Documentation Verification Report

Ker

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

Statistics

MetricCount
DefinitionsdecidableMemKer, eqLocus, ker, ofInjective, ofLeftInverse, range, rangeRestrict, orderIso, decidableMemKer, eqLocus, ker, ofInjective, ofLeftInverse, range, rangeRestrict, orderIso
16
TheoremsaddSubgroupOf_range_eq_of_le, apply_ofInjective_symm, coe_comp_rangeRestrict, coe_ker, coe_range, coe_rangeRestrict, comap_bot, comap_ker, eqLocus_same, eqOn_closure, eq_iff, eq_of_eqOn_dense, eq_of_eqOn_top, ker_codRestrict, ker_comp_addEquiv, ker_eq_bot_iff, ker_eq_top_iff, ker_id, ker_prod, ker_rangeRestrict, ker_restrict, ker_toAddSubmonoid, ker_toHomAddUnits, ker_zero, map_range, mem_ker, mem_range, normal_ker, ofInjective_apply, ofLeftInverse_apply, ofLeftInverse_symm_apply, rangeRestrict_injective_iff, rangeRestrict_surjective, range_comp, range_eq_bot_iff, range_eq_map, range_eq_top, range_eq_top_of_surjective, range_isAddCommutative, range_le_ker_iff, range_zero, restrict_range, sub_mem_ker_iff, subtype_comp_rangeRestrict, orderIso_apply_coe, orderIso_symm_apply, addSubgroupOf_sup, closure_preimage_eq_top, codisjoint_addSubgroupOf_sup, comap_injective, comap_le_comap_of_le_range, comap_le_comap_of_surjective, comap_lt_comap_of_surjective, comap_map_eq, comap_map_eq_self, comap_map_eq_self_of_injective, comap_sup_eq, comap_sup_eq_of_le_range, forall, inclusion_range, ker_addSubgroupMap, ker_inclusion, ker_le_comap, ker_subtype, map_comap_eq, map_comap_eq_self, map_comap_eq_self_of_surjective, map_eq_bot_iff, map_eq_bot_iff_of_injective, map_eq_map_iff, map_eq_range_iff, map_injective, map_injective_of_ker_le, map_le_map_iff, map_le_map_iff', map_le_map_iff_of_injective, map_le_range, map_lt_map_iff_of_injective, map_subtype_le, map_subtype_le_map_subtype, map_subtype_lt_map_subtype, range_subtype, subtype_range, apply_ofInjective_symm, coe_comp_rangeRestrict, coe_ker, coe_range, coe_rangeRestrict, coe_toAdditive_ker, coe_toAdditive_range, coe_toMultiplicative_ker, coe_toMultiplicative_range, comap_bot, comap_ker, div_mem_ker_iff, eqLocus_same, eqOn_closure, eq_iff, eq_of_eqOn_dense, eq_of_eqOn_top, ker_codRestrict, ker_comp_mulEquiv, ker_eq_bot_iff, ker_eq_top_iff, ker_id, ker_one, ker_prod, ker_rangeRestrict, ker_restrict, ker_toHomUnits, ker_toSubmonoid, map_range, mem_ker, mem_range, normal_ker, ofInjective_apply, ofLeftInverse_apply, ofLeftInverse_symm_apply, rangeRestrict_injective_iff, rangeRestrict_surjective, range_comp, range_eq_bot_iff, range_eq_map, range_eq_top, range_eq_top_of_surjective, range_isMulCommutative, range_le_ker_iff, range_one, restrict_range, subgroupOf_range_eq_of_le, subtype_comp_rangeRestrict, orderIso_apply_coe, orderIso_symm_apply, closure_preimage_eq_top, codisjoint_subgroupOf_sup, comap_injective, comap_le_comap_of_le_range, comap_le_comap_of_surjective, comap_lt_comap_of_surjective, comap_map_eq, comap_map_eq_self, comap_map_eq_self_of_injective, comap_sup_eq, comap_sup_eq_of_le_range, forall, inclusion_range, ker_inclusion, ker_le_comap, ker_subgroupMap, ker_subtype, map_comap_eq, map_comap_eq_self, map_comap_eq_self_of_surjective, map_eq_bot_iff, map_eq_bot_iff_of_injective, map_eq_map_iff, map_eq_range_iff, map_injective, map_injective_of_ker_le, map_le_map_iff, map_le_map_iff', map_le_map_iff_of_injective, map_le_range, map_lt_map_iff_of_injective, map_subtype_le, map_subtype_le_map_subtype, map_subtype_lt_map_subtype, range_subtype, subgroupOf_sup, subtype_range, sup_subgroupOf_eq
171
Total187

