Documentation Verification Report

Operations

📁 Source: Mathlib/Algebra/Group/Subsemigroup/Operations.lean

Statistics

MetricCount
DefinitionsofLeftInverse, subsemigroupCongr, subsemigroupMap, codRestrict, restrict, srange, srangeRestrict, subsemigroupComap, subsemigroupMap, comap, equivMapOfInjective, gciMapComap, giMapComap, inclusion, map, prod, prodEquiv, toSubsemigroup, toSubsemigroup', topEquiv, ofLeftInverse, subsemigroupCongr, subsemigroupMap, codRestrict, restrict, srange, srangeRestrict, subsemigroupComap, subsemigroupMap, comap, equivMapOfInjective, gciMapComap, giMapComap, inclusion, map, prod, prodEquiv, toAddSubsemigroup, toAddSubsemigroup', topEquiv
40
TheoremsofLeftInverse_apply, ofLeftInverse_symm_apply, subsemigroupMap_apply_coe, subsemigroupMap_symm_apply_coe, codRestrict_apply_coe, coe_srange, coe_srangeRestrict, map_mclosure, map_srange, mclosure_preimage_le, mem_srange, prod_map_comap_prod', restrict_apply, srangeRestrict_surjective, srange_eq_map, srange_eq_top_iff_surjective, srange_eq_top_of_surjective, srange_mk, subsemigroupComap_apply_coe, subsemigroupMap_apply_coe, subsemigroupMap_surjective, apply_coe_mem_map, bot_prod_bot, closure_closure_coe_preimage, coe_comap, coe_equivMapOfInjective_apply, coe_map, coe_prod, coe_toSubsemigroup_apply, coe_toSubsemigroup_symm_apply, comap_comap, comap_equiv_eq_map_symm, comap_iInf, comap_iInf_map_of_injective, comap_iSup_map_of_injective, comap_id, comap_inf, comap_inf_map_of_injective, comap_injective_of_surjective, comap_le_comap_iff_of_surjective, comap_map_comap, comap_map_eq_of_injective, comap_strictMono_of_surjective, comap_sup_map_of_injective, comap_surjective_of_injective, comap_top, eq_top_iff', gc_map_comap, le_comap_map, le_comap_of_map_le, le_prod_iff, map_bot, map_comap_eq, map_comap_eq_of_surjective, map_comap_eq_self, map_comap_le, map_comap_map, map_equiv_eq_comap_symm, map_equiv_top, map_iInf, map_iInf_comap_of_surjective, map_iSup, map_iSup_comap_of_surjective, map_id, map_inf, map_inf_comap_of_surjective, map_injective_of_injective, map_le_iff_le_comap, map_le_map_iff_of_injective, map_le_of_le_comap, map_map, map_strictMono_of_injective, map_sup, map_sup_comap_of_surjective, map_surjective_of_surjective, mem_comap, mem_map, mem_map_equiv, mem_map_iff_mem, mem_map_of_mem, mem_prod, monotone_comap, monotone_map, prod_eq_top_iff, prod_mono, prod_top, range_subtype, srange_fst, srange_snd, toSubsemigroup'_closure, toSubsemigroup_closure, topEquiv_apply, topEquiv_symm_apply_coe, topEquiv_toAddHom, top_prod, top_prod_top, ofLeftInverse_apply, ofLeftInverse_symm_apply, subsemigroupMap_apply_coe, subsemigroupMap_symm_apply_coe, codRestrict_apply_coe, coe_srange, coe_srangeRestrict, map_mclosure, map_srange, mclosure_preimage_le, mem_srange, prod_map_comap_prod', restrict_apply, srangeRestrict_surjective, srange_eq_map, srange_eq_top_iff_surjective, srange_eq_top_of_surjective, srange_mk, subsemigroupComap_apply_coe, subsemigroupMap_apply_coe, subsemigroupMap_surjective, apply_coe_mem_map, bot_prod_bot, closure_closure_coe_preimage, coe_comap, coe_equivMapOfInjective_apply, coe_map, coe_prod, coe_toAddSubsemigroup_apply, coe_toAddSubsemigroup_symm_apply, comap_comap, comap_equiv_eq_map_symm, comap_iInf, comap_iInf_map_of_injective, comap_iSup_map_of_injective, comap_id, comap_inf, comap_inf_map_of_injective, comap_injective_of_surjective, comap_le_comap_iff_of_surjective, comap_map_comap, comap_map_eq_of_injective, comap_strictMono_of_surjective, comap_sup_map_of_injective, comap_surjective_of_injective, comap_top, eq_top_iff', gc_map_comap, le_comap_map, le_comap_of_map_le, le_prod_iff, map_bot, map_comap_eq, map_comap_eq_of_surjective, map_comap_eq_self, map_comap_le, map_comap_map, map_equiv_eq_comap_symm, map_equiv_top, map_iInf, map_iInf_comap_of_surjective, map_iSup, map_iSup_comap_of_surjective, map_id, map_inf, map_inf_comap_of_surjective, map_injective_of_injective, map_le_iff_le_comap, map_le_map_iff_of_injective, map_le_of_le_comap, map_map, map_strictMono_of_injective, map_sup, map_sup_comap_of_surjective, map_surjective_of_surjective, mem_comap, mem_map, mem_map_equiv, mem_map_iff_mem, mem_map_of_mem, mem_prod, monotone_comap, monotone_map, prod_eq_top_iff, prod_mono, prod_top, range_subtype, srange_fst, srange_snd, toAddSubsemigroup'_closure, toAddSubsemigroup_closure, topEquiv_apply, topEquiv_symm_apply_coe, topEquiv_toMulHom, top_prod, top_prod_top
192
Total232

