoidHom_ker, subgroupOfEquivOfLe_symm_apply_coe_coe, inf_subgroupOf_inf_normal_of_left, subgroupOf_eq_bot, forall, quotientEquivProdOfLE_symm_apply, quotientEquivProdOfLE'_symm_apply, QuotientGroup.quotientMapSubgroupOfOfLe_mk, inf_subgroupOf_right, exists_leftTransversal_of_FiniteIndex, Ideal.Quotient.stabilizerQuotientInertiaEquiv_mk, subgroupOf_sup, quotientSubgroupOfMapOfLE_apply_mk, quotientiInfSubgroupOfEmbedding_apply_mk, Action.FintypeCat.quotientToEndHom_mk, subgroupOf_map_subtype, sup_subgroupOf_eq, normal_subgroupOf, normal_subgroupOf_iff_le_normalizer, subgroupOfContinuousMulEquivOfLe_apply, MulAction.orbitRel_subgroupOf, IsFiniteRelIndex.to_finiteIndex_subgroupOf, SlashInvariantForm.coe_trace, bot_subgroupOf, Normal.subgroupOf, ker_subgroupMap, Ideal.Quotient.ker_stabilizerHom, comap_inclusion_subgroupOf, subgroupOfContinuousMulEquivOfLe_symm_apply, inclusion_range, ModularForm.coe_norm, Sylow.coe_subtype, quotientiInfSubgroupOfEmbedding_apply, normal_subgroupOf_of_le_normalizer, quotientEquivProdOfLE'_apply, codisjoint_subgroupOf_sup, subgroupOfEquivOfLe_apply_coe, coe_subgroupOf, top_subgroupOf, normal_in_normalizer, subgroupOf_bot_eq_top, inf_subgroupOf_left, ModularForm.coe_trace, mem_subgroupOf, Ideal.instNormalSubtypeMemSubgroupStabilizerSubgroupOfInertia, ValuationSubring.unitsModPrincipalUnitsEquivResidueFieldUnits_comp_quotientGroup_mk, IsSubnormal.isSubnormal_iff, SlashInvariantForm.coe_norm, comap_subtype, IsDedekindDomain.selmerGroup.valuation_ker_eq, MonoidHom.ker_restrict, subgroupOf_bot_eq_bot, IsSubnormal.exists_chain, inf_subgroupOf_inf_normal_of_right, MapSubtype.orderIso_symm_apply
subgroupOfEquivOfLe 📖CompOp
4 mathmath: subgroupOfContinuousMulEquivOfLe_toMulEquiv, subgroupOfEquivOfLe_symm_apply_coe_coe, subgroupOfContinuousMulEquivOfLe_apply, subgroupOfEquivOfLe_apply_coe

Theorems

NameKindAssumesProvesValidatesDepends On
apply_coe_mem_map 📖mathematicalSubgroup
SetLike.instMembership
instSetLike
map
DFunLike.coe
MonoidHom
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
MonoidHom.instFunLike
mem_map_of_mem
Subtype.prop
bot_subgroupOf 📖mathematicalsubgroupOf
Bot.bot
Subgroup
instBot
SetLike.instMembership
instSetLike
toGroup
ext
codisjoint_map 📖mathematicalDFunLike.coe
MonoidHom
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
MonoidHom.instFunLike
Codisjoint
Subgroup
instPartialOrder
BoundedOrder.toOrderTop
Preorder.toLE
PartialOrder.toPreorder
CompleteLattice.toBoundedOrder
instCompleteLattice
mapcodisjoint_iff
map_sup
map_top_of_surjective
coe_comap 📖mathematicalSetLike.coe
Subgroup
instSetLike
comap
Set.preimage
DFunLike.coe
MonoidHom
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
MonoidHom.instFunLike
coe_equivMapOfInjective_apply 📖mathematicalDFunLike.coe
MonoidHom
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
MonoidHom.instFunLike
Subgroup
SetLike.instMembership
instSetLike
map
MulEquiv
mul
EquivLike.toFunLike
MulEquiv.instEquivLike
equivMapOfInjective
coe_map 📖mathematicalSetLike.coe
Subgroup
instSetLike
map
Set.image
DFunLike.coe
MonoidHom
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
MonoidHom.instFunLike
coe_subgroupOf 📖mathematicalSetLike.coe
Subgroup
SetLike.instMembership
instSetLike
toGroup
subgroupOf
Set.preimage
DFunLike.coe
MonoidHom
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
MonoidHom.instFunLike
subtype
comap_comap 📖mathematicalcomap
MonoidHom.comp
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
comap_equiv_eq_map_symm 📖mathematicalcomap
MonoidHomClass.toMonoidHom
MulEquiv
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
EquivLike.toFunLike
MulEquiv.instEquivLike
MulEquivClass.instMonoidHomClass
MulEquiv.instMulEquivClass
map
MulEquiv.symm
MulEquivClass.instMonoidHomClass