AddMonoidHom

Definitions

NameCategoryTheorems
decidableMemKer 📖CompOp
eqLocus 📖CompOp
1 mathmath: eqLocus_same
ker 📖CompOp
92 mathmath: QuotientAddGroup.kerLift_mk, coe_ker, Function.Exact.addMonoidHom_ker_eq, normal_ker, AddCircle.isAddQuotientCoveringMap_zsmul_of_ne_zero, AddSubgroup.map_eq_map_iff, liftOfRightInverse_comp_apply, ker_comp_addEquiv, AddSubgroup.map_eq_range_iff, AddSubgroup.comap_map_eq, AddCircle.isAddQuotientCoveringMap_nsmul_of_ne_zero, QuotientAddGroup.ker_map, AddCircle.isAddQuotientCoveringMap_nsmul, ker_fst, ker_eq_bot_iff, QuotientAddGroup.ker_mk', ker_restrict, ker_prod, CategoryTheory.ShortComplex.abToCycles_apply_coe, AddSubgroup.relIndex_map_map, CategoryTheory.ShortComplex.Exact.ab_range_eq_ker, AddSubgroup.ker_addSubgroupMap, AddSubgroup.index_ker, AddGroupExtension.range_inl_eq_ker_rightHom, CategoryTheory.ShortComplex.abLeftHomologyData_π, ker_id, fiberEquivKer_apply, CategoryTheory.ShortComplex.exact_iff_surjective_abToCycles, AddSubgroup.ker_le_comap, ker_eq_bot_of_cancel, AddSubgroup.map_le_map_iff, comap_ker, AddSubgroup.index_map, zmultiplesHom_ker_eq, ker_toHomAddUnits, QuotientAddGroup.ker_le_range_iff, CategoryTheory.ShortComplex.abLeftHomologyData_K_coe, IsUniformAddGroup.uniformContinuous_iff_isOpen_ker, IsAddCyclic.card_nsmulAddMonoidHom_ker, ker_snd, liftOfRightInverse_comp, AddSubgroup.map_eq_bot_iff, DFinsupp.ker_mapRangeAddMonoidHom, AddSubgroup.ker_subtype, DirectSum.ker_map, CategoryTheory.ShortComplex.ab_exact_iff_ker_le_range, CategoryTheory.ShortComplex.abLeftHomologyData_f', QuotientAddGroup.quotientKerEquivOfRightInverse_symm_apply, AddCommGrpCat.kernelIsoKer_inv_comp_ι, coe_toIntLinearMap_ker, CategoryTheory.ShortComplex.abLeftHomologyData_i, QuotientAddGroup.quotientKerEquivOfRightInverse_apply, sub_mem_ker_iff, fiberEquivKer_symm_apply, ZMod.ker_intCastAddHom, ker_codRestrict, QuotientAddGroup.con_ker_eq_addConKer, finite_iff_finite_ker_range, AddSubgroup.ker_saturated, AddCircle.isAddQuotientCoveringMap_zsmul, range_le_ker_iff, ker_rangeRestrict, AddSubgroup.index_range, AddCommGrpCat.kernelIsoKer_hom_comp_subtype, ker_eq_top_iff, ker_toAddSubmonoid, comap_bot, QuotientAddGroup.kerLift_mk', ker_prodMap, QuotientAddGroup.kerLift_injective, eq_iff, exact_iff, AddSubgroup.finiteIndex_ker, CategoryTheory.ShortComplex.ab_exact_iff_range_eq_ker, AddGrpCat.ker_eq_bot_of_mono, IsAddCyclic.index_nsmulAddMonoidHom_ker, NumberField.Units.dirichletUnitTheorem.logEmbedding_ker, AddSubgroup.relIndex_ker, CategoryTheory.ShortComplex.abLeftHomologyData_H_coe, AddCommGrpCat.ker_eq_bot_of_mono, mem_ker, QuotientAddGroup.rangeKerLift_injective, AddCommGrpCat.mono_iff_ker_eq_bot, LinearMap.ker_toAddSubgroup, ker_zero, QuotientAddGroup.rangeKerLift_surjective, MonoidHom.coe_toAdditive_ker, AddSubgroup.map_le_map_iff', AddGrpCat.mono_iff_ker_eq_bot, MonoidHom.coe_toMultiplicative_ker, AddSubgroup.ker_inclusion, CategoryTheory.ShortComplex.abCyclesIso_inv_apply_iCycles
ofInjective 📖CompOp
2 mathmath: apply_ofInjective_symm, ofInjective_apply
ofLeftInverse 📖CompOp
2 mathmath: ofLeftInverse_symm_apply, ofLeftInverse_apply
range 📖CompOp
92 mathmath: coe_rangeRestrict, Function.Exact.addMonoidHom_ker_eq, DFinsupp.range_mapRangeAddMonoidHom, range_comp, LinearMap.range_toAddSubgroup, noncommPiCoprod_range, AddSubgroup.map_eq_range_iff, QuotientAddGroup.equivQuotientZSMulOfEquiv_symm, MonoidHom.coe_toMultiplicative_range, IsAddCyclic.index_nsmulAddMonoidHom_range, Int.range_castAddHom, AddSubgroup.subtype_range, rangeRestrict_surjective, apply_ofInjective_symm, exists_range_eq_graph, AddSubgroup.noncommPiCoprod_range, range_isAddCommutative, AddSubgroup.card_range_dvd, range_eq_map, rangeRestrict_injective_iff, CategoryTheory.ShortComplex.Exact.ab_range_eq_ker, QuotientAddGroup.equivQuotientZSMulOfEquiv_trans, ofLeftInverse_symm_apply, AddSubgroup.index_ker, AddGroupExtension.range_inl_eq_ker_rightHom, CategoryTheory.ShortComplex.abLeftHomologyData_π, map_range, subtype_comp_rangeRestrict, AddGroupExtension.normal_inl_range, graph_eq_range_prod, AddSubgroup.range_subtype, AddSubgroup.goursat_surjective, AddSubgroup.index_map, AddSubgroup.range_zmultiplesHom, AddMonoid.Coprod.range_eq, AddCommGrpCat.range_eq_top_of_epi, FreeAddGroup.closure_eq_range, QuotientAddGroup.ker_le_range_iff, range_eq_top, ofLeftInverse_apply, range_eq_bot_iff, AddSubgroup.map_comap_eq, range_eq_top_of_surjective, QuotientAddGroup.homQuotientZSMulOfHom_comp_of_rightInverse, AddSubgroup.index_comap, coe_comp_rangeRestrict, CategoryTheory.ShortComplex.ab_exact_iff_ker_le_range, DirectSum.range_map, AddSubgroup.index_map_of_injective, AddMonoid.Coprod.codisjoint_range_inl_range_inr, restrict_range, AddCommGrpCat.epi_iff_range_eq_top, AddGroupExtension.Section.add_add_add_neg_mem_range_inl, AddMonoid.Coprod.range_swap, MonoidHom.coe_toAdditive_range, AddMonoid.Coprod.range_lift, FreeAddGroup.range_lift_le, coe_toIntLinearMap_range, Function.Exact.addMonoidHom_rangeRestrict, Function.Exact.iff_addMonoidHom_rangeRestrict, finite_iff_finite_ker_range, QuotientAddGroup.range_mk', AddGrpCat.epi_iff_range_eq_top, QuotientAddGroup.equivQuotientZSMulOfEquiv_refl, AddGroup.fg_range, range_le_ker_iff, ker_rangeRestrict, AddSubgroup.index_range, range_zero, independent_range_of_coprime_order, exact_iff, AddSubgroup.inclusion_range, CategoryTheory.ShortComplex.ab_exact_iff_range_eq_ker, AddGroup.rank_range_le, AddMonoid.Coprod.range_inl_sup_range_inr, exists_addEquiv_range_eq_graph, AddGroupExtension.Section.add_neg_mem_range_inl, range_eq_top_of_cancel, coe_range, CategoryTheory.ShortComplex.abLeftHomologyData_H_coe, QuotientAddGroup.rangeKerLift_injective, mem_range, AddGroupExtension.Section.neg_add_mem_range_inl, QuotientAddGroup.rangeKerLift_surjective, QuotientAddGroup.homQuotientZSMulOfHom_comp, AddSubgroup.fg_iff_exists_fin_addMonoidHom, ofInjective_apply, FreeAddGroup.range_lift_eq_closure, AddGroupExtension.Section.add_neg_add_add_mem_range_inl, QuotientAddGroup.homQuotientZSMulOfHom_id, IsAddCyclic.card_nsmulAddMonoidHom_range, AddSubgroup.map_le_range
rangeRestrict 📖CompOp
8 mathmath: coe_rangeRestrict, rangeRestrict_surjective, rangeRestrict_injective_iff, subtype_comp_rangeRestrict, coe_comp_rangeRestrict, Function.Exact.addMonoidHom_rangeRestrict, Function.Exact.iff_addMonoidHom_rangeRestrict, ker_rangeRestrict