AddEquiv

Definitions

NameCategoryTheorems
ofLeftInverse 📖CompOp
2 mathmath: ofLeftInverse_apply, ofLeftInverse_symm_apply
subsemigroupCongr 📖CompOp
1 mathmath: strictMono_subsemigroupCongr
subsemigroupMap 📖CompOp
2 mathmath: subsemigroupMap_apply_coe, subsemigroupMap_symm_apply_coe

Theorems

NameKindAssumesProvesValidatesDepends On
ofLeftInverse_apply 📖mathematicalDFunLike.coe
AddHom
AddHom.funLike
AddEquiv
AddSubsemigroup
SetLike.instMembership
AddSubsemigroup.instSetLike
AddHom.srange
AddMemClass.add
AddSubsemigroup.instAddMemClass
EquivLike.toFunLike
instEquivLike
ofLeftInverse
AddHom.srangeRestrict
AddSubsemigroup.instAddMemClass
ofLeftInverse_symm_apply 📖mathematicalDFunLike.coe
AddHom
AddHom.funLike
AddEquiv
AddSubsemigroup
SetLike.instMembership
AddSubsemigroup.instSetLike
AddHom.srange
AddMemClass.add
AddSubsemigroup.instAddMemClass
EquivLike.toFunLike
instEquivLike
symm
ofLeftInverse
AddSubsemigroup.instAddMemClass
subsemigroupMap_apply_coe 📖mathematicalAddSubsemigroup
SetLike.instMembership
AddSubsemigroup.instSetLike
AddSubsemigroup.map
AddHomClass.toAddHom
AddEquiv
EquivLike.toFunLike
instEquivLike
DFunLike.coe
AddEquivClass.instAddHomClass
instAddEquivClass
AddMemClass.add
AddSubsemigroup.instAddMemClass
subsemigroupMap
AddEquivClass.instAddHomClass
instAddEquivClass
AddSubsemigroup.instAddMemClass
subsemigroupMap_symm_apply_coe 📖mathematicalAddSubsemigroup
SetLike.instMembership
AddSubsemigroup.instSetLike
DFunLike.coe
AddEquiv
AddSubsemigroup.map
AddHomClass.toAddHom
EquivLike.toFunLike
instEquivLike
AddEquivClass.instAddHomClass
instAddEquivClass
AddMemClass.add
AddSubsemigroup.instAddMemClass
symm
subsemigroupMap
AddEquivClass.instAddHomClass
instAddEquivClass
AddSubsemigroup.instAddMemClass