MulEquiv.instMulEquivClass
map_equiv_eq_comap_symm
comap_equiv_eq_map_symm' 📖mathematicalcomap
MulEquiv.toMonoidHom
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
map
MulEquiv.symm
MulOne.toMul
MulOneClass.toMulOne
MulEquivClass.instMonoidHomClass
MulEquiv.instMulEquivClass
map_equiv_eq_comap_symm
comap_iInf 📖mathematicalcomap
iInf
Subgroup
instInfSet
GaloisConnection.u_iInf
gc_map_comap
comap_id 📖mathematicalcomap
MonoidHom.id
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
ext
comap_inclusion_subgroupOf 📖mathematicalSubgroup
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
comap
SetLike.instMembership
instSetLike
toGroup
inclusion
subgroupOf
comap_inf 📖mathematicalcomap
Subgroup
instMin
GaloisConnection.u_inf
gc_map_comap
comap_injective_isMulCommutative 📖mathematicalDFunLike.coe
MonoidHom
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
MonoidHom.instFunLike
IsMulCommutative
Subgroup
SetLike.instMembership
instSetLike
comap
mul
mul_comm
map_mul
MonoidHomClass.toMulHomClass
MonoidHom.instMonoidHomClass
coe_mul
comap_mono 📖mathematicalSubgroup
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
comapSet.preimage_mono
comap_subtype 📖mathematicalcomap
Subgroup
SetLike.instMembership
instSetLike
toGroup
subtype
subgroupOf
comap_sup_comap_le 📖mathematicalSubgroup
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
SemilatticeSup.toMax
Lattice.toSemilatticeSup
CompleteLattice.toLattice
instCompleteLattice
comap
Monotone.le_map_sup
comap_mono
comap_toSubmonoid 📖mathematicaltoSubmonoid
comap
MonoidHomClass.toMonoidHom
MulEquiv
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
EquivLike.toFunLike
MulEquiv.instEquivLike
MulEquivClass.instMonoidHomClass
MulEquiv.instMulEquivClass
Submonoid.comap
MonoidHom
MonoidHom.instFunLike
MonoidHom.instMonoidHomClass
MulEquiv.toMonoidHom
MulEquivClass.instMonoidHomClass
MulEquiv.instMulEquivClass
comap_top 📖mathematicalcomap
Top.top
Subgroup
instTop
GaloisConnection.u_top
gc_map_comap
disjoint_map 📖mathematicalDFunLike.coe
MonoidHom
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
MonoidHom.instFunLike
Disjoint
Subgroup
instPartialOrder
BoundedOrder.toOrderBot
Preorder.toLE
PartialOrder.toPreorder
CompleteLattice.toBoundedOrder
instCompleteLattice
mapdisjoint_iff
map_inf
map_bot
equivMapOfInjective_coe_mulEquiv 📖mathematicalequivMapOfInjective
MonoidHomClass.toMonoidHom
MulEquiv
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
EquivLike.toFunLike
MulEquiv.instEquivLike
MulEquivClass.instMonoidHomClass
MulEquiv.instMulEquivClass
EquivLike.injective
MulEquiv.subgroupMap
MulEquiv.ext
MulEquivClass.instMonoidHomClass
MulEquiv.instMulEquivClass
EquivLike.injective
gc_map_comap 📖mathematicalGaloisConnection
Subgroup
PartialOrder.toPreorder
instPartialOrder
map
comap
map_le_iff_le_comap
iSup_comap_le 📖mathematicalSubgroup
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
iSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
instCompleteLattice
comap
Monotone.le_map_iSup
comap_mono
inf_subgroupOf_left 📖mathematicalsubgroupOf
Subgroup
instMin
inf_comm
inf_subgroupOf_right
inf_subgroupOf_right 📖mathematicalsubgroupOf
Subgroup
instMin
inf_right_idem
le_comap_map 📖mathematicalSubgroup
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
comap
map
GaloisConnection.le_u_l
gc_map_comap
map_bot 📖mathematicalmap
Bot.bot
Subgroup
instBot
GaloisConnection.l_bot
gc_map_comap
map_comap_le 📖mathematicalSubgroup
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
map
comap
GaloisConnection.l_u_le
gc_map_comap
map_eq_comap_of_inverse 📖mathematicalDFunLike.coe
MonoidHom
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
MonoidHom.instFunLike
map
comap
SetLike.ext'
coe_map
coe_comap
Set.image_eq_preimage_of_inverse