Theorems

NameKindAssumesProvesValidatesDepends On
addSubgroupOf_range_eq_of_le 📖mathematicalAddSubgroup
Preorder.toLE
PartialOrder.toPreorder
AddSubgroup.instPartialOrder
range
AddSubgroup.addSubgroupOf
SetLike.instMembership
AddSubgroup.instSetLike
AddSubgroup.toAddGroup
codRestrict
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddSubgroupClass.toAddSubmonoidClass
AddSubgroup.instAddSubgroupClass
DFunLike.coe
AddMonoidHom
AddZeroClass.toAddZero
instFunLike
AddSubgroup.ext
AddSubgroupClass.toAddSubmonoidClass
AddSubgroup.instAddSubgroupClass
apply_ofInjective_symm 📖mathematicalDFunLike.coe
AddMonoidHom
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
instFunLike
AddEquiv
AddSubgroup
SetLike.instMembership
AddSubgroup.instSetLike
range
AddSubgroup.add
AddZero.toAdd
EquivLike.toFunLike
AddEquiv.instEquivLike
AddEquiv.symm
ofInjective
AddEquiv.apply_symm_apply
coe_comp_rangeRestrict 📖mathematicalAddSubgroup
SetLike.instMembership
AddSubgroup.instSetLike
range
DFunLike.coe
AddMonoidHom
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddSubgroup.toAddGroup
instFunLike
rangeRestrict
coe_ker 📖mathematicalSetLike.coe
AddSubgroup
AddSubgroup.instSetLike
ker
Set.preimage
DFunLike.coe
AddMonoidHom
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
instFunLike
Set
Set.instSingletonSet
AddZero.toZero
coe_range 📖mathematicalSetLike.coe
AddSubgroup
AddSubgroup.instSetLike
range
Set.range
DFunLike.coe
AddMonoidHom
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
instFunLike
coe_rangeRestrict 📖mathematicalAddSubgroup
SetLike.instMembership
AddSubgroup.instSetLike
range
DFunLike.coe
AddMonoidHom
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddSubgroup.toAddGroup
instFunLike
rangeRestrict
comap_bot 📖mathematicalAddSubgroup.comap
Bot.bot
AddSubgroup
AddSubgroup.instBot
ker
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
comap_ker 📖mathematicalAddSubgroup.comap
ker
comp
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
eqLocus_same 📖mathematicaleqLocus
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
Top.top
AddSubgroup
AddSubgroup.instTop
SetLike.ext
eqOn_closure 📖mathematicalSet.EqOn
DFunLike.coe
AddMonoidHom
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
instFunLike
SetLike.coe
AddSubgroup
AddSubgroup.instSetLike
AddSubgroup.closure
AddSubgroup.closure_le
eq_iff 📖mathematicalDFunLike.coe
AddMonoidHom
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
instFunLike
AddSubgroup
SetLike.instMembership
AddSubgroup.instSetLike
ker
AddZero.toAdd
NegZeroClass.toNeg
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
AddGroup.toSubtractionMonoid
mem_ker
map_add
AddMonoidHomClass.toAddHomClass
instAddMonoidHomClass
neg_add_cancel
map_zero
AddMonoidHomClass.toZeroHomClass
zero_add
add_neg_cancel
add_assoc
add_zero
eq_of_eqOn_dense 📖AddSubgroup.closure
Top.top
AddSubgroup
AddSubgroup.instTop
Set.EqOn
DFunLike.coe
AddMonoidHom
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
instFunLike
eq_of_eqOn_top
eqOn_closure
eq_of_eqOn_top 📖Set.EqOn
DFunLike.coe
AddMonoidHom
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
instFunLike
SetLike.coe
AddSubgroup
AddSubgroup.instSetLike
Top.top
AddSubgroup.instTop
ext
ker_codRestrict 📖mathematicalSetLike.instMembership
DFunLike.coe
AddMonoidHom
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
instFunLike
ker
AddSubmonoidClass.toAddMonoid
codRestrict
SetLike.ext
ker_comp_addEquiv 📖mathematicalker
comp
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddMonoidHomClass.toAddMonoidHom
AddEquiv
AddZero.toAdd
EquivLike.toFunLike
AddEquiv.instEquivLike
AddEquivClass.instAddMonoidHomClass
AddEquiv.instAddEquivClass
AddSubgroup.map
AddEquiv.symm
AddEquivClass.instAddMonoidHomClass
AddEquiv.instAddEquivClass
comap_ker
AddSubgroup.comap_equiv_eq_map_symm
ker_eq_bot_iff 📖mathematicalker
Bot.bot
AddSubgroup
AddSubgroup.instBot
DFunLike.coe
AddMonoidHom
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
instFunLike
neg_add_eq_zero
AddSubgroup.mem_bot
eq_iff
bot_unique
map_zero
ker_eq_top_iff 📖mathematicalker
Top.top
AddSubgroup
AddSubgroup.instTop
AddMonoidHom
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
instZeroAddMonoidHom
top_le_iff
SetLike.le_def
instIsConcreteLE
AddSubgroup.mem_top
mem_mker
ext_iff
ker_id 📖mathematicalker
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
id
AddZeroClass.toAddZero
Bot.bot
AddSubgroup
AddSubgroup.instBot
ker_prod 📖mathematicalker
Prod.instAddZeroClass
prod
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddSubgroup
AddSubgroup.instMin
SetLike.ext
Prod.mk_eq_zero
ker_rangeRestrict 📖mathematicalker
AddSubgroup
SetLike.instMembership
AddSubgroup.instSetLike
range
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddSubgroup.toAddGroup
rangeRestrict
ker_codRestrict
ker_restrict 📖mathematicalker
AddSubgroup
SetLike.instMembership
AddSubgroup.instSetLike
AddSubgroup.toAddGroup
restrict
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddSubgroupClass.toAddSubmonoidClass
AddSubgroup.instAddSubgroupClass
AddSubgroup.addSubgroupOf
AddSubgroupClass.toAddSubmonoidClass
AddSubgroup.instAddSubgroupClass
ker_toAddSubmonoid 📖mathematicalAddSubgroup.toAddSubmonoid
ker
mker
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddMonoidHom
AddZeroClass.toAddZero
instFunLike
instAddMonoidHomClass
ker_toHomAddUnits 📖mathematicalker
AddUnits
AddUnits.instAddZeroClass
toHomAddUnits
AddMonoid.toAddZeroClass
AddSubgroup.ext
mem_ker
AddUnits.ext_iff
ker_zero 📖mathematicalker
AddMonoidHom
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
instZeroAddMonoidHom
Top.top
AddSubgroup
AddSubgroup.instTop
SetLike.ext
map_range 📖mathematicalAddSubgroup.map
range
comp
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
range_eq_map
AddSubgroup.map_map
mem_ker 📖mathematicalAddSubgroup
SetLike.instMembership
AddSubgroup.instSetLike
ker
DFunLike.coe
AddMonoidHom
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
instFunLike
AddZero.toZero
mem_range 📖mathematicalAddSubgroup
SetLike.instMembership
AddSubgroup.instSetLike
range
DFunLike.coe
AddMonoidHom
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
instFunLike
normal_ker 📖mathematicalAddSubgroup.Normal
ker
mem_ker
map_add
AddMonoidHomClass.toAddHomClass
instAddMonoidHomClass
add_zero
map_add_eq_zero
add_neg_cancel
ofInjective_apply 📖mathematicalDFunLike.coe
AddMonoidHom
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
instFunLike
AddSubgroup
SetLike.instMembership
AddSubgroup.instSetLike
range
AddEquiv
AddZero.toAdd
AddSubgroup.add
EquivLike.toFunLike
AddEquiv.instEquivLike
ofInjective
ofLeftInverse_apply 📖mathematicalDFunLike.coe
AddMonoidHom
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
instFunLike
AddSubgroup
SetLike.instMembership
AddSubgroup.instSetLike
range
AddEquiv
AddZero.toAdd
AddSubgroup.add
EquivLike.toFunLike
AddEquiv.instEquivLike
ofLeftInverse
ofLeftInverse_symm_apply 📖mathematicalDFunLike.coe
AddMonoidHom
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
instFunLike
AddEquiv
AddSubgroup
SetLike.instMembership
AddSubgroup.instSetLike
range
AddSubgroup.add
AddZero.toAdd
EquivLike.toFunLike
AddEquiv.instEquivLike
AddEquiv.symm
ofLeftInverse
rangeRestrict_injective_iff 📖mathematicalAddSubgroup
SetLike.instMembership
AddSubgroup.instSetLike
range
DFunLike.coe
AddMonoidHom
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddSubgroup.toAddGroup
instFunLike
rangeRestrict
Set.injective_codRestrict
rangeRestrict_surjective 📖mathematicalAddSubgroup
SetLike.instMembership
AddSubgroup.instSetLike
range
DFunLike.coe
AddMonoidHom
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddSubgroup.toAddGroup
instFunLike
rangeRestrict
range_comp 📖mathematicalrange
comp
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddSubgroup.map
map_range
range_eq_bot_iff 📖mathematicalrange
Bot.bot
AddSubgroup
AddSubgroup.instBot
AddMonoidHom
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
instZeroAddMonoidHom
le_bot_iff
range_eq_map
AddSubgroup.map_le_iff_le_comap
top_le_iff
comap_bot
ker_eq_top_iff
range_eq_map 📖mathematicalrange
AddSubgroup.map
Top.top
AddSubgroup
AddSubgroup.instTop
AddSubgroup.ext
mem_range
AddSubgroup.mem_map
AddSubgroup.mem_top
range_eq_top 📖mathematicalrange
Top.top
AddSubgroup
AddSubgroup.instTop
DFunLike.coe
AddMonoidHom
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
instFunLike
SetLike.ext'_iff
coe_range
AddSubgroup.coe_top
Set.range_eq_univ
range_eq_top_of_surjective 📖mathematicalDFunLike.coe
AddMonoidHom
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
instFunLike
range
Top.top
AddSubgroup
AddSubgroup.instTop
range_eq_top
range_isAddCommutative 📖mathematicalIsAddCommutative
AddSubgroup
SetLike.instMembership
AddSubgroup.instSetLike
range
AddCommGroup.toAddGroup
AddSubgroup.add
AddSubgroup.map_isAddCommutative
AddSubgroup.addCommGroup_isAddCommutative
range_eq_map
range_le_ker_iff 📖mathematicalAddSubgroup
Preorder.toLE
PartialOrder.toPreorder
AddSubgroup.instPartialOrder
range
ker
comp
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddMonoidHom
instZeroAddMonoidHom
ext
DFunLike.congr_fun
range_zero 📖mathematicalrange
AddMonoidHom
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
instZeroAddMonoidHom
Bot.bot
AddSubgroup
AddSubgroup.instBot
SetLike.ext
mem_range
Zero.instNonempty
AddSubgroup.mem_bot
comm
IsEquiv.toSymm
eq_isEquiv
restrict_range 📖mathematicalrange
AddSubgroup
SetLike.instMembership
AddSubgroup.instSetLike
AddSubgroup.toAddGroup
restrict
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddSubgroupClass.toAddSubmonoidClass
AddSubgroup.instAddSubgroupClass
AddSubgroup.map
AddSubgroupClass.toAddSubmonoidClass
AddSubgroup.instAddSubgroupClass
SetLike.ext_iff
mem_range
AddSubgroup.mem_map
SetLike.exists
Zero.instNonempty
sub_mem_ker_iff 📖mathematicalAddSubgroup
SetLike.instMembership
AddSubgroup.instSetLike
ker
SubNegMonoid.toSub
AddGroup.toSubNegMonoid
DFunLike.coe
AddMonoidHom
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
instFunLike
sub_add_cancel
map_add
AddMonoidHomClass.toAddHomClass
instAddMonoidHomClass
mem_ker
zero_add
sub_eq_add_neg
add_neg_cancel
map_zero
AddMonoidHomClass.toZeroHomClass
subtype_comp_rangeRestrict 📖mathematicalcomp
AddSubgroup
SetLike.instMembership
AddSubgroup.instSetLike
range
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddSubgroup.toAddGroup
AddSubgroup.subtype
rangeRestrict
ext
coe_rangeRestrict