AddHom

Definitions

NameCategoryTheorems
codRestrict 📖CompOp
1 mathmath: codRestrict_apply_coe
restrict 📖CompOp
1 mathmath: restrict_apply
srange 📖CompOp
15 mathmath: coe_srangeRestrict, srangeRestrict_surjective, srange_eq_top_of_surjective, srange_eq_top_iff_surjective, AddSubsemigroup.srange_snd, AddEquiv.ofLeftInverse_apply, AddSubsemigroup.map_comap_eq, srange_mk, srange_eq_map, AddSubsemigroup.range_subtype, map_srange, AddSubsemigroup.srange_fst, mem_srange, AddEquiv.ofLeftInverse_symm_apply, coe_srange
srangeRestrict 📖CompOp
3 mathmath: coe_srangeRestrict, srangeRestrict_surjective, AddEquiv.ofLeftInverse_apply
subsemigroupComap 📖CompOp
1 mathmath: subsemigroupComap_apply_coe
subsemigroupMap 📖CompOp
2 mathmath: subsemigroupMap_apply_coe, subsemigroupMap_surjective

Theorems

NameKindAssumesProvesValidatesDepends On
codRestrict_apply_coe 📖mathematicalSetLike.instMembership
DFunLike.coe
AddHom
funLike
AddMemClass.add
codRestrict
coe_srange 📖mathematicalSetLike.coe
AddSubsemigroup
AddSubsemigroup.instSetLike
srange
Set.range
DFunLike.coe
AddHom
funLike
coe_srangeRestrict 📖mathematicalAddSubsemigroup
SetLike.instMembership
AddSubsemigroup.instSetLike
srange
DFunLike.coe
AddHom
AddMemClass.add
AddSubsemigroup.instAddMemClass
funLike
srangeRestrict
AddSubsemigroup.instAddMemClass
map_mclosure 📖mathematicalAddSubsemigroup.map
AddSubsemigroup.closure
Set.image
DFunLike.coe
AddHom
funLike
GaloisConnection.l_comm_of_u_comm
Set.image_preimage
AddSubsemigroup.gc_map_comap
GaloisInsertion.gc
map_srange 📖mathematicalAddSubsemigroup.map
srange
comp
srange_eq_map
AddSubsemigroup.map_map
mclosure_preimage_le 📖mathematicalAddSubsemigroup
Preorder.toLE
PartialOrder.toPreorder
AddSubsemigroup.instPartialOrder
AddSubsemigroup.closure
Set.preimage
DFunLike.coe
AddHom
funLike
AddSubsemigroup.comap
AddSubsemigroup.closure_le
SetLike.mem_coe
AddSubsemigroup.mem_comap
AddSubsemigroup.subset_closure
mem_srange 📖mathematicalAddSubsemigroup
SetLike.instMembership
AddSubsemigroup.instSetLike
srange
DFunLike.coe
AddHom
funLike
prod_map_comap_prod' 📖mathematicalAddSubsemigroup.comap
Prod.instAdd
prodMap
AddSubsemigroup.prod
SetLike.coe_injective
Set.preimage_prod_map_prod
restrict_apply 📖mathematicalDFunLike.coe
AddHom
SetLike.instMembership
AddMemClass.add
funLike
restrict
srangeRestrict_surjective 📖mathematicalAddSubsemigroup
SetLike.instMembership
AddSubsemigroup.instSetLike
srange
DFunLike.coe
AddHom
AddMemClass.add
AddSubsemigroup.instAddMemClass
funLike
srangeRestrict
AddSubsemigroup.instAddMemClass
srange_eq_map 📖mathematicalsrange
AddSubsemigroup.map
Top.top
AddSubsemigroup
AddSubsemigroup.instTop
AddSubsemigroup.copy_eq
srange_eq_top_iff_surjective 📖mathematicalsrange
Top.top
AddSubsemigroup
AddSubsemigroup.instTop
DFunLike.coe
AddHom
funLike
SetLike.ext'_iff
coe_srange
AddSubsemigroup.coe_top
Set.range_eq_univ
srange_eq_top_of_surjective 📖mathematicalDFunLike.coe
AddHom
funLike
srange
Top.top
AddSubsemigroup
AddSubsemigroup.instTop
srange_eq_top_iff_surjective
srange_mk 📖mathematicalsrange
Set.range
subsemigroupComap_apply_coe 📖mathematicalAddSubsemigroup
SetLike.instMembership
AddSubsemigroup.instSetLike
DFunLike.coe
AddHom
AddSubsemigroup.comap
AddMemClass.add
AddSubsemigroup.instAddMemClass
funLike
subsemigroupComap
AddSubsemigroup.instAddMemClass
subsemigroupMap_apply_coe 📖mathematicalAddSubsemigroup
SetLike.instMembership
AddSubsemigroup.instSetLike
AddSubsemigroup.map
DFunLike.coe
AddHom
AddMemClass.add
AddSubsemigroup.instAddMemClass
funLike
subsemigroupMap
AddSubsemigroup.instAddMemClass
subsemigroupMap_surjective 📖mathematicalAddSubsemigroup
SetLike.instMembership
AddSubsemigroup.instSetLike
AddSubsemigroup.map
DFunLike.coe
AddHom
AddMemClass.add
AddSubsemigroup.instAddMemClass
funLike
subsemigroupMap
AddSubsemigroup.instAddMemClass