map_equiv_eq_comap_symm 📖mathematicalmap
MonoidHomClass.toMonoidHom
MulEquiv
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
EquivLike.toFunLike
MulEquiv.instEquivLike
MulEquivClass.instMonoidHomClass
MulEquiv.instMulEquivClass
comap
MulEquiv.symm
map_equiv_eq_comap_symm'
map_equiv_eq_comap_symm' 📖mathematicalmap
MulEquiv.toMonoidHom
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
comap
MulEquiv.symm
MulOne.toMul
MulOneClass.toMulOne
SetLike.coe_injective
Equiv.image_eq_preimage_symm
map_equiv_top 📖mathematicalmap
MonoidHomClass.toMonoidHom
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
EquivLike.toFunLike
MulEquivClass.instMonoidHomClass
Top.top
Subgroup
instTop
map_top_of_surjective
MulEquivClass.instMonoidHomClass
EquivLike.surjective
map_iInf 📖mathematicalDFunLike.coe
MonoidHom
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
MonoidHom.instFunLike
map
iInf
Subgroup
instInfSet
SetLike.coe_injective
coe_iInf
Set.InjOn.image_iInter_eq
Set.injOn_of_injective
map_iSup 📖mathematicalmap
iSup
Subgroup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
instCompleteLattice
GaloisConnection.l_iSup
gc_map_comap
map_id 📖mathematicalmap
MonoidHom.id
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
SetLike.coe_injective
Set.image_id
map_inf 📖mathematicalDFunLike.coe
MonoidHom
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
MonoidHom.instFunLike
map
Subgroup
instMin
SetLike.coe_injective
Set.image_inter
map_inf_eq 📖mathematicalDFunLike.coe
MonoidHom
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
MonoidHom.instFunLike
map
Subgroup
instMin
SetLike.coe_set_eq
Set.image_inter
map_inf_le 📖mathematicalSubgroup
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
map
instMin
le_inf
map_mono
inf_le_left
inf_le_right
map_isMulCommutative 📖mathematicalIsMulCommutative
Subgroup
SetLike.instMembership
instSetLike
map
mul
coe_mul
map_mul
MonoidHomClass.toMulHomClass
MonoidHom.instMonoidHomClass
mul_comm
map_le_iff_le_comap 📖mathematicalSubgroup
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
map
comap
Set.image_subset_iff
map_map 📖mathematicalmap
MonoidHom.comp
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
SetLike.coe_injective
Set.image_image
map_mono 📖mathematicalSubgroup
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
mapSet.image_mono
map_one_eq_bot 📖mathematicalmap
MonoidHom
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
instOneMonoidHom
Bot.bot
Subgroup
instBot
eq_bot_iff
SubmonoidClass.toOneMemClass
SubgroupClass.toSubmonoidClass
instSubgroupClass
map_subgroupOf_eq_of_le 📖mathematicalSubgroup
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
map
SetLike.instMembership
instSetLike
toGroup
subtype
subgroupOf
subgroupOf_map_subtype
inf_eq_left
map_sup 📖mathematicalmap
Subgroup
SemilatticeSup.toMax
Lattice.toSemilatticeSup
CompleteLattice.toLattice
instCompleteLattice
GaloisConnection.l_sup
gc_map_comap
map_symm_eq_iff_map_eq 📖mathematicalmap
MonoidHomClass.toMonoidHom
MulEquiv
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
EquivLike.toFunLike
MulEquiv.instEquivLike
MulEquivClass.instMonoidHomClass
MulEquiv.instMulEquivClass
MulEquiv.symm
MulEquivClass.instMonoidHomClass
MulEquiv.instMulEquivClass
map_map
MulEquiv.coe_monoidHom_trans
MulEquiv.symm_trans_self
MulEquiv.coe_monoidHom_refl
map_id
MulEquiv.self_trans_symm
map_toSubmonoid 📖mathematicaltoSubmonoid
map
Submonoid.map
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
MonoidHom
MulOneClass.toMulOne
MonoidHom.instFunLike
MonoidHom.instMonoidHomClass
map_top_of_surjective 📖mathematicalDFunLike.coe
MonoidHom
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
MonoidHom.instFunLike
map
Top.top
Subgroup
instTop
eq_top_iff
mem_comap 📖mathematicalSubgroup