AddSubgroup

Theorems

NameKindAssumesProvesValidatesDepends On
addSubgroupOf_sup 📖mathematicalAddSubgroup
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
addSubgroupOf
SemilatticeSup.toMax
Lattice.toSemilatticeSup
CompleteLattice.toLattice
instCompleteLattice
SetLike.instMembership
instSetLike
toAddGroup
map_injective_of_ker_le
ker_le_comap
le_trans
le_sup_left
map_comap_eq
range_subtype
map_sup
inf_of_le_right
sup_le
closure_preimage_eq_top 📖mathematicalclosure
AddSubgroup
SetLike.instMembership
instSetLike
toAddGroup
Set.preimage
DFunLike.coe
AddMonoidHom
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddMonoidHom.instFunLike
subtype
Top.top
instTop
closure_closure_coe_preimage
codisjoint_addSubgroupOf_sup 📖mathematicalCodisjoint
AddSubgroup
SetLike.instMembership
instSetLike
SemilatticeSup.toMax
Lattice.toSemilatticeSup
CompleteLattice.toLattice
instCompleteLattice
toAddGroup
instPartialOrder
BoundedOrder.toOrderTop
Preorder.toLE
PartialOrder.toPreorder
CompleteLattice.toBoundedOrder
addSubgroupOf
codisjoint_iff
addSubgroupOf_sup
le_sup_left
le_sup_right
addSubgroupOf_self
comap_injective 📖mathematicalDFunLike.coe
AddMonoidHom
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddMonoidHom.instFunLike
AddSubgroup
comap
le_antisymm_iff
comap_le_comap_of_surjective
comap_le_comap_of_le_range 📖mathematicalAddSubgroup
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
AddMonoidHom.range
comapLE.le.trans
Eq.ge
map_comap_eq_self
map_le_iff_le_comap
comap_mono
comap_le_comap_of_surjective 📖mathematicalDFunLike.coe
AddMonoidHom
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddMonoidHom.instFunLike
AddSubgroup
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
comap
comap_le_comap_of_le_range
le_top
AddMonoidHom.range_eq_top
comap_lt_comap_of_surjective 📖mathematicalDFunLike.coe
AddMonoidHom
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddMonoidHom.instFunLike
AddSubgroup
Preorder.toLT
PartialOrder.toPreorder
instPartialOrder
comap
lt_iff_le_not_ge
comap_le_comap_of_surjective
comap_map_eq 📖mathematicalcomap
map
AddSubgroup
SemilatticeSup.toMax
Lattice.toSemilatticeSup
CompleteLattice.toLattice
instCompleteLattice
AddMonoidHom.ker
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
le_antisymm
mem_comap
mem_map
add_neg_cancel_left
add_mem_sup
AddMonoidHom.mem_ker
map_add
AddMonoidHomClass.toAddHomClass
AddMonoidHom.instAddMonoidHomClass
map_neg
neg_add_cancel
sup_le
le_comap_map
ker_le_comap
comap_map_eq_self 📖mathematicalAddSubgroup
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
AddMonoidHom.ker
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
comap
map
comap_map_eq
sup_eq_left
comap_map_eq_self_of_injective 📖mathematicalDFunLike.coe
AddMonoidHom
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddMonoidHom.instFunLike
comap
map
comap_map_eq_self
bot_le
AddMonoidHom.ker_eq_bot_iff
comap_sup_eq 📖mathematicalDFunLike.coe
AddMonoidHom
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddMonoidHom.instFunLike
AddSubgroup
SemilatticeSup.toMax
Lattice.toSemilatticeSup
CompleteLattice.toLattice
instCompleteLattice
comap
comap_sup_eq_of_le_range
le_top
AddMonoidHom.range_eq_top
comap_sup_eq_of_le_range 📖mathematicalAddSubgroup
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
AddMonoidHom.range
SemilatticeSup.toMax
Lattice.toSemilatticeSup
CompleteLattice.toLattice
instCompleteLattice
comap
map_injective_of_ker_le
LE.le.trans
ker_le_comap
le_sup_left
map_comap_eq
map_sup
inf_eq_right
sup_le
forall 📖mathematicaladdSubgroupOfEquiv.forall_congr_left
inclusion_range 📖mathematicalAddSubgroup
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
AddMonoidHom.range
SetLike.instMembership
instSetLike
toAddGroup
inclusion
addSubgroupOf
ext
Set.ext_iff
Set.range_inclusion
ker_addSubgroupMap 📖mathematicalAddMonoidHom.ker
AddSubgroup
SetLike.instMembership
instSetLike
toAddGroup
map
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddMonoidHom.addSubgroupMap
addSubgroupOf
ext
ker_inclusion 📖mathematicalAddSubgroup
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
AddMonoidHom.ker
SetLike.instMembership
instSetLike
toAddGroup
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
inclusion
Bot.bot
instBot
AddMonoidHom.ker_eq_bot_iff
Set.inclusion_injective
ker_le_comap 📖mathematicalAddSubgroup
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
AddMonoidHom.ker
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
comap
comap_mono
bot_le
AddMonoidHom.comap_bot
ker_subtype 📖mathematicalAddMonoidHom.ker
AddSubgroup
SetLike.instMembership
instSetLike
toAddGroup
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
subtype
Bot.bot
instBot
AddMonoidHom.ker_eq_bot_iff
Subtype.coe_injective
map_comap_eq 📖mathematicalmap
comap
AddSubgroup
instMin
AddMonoidHom.range
SetLike.ext'
coe_map
coe_comap
Set.image_preimage_eq_inter_range
coe_inf
AddMonoidHom.coe_range
Set.inter_comm
map_comap_eq_self 📖mathematicalAddSubgroup
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
AddMonoidHom.range
map
comap
map_comap_eq
inf_eq_right
map_comap_eq_self_of_surjective 📖mathematicalDFunLike.coe
AddMonoidHom
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddMonoidHom.instFunLike
map
comap
map_comap_eq_self
le_top
AddMonoidHom.range_eq_top
map_eq_bot_iff 📖mathematicalmap
Bot.bot
AddSubgroup
instBot
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
AddMonoidHom.ker
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
GaloisConnection.l_eq_bot
gc_map_comap
map_eq_bot_iff_of_injective 📖mathematicalDFunLike.coe
AddMonoidHom
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddMonoidHom.instFunLike
map
Bot.bot
AddSubgroup
instBot
map_eq_bot_iff
AddMonoidHom.ker_eq_bot_iff
le_bot_iff
map_eq_map_iff 📖mathematicalmap
AddSubgroup
SemilatticeSup.toMax
Lattice.toSemilatticeSup
CompleteLattice.toLattice
instCompleteLattice
AddMonoidHom.ker
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
le_antisymm_iff
map_le_map_iff'
map_eq_range_iff 📖mathematicalmap
AddMonoidHom.range
Codisjoint
AddSubgroup
instPartialOrder
BoundedOrder.toOrderTop
Preorder.toLE
PartialOrder.toPreorder
CompleteLattice.toBoundedOrder
instCompleteLattice
AddMonoidHom.ker
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddMonoidHom.range_eq_map
map_eq_map_iff
codisjoint_iff
top_sup_eq
map_injective 📖mathematicalDFunLike.coe
AddMonoidHom
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddMonoidHom.instFunLike
AddSubgroup
map
comap_map_eq_self_of_injective
map_injective_of_ker_le 📖AddSubgroup
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
AddMonoidHom.ker
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
map
sup_of_le_left
comap_map_eq
map_le_map_iff 📖mathematicalAddSubgroup
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
map
SemilatticeSup.toMax
Lattice.toSemilatticeSup
CompleteLattice.toLattice
instCompleteLattice
AddMonoidHom.ker
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
map_le_iff_le_comap
comap_map_eq
map_le_map_iff' 📖mathematicalAddSubgroup
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
map
SemilatticeSup.toMax
Lattice.toSemilatticeSup
CompleteLattice.toLattice
instCompleteLattice
AddMonoidHom.ker
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
map_le_map_iff
sup_le_iff
le_sup_right
map_le_map_iff_of_injective 📖mathematicalDFunLike.coe
AddMonoidHom
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddMonoidHom.instFunLike
AddSubgroup
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
map
map_le_iff_le_comap
comap_map_eq_self_of_injective
map_le_range 📖mathematicalAddSubgroup
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
map
AddMonoidHom.range
map_mono
le_top
AddMonoidHom.range_eq_map
map_lt_map_iff_of_injective 📖mathematicalDFunLike.coe
AddMonoidHom
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddMonoidHom.instFunLike
AddSubgroup
Preorder.toLT
PartialOrder.toPreorder
instPartialOrder
map
lt_iff_lt_of_le_iff_le'
map_le_map_iff_of_injective
map_subtype_le 📖mathematicalAddSubgroup
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
map
SetLike.instMembership
instSetLike
toAddGroup
subtype
LE.le.trans_eq
map_le_range
range_subtype
map_subtype_le_map_subtype 📖mathematicalAddSubgroup
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
map
SetLike.instMembership
instSetLike
toAddGroup
subtype
map_le_map_iff_of_injective
subtype_injective
map_subtype_lt_map_subtype 📖mathematicalAddSubgroup
Preorder.toLT
PartialOrder.toPreorder
instPartialOrder
map
SetLike.instMembership
instSetLike
toAddGroup
subtype
map_lt_map_iff_of_injective
subtype_injective
range_subtype 📖mathematicalAddMonoidHom.range
AddSubgroup
SetLike.instMembership
instSetLike
toAddGroup
subtype
SetLike.coe_injective
AddMonoidHom.coe_range
Subtype.range_coe
subtype_range 📖mathematicalAddMonoidHom.range
AddSubgroup
SetLike.instMembership
instSetLike
toAddGroup
subtype
range_subtype

AddSubgroup.MapSubtype

Definitions

NameCategoryTheorems
orderIso 📖CompOp
2 mathmath: orderIso_apply_coe, orderIso_symm_apply

Theorems

NameKindAssumesProvesValidatesDepends On
orderIso_apply_coe 📖mathematicalAddSubgroup
Preorder.toLE
PartialOrder.toPreorder
AddSubgroup.instPartialOrder
DFunLike.coe
RelIso
SetLike.instMembership
AddSubgroup.instSetLike
AddSubgroup.toAddGroup
RelIso.instFunLike
orderIso
AddSubgroup.map
AddSubgroup.subtype
orderIso_symm_apply 📖mathematicalDFunLike.coe
OrderIso
AddSubgroup
Preorder.toLE
PartialOrder.toPreorder
AddSubgroup.instPartialOrder
SetLike.instMembership
AddSubgroup.instSetLike
AddSubgroup.toAddGroup
instFunLikeOrderIso
OrderIso.symm
orderIso
AddSubgroup.addSubgroupOf