AddSubsemigroup

Definitions

NameCategoryTheorems
comap 📖CompOp
38 mathmath: AddHom.prod_map_comap_prod', map_inf_comap_of_surjective, comap_injective_of_surjective, comap_comap, comap_iInf, comap_equiv_eq_map_symm, comap_inf, comap_sup_map_of_injective, le_comap_map, map_comap_eq, comap_inf_map_of_injective, comap_id, map_iInf_comap_of_surjective, map_equiv_eq_comap_symm, map_comap_eq_of_surjective, comap_iSup_map_of_injective, comap_strictMono_of_surjective, comap_iInf_map_of_injective, map_iSup_comap_of_surjective, mem_comap, comap_top, map_comap_map, map_comap_le, le_comap_of_map_le, monotone_comap, top_prod, map_sup_comap_of_surjective, AddHom.subsemigroupComap_apply_coe, coe_comap, comap_map_comap, map_le_iff_le_comap, comap_le_comap_iff_of_surjective, AddHom.mclosure_preimage_le, comap_surjective_of_injective, map_comap_eq_self, gc_map_comap, comap_map_eq_of_injective, prod_top
equivMapOfInjective 📖CompOp
1 mathmath: coe_equivMapOfInjective_apply
gciMapComap 📖CompOp
giMapComap 📖CompOp
inclusion 📖CompOp
map 📖CompOp
49 mathmath: AddHom.subsemigroupMap_apply_coe, map_inf_comap_of_surjective, mem_map_equiv, AddHom.subsemigroupMap_surjective, map_sup, map_le_map_iff_of_injective, map_iSup, map_injective_of_injective, comap_equiv_eq_map_symm, mem_map_of_mem, map_bot, comap_sup_map_of_injective, le_comap_map, le_prod_iff, map_comap_eq, AddEquiv.subsemigroupMap_apply_coe, coe_map, comap_inf_map_of_injective, AddHom.srange_eq_map, map_iInf_comap_of_surjective, map_equiv_eq_comap_symm, map_comap_eq_of_surjective, comap_iSup_map_of_injective, map_equiv_top, coe_equivMapOfInjective_apply, comap_iInf_map_of_injective, map_iSup_comap_of_surjective, mem_map, map_id, map_comap_map, map_comap_le, map_surjective_of_surjective, map_sup_comap_of_surjective, map_map, mem_map_iff_mem, AddHom.map_srange, comap_map_comap, map_le_iff_le_comap, AddEquiv.subsemigroupMap_symm_apply_coe, map_strictMono_of_injective, map_inf, monotone_map, map_iInf, apply_coe_mem_map, map_comap_eq_self, map_le_of_le_comap, gc_map_comap, comap_map_eq_of_injective, AddHom.map_mclosure
prod 📖CompOp
10 mathmath: AddHom.prod_map_comap_prod', prod_eq_top_iff, coe_prod, mem_prod, le_prod_iff, top_prod_top, bot_prod_bot, top_prod, prod_mono, prod_top
prodEquiv 📖CompOp
toSubsemigroup 📖CompOp
3 mathmath: coe_toSubsemigroup_symm_apply, coe_toSubsemigroup_apply, toSubsemigroup_closure
toSubsemigroup' 📖CompOp
1 mathmath: toSubsemigroup'_closure
topEquiv 📖CompOp
4 mathmath: topEquiv_apply, topEquiv_symm_apply_coe, strictMono_topEquiv, topEquiv_toAddHom