SetLike.instMembership
instSetLike
comap
DFunLike.coe
MonoidHom
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
MonoidHom.instFunLike
mem_map 📖mathematicalSubgroup
SetLike.instMembership
instSetLike
map
DFunLike.coe
MonoidHom
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
MonoidHom.instFunLike
mem_map_equiv 📖mathematicalSubgroup
SetLike.instMembership
instSetLike
map
MulEquiv.toMonoidHom
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
DFunLike.coe
MulEquiv
MulOne.toMul
MulOneClass.toMulOne
EquivLike.toFunLike
MulEquiv.instEquivLike
MulEquiv.symm
Set.mem_image_equiv
mem_map_iff_mem 📖mathematicalDFunLike.coe
MonoidHom
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
MonoidHom.instFunLike
Subgroup
SetLike.instMembership
instSetLike
map
Function.Injective.mem_set_image
mem_map_of_mem 📖mathematicalSubgroup
SetLike.instMembership
instSetLike
map
DFunLike.coe
MonoidHom
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
MonoidHom.instFunLike
Set.mem_image_of_mem
mem_subgroupOf 📖mathematicalSubgroup
SetLike.instMembership
instSetLike
toGroup
subgroupOf
subgroupOfEquivOfLe_apply_coe 📖mathematicalSubgroup
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
SetLike.instMembership
instSetLike
DFunLike.coe
MulEquiv
toGroup
subgroupOf
mul
EquivLike.toFunLike
MulEquiv.instEquivLike
subgroupOfEquivOfLe
subgroupOfEquivOfLe_symm_apply_coe_coe 📖mathematicalSubgroup
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
SetLike.instMembership
instSetLike
toGroup
subgroupOf
DFunLike.coe
MulEquiv
mul
EquivLike.toFunLike
MulEquiv.instEquivLike
MulEquiv.symm
subgroupOfEquivOfLe
subgroupOf_bot_eq_bot 📖mathematicalsubgroupOf
Bot.bot
Subgroup
instBot
SetLike.instMembership
instSetLike
toGroup
Unique.instSubsingleton
subgroupOf_bot_eq_top 📖mathematicalsubgroupOf
Bot.bot
Subgroup
instBot
Top.top
SetLike.instMembership
instSetLike
toGroup
instTop
Unique.instSubsingleton
subgroupOf_eq_bot 📖mathematicalsubgroupOf
Bot.bot
Subgroup
SetLike.instMembership
instSetLike
toGroup
instBot
Disjoint
instPartialOrder
BoundedOrder.toOrderBot
Preorder.toLE
PartialOrder.toPreorder
CompleteLattice.toBoundedOrder
instCompleteLattice
disjoint_iff
bot_subgroupOf
bot_inf_eq
subgroupOf_eq_top 📖mathematicalsubgroupOf
Top.top
Subgroup
SetLike.instMembership
instSetLike
toGroup
instTop
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
top_subgroupOf
top_inf_eq
inf_eq_right
subgroupOf_inj 📖mathematicalsubgroupOf
Subgroup
instMin
subgroupOf_isMulCommutative 📖mathematicalIsMulCommutative
Subgroup
SetLike.instMembership
instSetLike
toGroup
subgroupOf
mul
comap_injective_isMulCommutative
Subtype.coe_injective
subgroupOf_map_subtype 📖mathematicalmap
Subgroup
SetLike.instMembership
instSetLike
toGroup
subtype
subgroupOf
instMin
SetLike.ext'
Subtype.image_preimage_coe
Set.inter_comm
subgroupOf_self 📖mathematicalsubgroupOf
Top.top
Subgroup
SetLike.instMembership
instSetLike
toGroup
instTop
top_unique
surjOn_iff_le_map 📖mathematicalSet.SurjOn
DFunLike.coe
MonoidHom
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
MonoidHom.instFunLike
SetLike.coe
Subgroup
instSetLike
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
map
toAddSubgroup_comap 📖mathematicalAddSubgroup.comap
Additive
Additive.addGroup
DFunLike.coe
Equiv
MonoidHom
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
AddMonoidHom
AddZeroClass.toAddZero
Additive.addZeroClass
EquivLike.toFunLike
Equiv.instEquivLike
MonoidHom.toAdditive
OrderIso
Subgroup
AddSubgroup
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
AddSubgroup.instPartialOrder
instFunLikeOrderIso
toAddSubgroup
comap
top_subgroupOf 📖mathematicalsubgroupOf
Top.top
Subgroup
instTop
SetLike.instMembership
instSetLike
toGroup

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