MonoidHom

Definitions

NameCategoryTheorems
decidableMemKer 📖CompOp
eqLocus 📖CompOp
1 mathmath: eqLocus_same
ker 📖CompOp
108 mathmath: comap_bot, ValuationSubring.coe_mem_principalUnitGroup_iff, Ideal.Quotient.map_ker_stabilizer_subtype, QuotientGroup.kerLift_mk, ker_transferSylow_disjoint, IsCyclic.isComplement', restrictHomKerEquiv_apply_coe, IsUniformGroup.uniformContinuous_iff_isOpen_ker, Function.MulExact.monoidHom_ker_eq, Subgroup.map_eq_map_iff, QuotientGroup.rangeKerLift_injective, ker_transferSylow_isComplement', ker_zpowGroupHom_eq_rootsOfUnity, Complex.isQuotientCoveringMap_npow, QuotientGroup.kerLift_mk', Submodule.ker_unitsToPic, fiberEquivKer_symm_apply, ker_rangeRestrict, ker_toHomUnits, ker_eq_top_iff, GrpCat.mono_iff_ker_eq_bot, QuotientGroup.quotientKerEquivOfRightInverse_apply, not_dvd_card_ker_transferSylow, Subgroup.index_ker, ker_prodMap, restrictHomKerEquiv_symm_coe_apply, GrpCat.ker_eq_bot_of_mono, Circle.isQuotientCoveringMap_zpow, Subgroup.normalizerMonoidHom_ker, Subgroup.ker_subtype, isQuotientCoveringMap_npow, Subgroup.relIndex_map_map, QuotientGroup.rangeKerLift_surjective, QuotientGroup.quotientKerEquivOfRightInverse_symm_apply, fiberEquivKer_apply, PresentedGroup.closure_rels_subset_ker, Subgroup.ker_inclusion, mem_ker, IsCyclic.card_powMonoidHom_ker, IsPGroup.ker_isPGroup_of_injective, Subgroup.map_eq_bot_iff, rootsOfUnity_eq_ker, QuotientGroup.ker_map, div_mem_ker_iff, QuotientGroup.kerLift_injective, Equiv.Perm.OnCycleFactors.mem_ker_toPermHom_iff, Subgroup.map_le_map_iff, Subgroup.comap_map_eq, QuotientGroup.con_ker_eq_conKer, Submodule.unitsQuotEquivRelPic_symm_apply, Subgroup.ker_le_comap, Subgroup.map_le_map_iff', Circle.isQuotientCoveringMap_npow, isQuotientCoveringMap_zpow, Subgroup.finiteIndex_ker, NumberField.IsCMField.unitsMulComplexConjInv_ker, IsCyclic.index_powMonoidHom_ker, CommGrpCat.mono_iff_ker_eq_bot, ClassGroup.equivPic_symm_apply, ker_eq_bot_of_cancel, Subgroup.map_eq_range_iff, ker_fst, ValuationSubring.principalUnitGroupEquiv_apply, IsDedekindDomain.selmerGroup.fromUnit_ker, eq_iff, Subgroup.ker_subgroupMap, Ideal.Quotient.ker_stabilizerHom, ker_eq_bot_iff, ker_comp_mulEquiv, ker_prod, normal_ker, finite_iff_finite_ker_range, CommGrpCat.ker_eq_bot_of_mono, Subgroup.normalCore_eq_ker, ker_codRestrict, DirichletCharacter.factorsThrough_iff_ker_unitsMap, zpowersHom_ker_eq, IntermediateField.restrictNormalHom_ker, liftOfRightInverse_comp, QuotientGroup.ker_le_range_iff, Subgroup.relIndex_ker, range_le_ker_iff, Subgroup.index_map, SemidirectProduct.range_inl_eq_ker_rightHom, ValuationSubring.ker_unitGroupToResidueFieldUnits, Abelianization.ker_of, mulExact_iff, ker_one, ClassGroup.equivPic_apply, QuotientGroup.ker_mk', Subgroup.index_range, ker_id, Equiv.Perm.OnCycleFactors.kerParam_range_eq, ker_snd, alternatingGroup_eq_sign_ker, GroupExtension.range_inl_eq_ker_rightHom, ker_toSubmonoid, liftOfRightInverse_comp_apply, coe_ker, coe_toAdditive_ker, Abelianization.commutator_subset_ker, Submodule.ker_unitsMap_spanSingleton, IsDedekindDomain.selmerGroup.valuation_ker_eq, comap_ker, ValuationSubring.principalUnitGroup_symm_apply, ker_restrict, Submodule.unitsQuotEquivRelPic_apply_coe, coe_toMultiplicative_ker
ofInjective 📖CompOp
3 mathmath: Monoid.PushoutI.NormalWord.cons_head, ofInjective_apply, apply_ofInjective_symm
ofLeftInverse 📖CompOp
2 mathmath: ofLeftInverse_symm_apply, ofLeftInverse_apply
range 📖CompOp
150 mathmath: GrpCat.SurjectiveOfEpiAuxs.τ_apply_fromCoset, QuotientGroup.homQuotientZPowOfHom_id, AlternatingMap.domCoprod.summand_mk'', GroupExtension.normal_inl_range, Fintype.card_coeSort_range, Subgroup.instHasDetOneRangeSpecialLinearGroupGeneralLinearGroupMapGL, Monoid.Coprod.range_inl_sup_range_inr, GroupExtension.Section.mul_inv_mem_range_inl, ClassGroup.Quot_mk_eq_mk, Function.MulExact.monoidHom_ker_eq, Subgroup.map_le_range, GroupExtension.Section.mul_inv_mul_mul_mem_range_inl, QuotientGroup.rangeKerLift_injective, Equiv.Perm.OnCycleFactors.mem_range_toPermHom_iff', AlternatingMap.domCoprod_coe, RootPairing.range_weylGroup_coweightHom, GrpCat.SurjectiveOfEpiAuxs.τ_symm_apply_infinity, mem_principal_ideals_iff, coe_toMultiplicative_range, Equiv.Perm.OnCycleFactors.kerParam_range_card, GrpCat.SurjectiveOfEpiAuxs.τ_apply_infinity, ofLeftInverse_symm_apply, Monoid.PushoutI.NormalWord.Transversal.compl, Submodule.ker_unitsToPic, Function.MulExact.monoidHom_rangeRestrict, Subgroup.IsArithmetic.is_commensurable, Matrix.GeneralLinearGroup.center_eq_range_scalar, Subgroup.map_comap_eq, ker_rangeRestrict, Subgroup.instIsArithmeticRangeSpecialLinearGroupFinOfNatNatIntGeneralLinearGroupRealMapGL, Equiv.Perm.OnCycleFactors.nat_card_range_toPermHom, map_range, noncommCoprod_range, Subgroup.IsArithmetic.isCusp_iff_isCusp_SL2Z, graph_eq_range_prod, isCusp_SL2Z_iff', Equiv.Perm.sumCongrHom.card_range, Subgroup.range_zpowersHom, Subgroup.index_ker, range_eq_map, range_one, range_comp, IsDedekindDomain.selmerGroup.monotone, GroupExtension.Section.inv_mul_mem_range_inl, range_eq_bot_iff, restrict_range, range_isMulCommutative, Monoid.CoprodI.range_eq_iSup, NumberField.IsCMField.indexRealUnits_mul_eq, subtype_comp_rangeRestrict, Subgroup.IsArithmetic.isFiniteRelIndexSL, map_commutator_eq, PrincipalIdeals.normal, QuotientGroup.rangeKerLift_surjective, Equiv.Perm.subtypeCongrHom.card_range, Monoid.Coprod.range_swap, Subgroup.card_range_dvd, CongruenceSubgroup.isArithmetic_conj_SL2Z, GrpCat.SurjectiveOfEpiAuxs.agree, Subgroup.index_map_of_injective, GroupExtension.Section.mul_mul_mul_inv_mem_range_inl, FreeGroup.range_lift_eq_closure, coe_comp_rangeRestrict, Submodule.range_unitsToPic, CommGrpCat.range_eq_top_of_epi, isCusp_SL2Z_iff, FreeGroup.closure_eq_range, Equiv.Perm.mem_sumCongrHom_range_of_perm_mapsTo_inl, Monoid.Coprod.range_lift, Submodule.unitsQuotEquivRelPic_symm_apply, QuotientGroup.range_mk', range_eq_top, Monoid.PushoutI.inf_of_range_eq_base_range, QuotientGroup.homQuotientZPowOfHom_comp_of_rightInverse, mem_range, rangeRestrict_surjective, RootPairing.range_weylGroupToPerm, Function.MulExact.iff_monoidHom_rangeRestrict, Group.rank_range_le, QuotientGroup.homQuotientZPowOfHom_comp, ClassGroup.equivPic_symm_apply, coe_rangeRestrict, Equiv.Perm.sigmaCongrRightHom.card_range, coe_toAdditive_range, Subgroup.map_eq_range_iff, range_eq_top_of_surjective, exists_range_eq_graph, noncommPiCoprod_range, IsCyclic.index_powMonoidHom_range, IsDedekindDomain.selmerGroup.fromUnit_ker, Matrix.GeneralLinearGroup.center_eq_range_units, Subgroup.goursat_surjective, range_eq_top_of_cancel, Subgroup.index_comap, ofLeftInverse_apply, QuotientGroup.equivQuotientZPowOfEquiv_trans, GrpCat.SurjectiveOfEpiAuxs.h_apply_fromCoset, rangeRestrict_injective_iff, cosetToCuspOrbit_apply_mk, Equiv.Perm.OnCycleFactors.mem_range_toPermHom_iff, IsDedekindDomain.selmerGroup.fromUnitLift_injective, Subgroup.inclusion_range, Equiv.Perm.OnCycleFactors.kerParam_range_eq_centralizer_of_count_le_one, Subgroup.strictPeriods_SL2Z, finite_iff_finite_ker_range, ofInjective_apply, Subgroup.subtype_range, coe_range, Equiv.Perm.OnCycleFactors.kerParam_range_le_centralizer, Subgroup.range_subtype, Monoid.Coprod.range_eq, ClassGroup.equiv_mk0, independent_range_of_coprime_order, Matrix.SpecialLinearGroup.discreteSpecialLinearGroupIntRange, QuotientGroup.ker_le_range_iff, QuotientGroup.equivQuotientZPowOfEquiv_refl, range_le_ker_iff, Subgroup.index_map, SemidirectProduct.range_inl_eq_ker_rightHom, IsCyclic.card_powMonoidHom_range, QuotientGroup.equivQuotientZPowOfEquiv_symm, Monoid.Coprod.codisjoint_range_inl_range_inr, GrpCat.epi_iff_range_eq_top, mulExact_iff, ClassGroup.equivPic_apply, IsDedekindDomain.HeightOneSpectrum.valuation_of_unit_mod_eq, RootPairing.range_weylGroup_weightHom, GrpCat.SurjectiveOfEpiAuxs.g_apply_fromCoset, Subgroup.index_range, AlternatingMap.domCoprod_apply, GrpCat.SurjectiveOfEpiAuxs.τ_symm_apply_fromCoset, Equiv.Perm.OnCycleFactors.kerParam_range_eq, CommGrpCat.epi_iff_range_eq_top, exists_mulEquiv_range_eq_graph, NumberField.IsCMField.map_unitsMulComplexConjInv_torsion, apply_ofInjective_symm, Subgroup.strictWidthInfty_SL2Z, GroupExtension.range_inl_eq_ker_rightHom, FreeGroup.range_lift_le, ClassGroup.mk_def, Group.fg_range, Subgroup.noncommPiCoprod_range, noncommCoprod_injective, NumberField.IsCMField.index_unitsMulComplexConjInv_range_dvd, Submodule.ker_unitsMap_spanSingleton, ClassGroup.equiv_mk, IsDedekindDomain.selmerGroup.valuation_ker_eq, Equiv.Perm.OnCycleFactors.range_toPermHom_eq_range_toPermHom', Submodule.unitsQuotEquivRelPic_apply_coe, AlternatingMap.domCoprod.summand_add_swap_smul_eq_zero
rangeRestrict 📖CompOp
8 mathmath: Function.MulExact.monoidHom_rangeRestrict, ker_rangeRestrict, subtype_comp_rangeRestrict, coe_comp_rangeRestrict, rangeRestrict_surjective, Function.MulExact.iff_monoidHom_rangeRestrict, coe_rangeRestrict, rangeRestrict_injective_iff