Theorems

NameKindAssumesProvesValidatesDepends On
apply_coe_mem_map 📖mathematicalAddSubsemigroup
SetLike.instMembership
instSetLike
map
DFunLike.coe
AddHom
AddHom.funLike
mem_map_of_mem
Subtype.prop
bot_prod_bot 📖mathematicalprod
Bot.bot
AddSubsemigroup
instBot
Prod.instAdd
SetLike.coe_injective
Set.prod_empty
closure_closure_coe_preimage 📖mathematicalclosure
AddSubsemigroup
SetLike.instMembership
instSetLike
AddMemClass.add
instAddMemClass
Set.preimage
Top.top
instTop
instAddMemClass
eq_top_iff
closure_induction
subset_closure
AddMemClass.add_mem
coe_comap 📖mathematicalSetLike.coe
AddSubsemigroup
instSetLike
comap
Set.preimage
DFunLike.coe
AddHom
AddHom.funLike
coe_equivMapOfInjective_apply 📖mathematicalDFunLike.coe
AddHom
AddHom.funLike
AddSubsemigroup
SetLike.instMembership
instSetLike
map
AddEquiv
AddMemClass.add
instAddMemClass
EquivLike.toFunLike
AddEquiv.instEquivLike
equivMapOfInjective
instAddMemClass
coe_map 📖mathematicalSetLike.coe
AddSubsemigroup
instSetLike
map
Set.image
DFunLike.coe
AddHom
AddHom.funLike
coe_prod 📖mathematicalSetLike.coe
AddSubsemigroup
Prod.instAdd
instSetLike
prod
SProd.sprod
Set
Set.instSProd
coe_toSubsemigroup_apply 📖mathematicalSetLike.coe
Subsemigroup
Multiplicative
Multiplicative.mul
Subsemigroup.instSetLike
DFunLike.coe
RelIso
AddSubsemigroup
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
Subsemigroup.instPartialOrder
RelIso.instFunLike
toSubsemigroup
Set.preimage
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
Multiplicative.toAdd
instSetLike
coe_toSubsemigroup_symm_apply 📖mathematicalSetLike.coe
AddSubsemigroup
instSetLike
DFunLike.coe
RelIso
Subsemigroup
Multiplicative
Multiplicative.mul
Preorder.toLE
PartialOrder.toPreorder
Subsemigroup.instPartialOrder
instPartialOrder
RelIso.instFunLike
RelIso.symm
toSubsemigroup
Set.preimage
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
Multiplicative.ofAdd
Subsemigroup.instSetLike
comap_comap 📖mathematicalcomap
AddHom.comp
comap_equiv_eq_map_symm 📖mathematicalcomap
AddHomClass.toAddHom
AddEquiv
EquivLike.toFunLike
AddEquiv.instEquivLike
AddEquivClass.instAddHomClass
AddEquiv.instAddEquivClass
map
AddEquiv.symm
AddEquivClass.instAddHomClass
AddEquiv.instAddEquivClass
map_equiv_eq_comap_symm
comap_iInf 📖mathematicalcomap
iInf
AddSubsemigroup
instInfSet
GaloisConnection.u_iInf
gc_map_comap
comap_iInf_map_of_injective 📖mathematicalDFunLike.coe
AddHom
AddHom.funLike
comap
iInf
AddSubsemigroup
instInfSet
map
GaloisCoinsertion.u_iInf_l
comap_iSup_map_of_injective 📖mathematicalDFunLike.coe
AddHom
AddHom.funLike
comap
iSup
AddSubsemigroup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
instCompleteLattice
map
GaloisCoinsertion.u_iSup_l
comap_id 📖mathematicalcomap
AddHom.id
ext
mem_comap
comap_inf 📖mathematicalcomap
AddSubsemigroup
instMin
GaloisConnection.u_inf
gc_map_comap
comap_inf_map_of_injective 📖mathematicalDFunLike.coe
AddHom
AddHom.funLike
comap
AddSubsemigroup
instMin
map
GaloisCoinsertion.u_inf_l