Theorems

NameKindAssumesProvesValidatesDepends On
apply_ofInjective_symm 📖mathematicalDFunLike.coe
MonoidHom
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
instFunLike
MulEquiv
Subgroup
SetLike.instMembership
Subgroup.instSetLike
range
Subgroup.mul
MulOne.toMul
EquivLike.toFunLike
MulEquiv.instEquivLike
MulEquiv.symm
ofInjective
MulEquiv.apply_symm_apply
coe_comp_rangeRestrict 📖mathematicalSubgroup
SetLike.instMembership
Subgroup.instSetLike
range
DFunLike.coe
MonoidHom
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
Subgroup.toGroup
instFunLike
rangeRestrict
coe_ker 📖mathematicalSetLike.coe
Subgroup
Subgroup.instSetLike
ker
Set.preimage
DFunLike.coe
MonoidHom
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
instFunLike
Set
Set.instSingletonSet
MulOne.toOne
coe_range 📖mathematicalSetLike.coe
Subgroup
Subgroup.instSetLike
range
Set.range
DFunLike.coe
MonoidHom
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
instFunLike
coe_rangeRestrict 📖mathematicalSubgroup
SetLike.instMembership
Subgroup.instSetLike
range
DFunLike.coe
MonoidHom
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
Subgroup.toGroup
instFunLike
rangeRestrict
coe_toAdditive_ker 📖mathematicalAddMonoidHom.ker
Additive
Additive.addGroup
Additive.addZeroClass
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
DFunLike.coe
Equiv
MonoidHom
MulOneClass.toMulOne
AddMonoidHom
AddZeroClass.toAddZero
EquivLike.toFunLike
Equiv.instEquivLike
toAdditive
OrderIso
Subgroup
AddSubgroup
Preorder.toLE
PartialOrder.toPreorder
Subgroup.instPartialOrder
AddSubgroup.instPartialOrder
instFunLikeOrderIso
Subgroup.toAddSubgroup
ker
coe_toAdditive_range 📖mathematicalAddMonoidHom.range
Additive
Additive.addGroup
DFunLike.coe
Equiv
MonoidHom
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
AddMonoidHom
AddZeroClass.toAddZero
Additive.addZeroClass
EquivLike.toFunLike
Equiv.instEquivLike
toAdditive
OrderIso
Subgroup
AddSubgroup
Preorder.toLE
PartialOrder.toPreorder
Subgroup.instPartialOrder
AddSubgroup.instPartialOrder
instFunLikeOrderIso
Subgroup.toAddSubgroup
range
coe_toMultiplicative_ker 📖mathematicalker
Multiplicative
Multiplicative.group
Multiplicative.mulOneClass
DFunLike.coe
Equiv
AddMonoidHom
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
MonoidHom
MulOneClass.toMulOne
EquivLike.toFunLike
Equiv.instEquivLike
AddMonoidHom.toMultiplicative
OrderIso
AddSubgroup
Subgroup
Preorder.toLE
PartialOrder.toPreorder
AddSubgroup.instPartialOrder
Subgroup.instPartialOrder
instFunLikeOrderIso
AddSubgroup.toSubgroup
AddMonoidHom.ker
coe_toMultiplicative_range 📖mathematicalrange
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
AddSubgroup.instPartialOrder
Subgroup.instPartialOrder
instFunLikeOrderIso
AddSubgroup.toSubgroup
AddMonoidHom.range
comap_bot 📖mathematicalSubgroup.comap
Bot.bot
Subgroup
Subgroup.instBot
ker
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
comap_ker 📖mathematicalSubgroup.comap
ker
comp
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
div_mem_ker_iff 📖mathematicalSubgroup
SetLike.instMembership
Subgroup.instSetLike
ker
DivInvMonoid.toDiv
Group.toDivInvMonoid
DFunLike.coe
MonoidHom
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
instFunLike
div_mul_cancel
map_mul
MonoidHomClass.toMulHomClass
instMonoidHomClass
mem_ker
one_mul
div_eq_mul_inv
mul_inv_cancel
map_one
MonoidHomClass.toOneHomClass
eqLocus_same 📖mathematicaleqLocus
DivInvMonoid.toMonoid
Group.toDivInvMonoid
Top.top
Subgroup
Subgroup.instTop
SetLike.ext
eqOn_closure 📖mathematicalSet.EqOn
DFunLike.coe
MonoidHom
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
instFunLike
SetLike.coe
Subgroup
Subgroup.instSetLike
Subgroup.closure
Subgroup.closure_le
eq_iff 📖mathematicalDFunLike.coe
MonoidHom
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
instFunLike
Subgroup
SetLike.instMembership
Subgroup.instSetLike
ker
MulOne.toMul
InvOneClass.toInv
DivInvOneMonoid.toInvOneClass
DivisionMonoid.toDivInvOneMonoid
Group.toDivisionMonoid
mem_ker
map_mul
MonoidHomClass.toMulHomClass
instMonoidHomClass
inv_mul_cancel
map_one
MonoidHomClass.toOneHomClass
one_mul
mul_inv_cancel
mul_assoc
mul_one
eq_of_eqOn_dense 📖Subgroup.closure
Top.top
Subgroup
Subgroup.instTop
Set.EqOn
DFunLike.coe
MonoidHom
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
instFunLike
eq_of_eqOn_top
eqOn_closure
eq_of_eqOn_top 📖Set.EqOn
DFunLike.coe
MonoidHom
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
instFunLike
SetLike.coe
Subgroup
Subgroup.instSetLike
Top.top
Subgroup.instTop
ext
ker_codRestrict 📖mathematicalSetLike.instMembership
DFunLike.coe
MonoidHom
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
instFunLike
ker
SubmonoidClass.toMonoid
codRestrict
SetLike.ext
ker_comp_mulEquiv 📖mathematicalker
comp
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
MonoidHomClass.toMonoidHom
MulEquiv
MulOne.toMul
EquivLike.toFunLike
MulEquiv.instEquivLike
MulEquivClass.instMonoidHomClass
MulEquiv.instMulEquivClass
Subgroup.map
MulEquiv.symm
MulEquivClass.instMonoidHomClass
MulEquiv.instMulEquivClass
comap_ker
Subgroup.comap_equiv_eq_map_symm
ker_eq_bot_iff 📖mathematicalker
Bot.bot
Subgroup
Subgroup.instBot
DFunLike.coe
MonoidHom
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
instFunLike
inv_mul_eq_one
Subgroup.mem_bot
eq_iff
bot_unique
map_one
ker_eq_top_iff 📖mathematicalker
Top.top
Subgroup
Subgroup.instTop
MonoidHom
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
instOneMonoidHom
instIsConcreteLE
ext_iff
ker_id 📖mathematicalker
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
id
MulOneClass.toMulOne
Bot.bot
Subgroup
Subgroup.instBot
ker_one 📖mathematicalker
MonoidHom
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
instOneMonoidHom
Top.top
Subgroup
Subgroup.instTop
SetLike.ext
ker_prod 📖mathematicalker
Prod.instMulOneClass
prod
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
Subgroup
Subgroup.instMin
SetLike.ext
Prod.mk_eq_one
ker_rangeRestrict 📖mathematicalker
Subgroup
SetLike.instMembership
Subgroup.instSetLike
range
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
Subgroup.toGroup
rangeRestrict
ker_codRestrict
ker_restrict 📖mathematicalker
Subgroup
SetLike.instMembership
Subgroup.instSetLike
Subgroup.toGroup
restrict
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
SubgroupClass.toSubmonoidClass
Subgroup.instSubgroupClass
Subgroup.subgroupOf
SubgroupClass.toSubmonoidClass
Subgroup.instSubgroupClass
ker_toHomUnits 📖mathematicalker
Units
Units.instMulOneClass
toHomUnits
Monoid.toMulOneClass
Subgroup.ext
ker_toSubmonoid 📖mathematicalSubgroup.toSubmonoid
ker
mker
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
MonoidHom
MulOneClass.toMulOne
instFunLike
instMonoidHomClass
map_range 📖mathematicalSubgroup.map
range
comp
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
range_eq_map
Subgroup.map_map
mem_ker 📖mathematicalSubgroup
SetLike.instMembership
Subgroup.instSetLike
ker
DFunLike.coe
MonoidHom
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
instFunLike
MulOne.toOne
mem_range 📖mathematicalSubgroup
SetLike.instMembership
Subgroup.instSetLike
range
DFunLike.coe
MonoidHom
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
instFunLike
normal_ker 📖mathematicalSubgroup.Normal
ker
mem_ker
map_mul
MonoidHomClass.toMulHomClass
instMonoidHomClass
mul_one
map_mul_eq_one
mul_inv_cancel
ofInjective_apply 📖mathematicalDFunLike.coe
MonoidHom
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
instFunLike
Subgroup
SetLike.instMembership
Subgroup.instSetLike
range
MulEquiv
MulOne.toMul
Subgroup.mul
EquivLike.toFunLike
MulEquiv.instEquivLike
ofInjective
ofLeftInverse_apply 📖mathematicalDFunLike.coe
MonoidHom
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
instFunLike
Subgroup
SetLike.instMembership
Subgroup.instSetLike
range
MulEquiv
MulOne.toMul
Subgroup.mul
EquivLike.toFunLike
MulEquiv.instEquivLike
ofLeftInverse
ofLeftInverse_symm_apply 📖mathematicalDFunLike.coe
MonoidHom
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
instFunLike
MulEquiv
Subgroup
SetLike.instMembership
Subgroup.instSetLike
range
Subgroup.mul
MulOne.toMul
EquivLike.toFunLike
MulEquiv.instEquivLike
MulEquiv.symm
ofLeftInverse
rangeRestrict_injective_iff 📖mathematicalSubgroup
SetLike.instMembership
Subgroup.instSetLike
range
DFunLike.coe
MonoidHom
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
Subgroup.toGroup
instFunLike
rangeRestrict
Set.injective_codRestrict
rangeRestrict_surjective 📖mathematicalSubgroup
SetLike.instMembership
Subgroup.instSetLike
range
DFunLike.coe
MonoidHom
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
Subgroup.toGroup
instFunLike
rangeRestrict
range_comp 📖mathematicalrange
comp
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
Subgroup.map
map_range
range_eq_bot_iff 📖mathematicalrange
Bot.bot
Subgroup
Subgroup.instBot
MonoidHom
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
instOneMonoidHom
le_bot_iff
range_eq_map
Subgroup.map_le_iff_le_comap
top_le_iff
comap_bot
ker_eq_top_iff
range_eq_map 📖mathematicalrange
Subgroup.map
Top.top
Subgroup
Subgroup.instTop
Subgroup.ext
range_eq_top 📖mathematicalrange
Top.top
Subgroup
Subgroup.instTop
DFunLike.coe
MonoidHom
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
instFunLike
SetLike.ext'_iff
coe_range
Subgroup.coe_top
Set.range_eq_univ
range_eq_top_of_surjective 📖mathematicalDFunLike.coe
MonoidHom
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
instFunLike
range
Top.top
Subgroup
Subgroup.instTop
range_eq_top
range_isMulCommutative 📖mathematicalIsMulCommutative
Subgroup
SetLike.instMembership
Subgroup.instSetLike
range
CommGroup.toGroup
Subgroup.mul
Subgroup.map_isMulCommutative
Subgroup.commGroup_isMulCommutative
range_eq_map
range_le_ker_iff 📖mathematicalSubgroup
Preorder.toLE
PartialOrder.toPreorder
Subgroup.instPartialOrder
range
ker
comp
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
MonoidHom
instOneMonoidHom
ext
DFunLike.congr_fun
range_one 📖mathematicalrange
MonoidHom
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
instOneMonoidHom
Bot.bot
Subgroup
Subgroup.instBot
SetLike.ext
One.instNonempty
comm
IsEquiv.toSymm
eq_isEquiv
restrict_range 📖mathematicalrange
Subgroup
SetLike.instMembership
Subgroup.instSetLike
Subgroup.toGroup
restrict
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
SubgroupClass.toSubmonoidClass
Subgroup.instSubgroupClass
Subgroup.map
SubgroupClass.toSubmonoidClass
Subgroup.instSubgroupClass
One.instNonempty
subgroupOf_range_eq_of_le 📖mathematicalSubgroup
Preorder.toLE
PartialOrder.toPreorder
Subgroup.instPartialOrder
range
Subgroup.subgroupOf
SetLike.instMembership
Subgroup.instSetLike
Subgroup.toGroup
codRestrict
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
SubgroupClass.toSubmonoidClass
Subgroup.instSubgroupClass
DFunLike.coe
MonoidHom
MulOneClass.toMulOne
instFunLike
Subgroup.ext
SubgroupClass.toSubmonoidClass
Subgroup.instSubgroupClass
subtype_comp_rangeRestrict 📖mathematicalcomp
Subgroup
SetLike.instMembership
Subgroup.instSetLike
range
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
Subgroup.toGroup
Subgroup.subtype
rangeRestrict
ext
coe_rangeRestrict

Subgroup

Theorems

NameKindAssumesProvesValidatesDepends On
closure_preimage_eq_top 📖mathematicalclosure
Subgroup
SetLike.instMembership
instSetLike
toGroup
Set.preimage
DFunLike.coe
MonoidHom
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
MonoidHom.instFunLike
subtype
Top.top
instTop
closure_closure_coe_preimage
codisjoint_subgroupOf_sup 📖mathematicalCodisjoint
Subgroup
SetLike.instMembership
instSetLike
SemilatticeSup.toMax
Lattice.toSemilatticeSup
CompleteLattice.toLattice
instCompleteLattice
toGroup
instPartialOrder
BoundedOrder.toOrderTop
Preorder.toLE
PartialOrder.toPreorder
CompleteLattice.toBoundedOrder
subgroupOf
codisjoint_iff
subgroupOf_sup
le_sup_left
le_sup_right
subgroupOf_self
comap_injective 📖mathematicalDFunLike.coe
MonoidHom
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
MonoidHom.instFunLike
Subgroup
comap
comap_le_comap_of_surjective
comap_le_comap_of_le_range 📖mathematicalSubgroup
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
MonoidHom.range
comapLE.le.trans
Eq.ge
map_comap_eq_self
map_le_iff_le_comap
comap_mono
comap_le_comap_of_surjective 📖mathematicalDFunLike.coe
MonoidHom
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
MonoidHom.instFunLike
Subgroup
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
comap
comap_le_comap_of_le_range
le_top
MonoidHom.range_eq_top
comap_lt_comap_of_surjective 📖mathematicalDFunLike.coe
MonoidHom
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
MonoidHom.instFunLike
Subgroup
Preorder.toLT
PartialOrder.toPreorder
instPartialOrder
comap
comap_le_comap_of_surjective
comap_map_eq 📖mathematicalcomap
map
Subgroup
SemilatticeSup.toMax
Lattice.toSemilatticeSup
CompleteLattice.toLattice
instCompleteLattice
MonoidHom.ker
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
le_antisymm
mul_inv_cancel_left
mul_mem_sup
map_mul
MonoidHomClass.toMulHomClass
MonoidHom.instMonoidHomClass
map_inv
inv_mul_cancel
sup_le
le_comap_map
ker_le_comap
comap_map_eq_self 📖mathematicalSubgroup
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
MonoidHom.ker
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
comap
map
comap_map_eq
sup_eq_left
comap_map_eq_self_of_injective 📖mathematicalDFunLike.coe
MonoidHom
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
MonoidHom.instFunLike
comap
map
comap_map_eq_self
bot_le
MonoidHom.ker_eq_bot_iff
comap_sup_eq 📖mathematicalDFunLike.coe
MonoidHom
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
MonoidHom.instFunLike
Subgroup
SemilatticeSup.toMax
Lattice.toSemilatticeSup
CompleteLattice.toLattice
instCompleteLattice
comap
comap_sup_eq_of_le_range
le_top
MonoidHom.range_eq_top
comap_sup_eq_of_le_range 📖mathematicalSubgroup
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
MonoidHom.range
SemilatticeSup.toMax
Lattice.toSemilatticeSup
CompleteLattice.toLattice
instCompleteLattice
comap
map_injective_of_ker_le
LE.le.trans
ker_le_comap
le_sup_left
map_comap_eq
map_sup
inf_eq_right
sup_le
forall 📖mathematicalsubgroupOfEquiv.forall_congr_left
inclusion_range 📖mathematicalSubgroup
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
MonoidHom.range
SetLike.instMembership
instSetLike
toGroup
inclusion
subgroupOf
ext
Set.ext_iff
Set.range_inclusion
ker_inclusion 📖mathematicalSubgroup
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
MonoidHom.ker
SetLike.instMembership
instSetLike
toGroup
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
inclusion
Bot.bot
instBot
MonoidHom.ker_eq_bot_iff
Set.inclusion_injective
ker_le_comap 📖mathematicalSubgroup
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
MonoidHom.ker
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
comap
comap_mono
bot_le
MonoidHom.comap_bot
ker_subgroupMap 📖mathematicalMonoidHom.ker
Subgroup
SetLike.instMembership
instSetLike
toGroup
map
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
MonoidHom.subgroupMap
subgroupOf
ext
ker_subtype 📖mathematicalMonoidHom.ker
Subgroup
SetLike.instMembership
instSetLike
toGroup
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
subtype
Bot.bot
instBot
MonoidHom.ker_eq_bot_iff
Subtype.coe_injective
map_comap_eq 📖mathematicalmap
comap
Subgroup
instMin
MonoidHom.range
SetLike.ext'
coe_map
coe_comap
Set.image_preimage_eq_inter_range
coe_inf
MonoidHom.coe_range
Set.inter_comm
map_comap_eq_self 📖mathematicalSubgroup
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
MonoidHom.range
map
comap
map_comap_eq
inf_eq_right
map_comap_eq_self_of_surjective 📖mathematicalDFunLike.coe
MonoidHom
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
MonoidHom.instFunLike
map
comap
map_comap_eq_self
le_top
MonoidHom.range_eq_top
map_eq_bot_iff 📖mathematicalmap
Bot.bot
Subgroup
instBot
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
MonoidHom.ker
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
GaloisConnection.l_eq_bot
gc_map_comap
map_eq_bot_iff_of_injective 📖mathematicalDFunLike.coe
MonoidHom
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
MonoidHom.instFunLike
map
Bot.bot
Subgroup
instBot
map_eq_bot_iff
MonoidHom.ker_eq_bot_iff
le_bot_iff
map_eq_map_iff 📖mathematicalmap
Subgroup
SemilatticeSup.toMax
Lattice.toSemilatticeSup
CompleteLattice.toLattice
instCompleteLattice
MonoidHom.ker
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
map_eq_range_iff 📖mathematicalmap
MonoidHom.range
Codisjoint
Subgroup
instPartialOrder
BoundedOrder.toOrderTop
Preorder.toLE
PartialOrder.toPreorder
CompleteLattice.toBoundedOrder
instCompleteLattice
MonoidHom.ker
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
MonoidHom.range_eq_map
map_eq_map_iff
codisjoint_iff
top_sup_eq
map_injective 📖mathematicalDFunLike.coe
MonoidHom
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
MonoidHom.instFunLike
Subgroup
map
comap_map_eq_self_of_injective
map_injective_of_ker_le 📖Subgroup
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
MonoidHom.ker
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
map
sup_of_le_left
comap_map_eq
map_le_map_iff 📖mathematicalSubgroup
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
map
SemilatticeSup.toMax
Lattice.toSemilatticeSup
CompleteLattice.toLattice
instCompleteLattice
MonoidHom.ker
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
map_le_iff_le_comap
comap_map_eq
map_le_map_iff' 📖mathematicalSubgroup
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
map
SemilatticeSup.toMax
Lattice.toSemilatticeSup
CompleteLattice.toLattice
instCompleteLattice
MonoidHom.ker
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
map_le_map_iff_of_injective 📖mathematicalDFunLike.coe
MonoidHom
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
MonoidHom.instFunLike
Subgroup
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
map
map_le_iff_le_comap
comap_map_eq_self_of_injective
map_le_range 📖mathematicalSubgroup
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
map
MonoidHom.range
map_mono
le_top
MonoidHom.range_eq_map
map_lt_map_iff_of_injective 📖mathematicalDFunLike.coe
MonoidHom
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
MonoidHom.instFunLike
Subgroup
Preorder.toLT
PartialOrder.toPreorder
instPartialOrder
map
lt_iff_lt_of_le_iff_le'
map_le_map_iff_of_injective
map_subtype_le 📖mathematicalSubgroup
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
map
SetLike.instMembership
instSetLike
toGroup
subtype
LE.le.trans_eq
map_le_range
range_subtype
map_subtype_le_map_subtype 📖mathematicalSubgroup
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
map
SetLike.instMembership
instSetLike
toGroup
subtype
map_le_map_iff_of_injective
subtype_injective
map_subtype_lt_map_subtype 📖mathematicalSubgroup
Preorder.toLT
PartialOrder.toPreorder
instPartialOrder
map
SetLike.instMembership
instSetLike
toGroup
subtype
map_lt_map_iff_of_injective
subtype_injective
range_subtype 📖mathematicalMonoidHom.range
Subgroup
SetLike.instMembership
instSetLike
toGroup
subtype
SetLike.coe_injective
MonoidHom.coe_range
Subtype.range_coe
subgroupOf_sup 📖mathematicalSubgroup
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
subgroupOf
SemilatticeSup.toMax
Lattice.toSemilatticeSup
CompleteLattice.toLattice
instCompleteLattice
SetLike.instMembership
instSetLike
toGroup
map_injective_of_ker_le
ker_le_comap
le_trans
le_sup_left
map_comap_eq
range_subtype
map_sup
inf_of_le_right
sup_le
subtype_range 📖mathematicalMonoidHom.range
Subgroup
SetLike.instMembership
instSetLike
toGroup
subtype
range_subtype
sup_subgroupOf_eq 📖mathematicalSubgroup
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
subgroupOf
SemilatticeSup.toMax
Lattice.toSemilatticeSup
CompleteLattice.toLattice
instCompleteLattice
SetLike.instMembership
instSetLike
toGroup
subgroupOf_sup

Subgroup.MapSubtype

Definitions

NameCategoryTheorems
orderIso 📖CompOp
2 mathmath: orderIso_apply_coe, orderIso_symm_apply

Theorems

NameKindAssumesProvesValidatesDepends On
orderIso_apply_coe 📖mathematicalSubgroup
Preorder.toLE
PartialOrder.toPreorder
Subgroup.instPartialOrder
DFunLike.coe
RelIso
SetLike.instMembership
Subgroup.instSetLike
Subgroup.toGroup
RelIso.instFunLike
orderIso
Subgroup.map
Subgroup.subtype
orderIso_symm_apply 📖mathematicalDFunLike.coe
OrderIso
Subgroup
Preorder.toLE
PartialOrder.toPreorder
Subgroup.instPartialOrder
SetLike.instMembership
Subgroup.instSetLike
Subgroup.toGroup
instFunLikeOrderIso
OrderIso.symm
orderIso
Subgroup.subgroupOf

---

← Back to Index