comap_injective_of_surjective 📖mathematicalDFunLike.coe
AddHom
AddHom.funLike
AddSubsemigroup
comap
GaloisInsertion.u_injective
comap_le_comap_iff_of_surjective 📖mathematicalDFunLike.coe
AddHom
AddHom.funLike
AddSubsemigroup
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
comap
GaloisInsertion.u_le_u_iff
comap_map_comap 📖mathematicalcomap
map
GaloisConnection.u_l_u_eq_u
gc_map_comap
comap_map_eq_of_injective 📖mathematicalDFunLike.coe
AddHom
AddHom.funLike
comap
map
GaloisCoinsertion.u_l_eq
comap_strictMono_of_surjective 📖mathematicalDFunLike.coe
AddHom
AddHom.funLike
StrictMono
AddSubsemigroup
PartialOrder.toPreorder
instPartialOrder
comap
GaloisInsertion.strictMono_u
comap_sup_map_of_injective 📖mathematicalDFunLike.coe
AddHom
AddHom.funLike
comap
AddSubsemigroup
SemilatticeSup.toMax
Lattice.toSemilatticeSup
CompleteLattice.toLattice
instCompleteLattice
map
GaloisCoinsertion.u_sup_l
comap_surjective_of_injective 📖mathematicalDFunLike.coe
AddHom
AddHom.funLike
AddSubsemigroup
comap
GaloisCoinsertion.u_surjective
comap_top 📖mathematicalcomap
Top.top
AddSubsemigroup
instTop
GaloisConnection.u_top
gc_map_comap
eq_top_iff' 📖mathematicalTop.top
AddSubsemigroup
instTop
SetLike.instMembership
instSetLike
eq_top_iff
mem_top
gc_map_comap 📖mathematicalGaloisConnection
AddSubsemigroup
PartialOrder.toPreorder
instPartialOrder
map
comap
map_le_iff_le_comap
le_comap_map 📖mathematicalAddSubsemigroup
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
comap
map
GaloisConnection.le_u_l
gc_map_comap
le_comap_of_map_le 📖mathematicalAddSubsemigroup
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
map
comapGaloisConnection.le_u
gc_map_comap
le_prod_iff 📖mathematicalAddSubsemigroup
Prod.instAdd
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
prod
map
AddHom.fst
AddHom.snd
map_bot 📖mathematicalmap
Bot.bot
AddSubsemigroup
instBot
GaloisConnection.l_bot
gc_map_comap
map_comap_eq 📖mathematicalmap
comap
AddSubsemigroup
instMin
AddHom.srange
SetLike.coe_injective
Set.image_preimage_eq_inter_range
map_comap_eq_of_surjective 📖mathematicalDFunLike.coe
AddHom
AddHom.funLike
map
comap
GaloisInsertion.l_u_eq
map_comap_eq_self 📖mathematicalAddSubsemigroup
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
AddHom.srange
map
comap
inf_of_le_left
map_comap_eq
map_comap_le 📖mathematicalAddSubsemigroup
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
map
comap
GaloisConnection.l_u_le
gc_map_comap
map_comap_map 📖mathematicalmap
comap
GaloisConnection.l_u_l_eq_l
gc_map_comap
map_equiv_eq_comap_symm 📖mathematicalmap
AddHomClass.toAddHom
AddEquiv
EquivLike.toFunLike
AddEquiv.instEquivLike
AddEquivClass.instAddHomClass
AddEquiv.instAddEquivClass
comap
AddEquiv.symm
SetLike.coe_injective
AddEquivClass.instAddHomClass
AddEquiv.instAddEquivClass
Equiv.image_eq_preimage_symm
map_equiv_top 📖mathematicalmap
AddHomClass.toAddHom
AddEquiv
EquivLike.toFunLike
AddEquiv.instEquivLike
AddEquivClass.instAddHomClass
AddEquiv.instAddEquivClass
Top.top
AddSubsemigroup
instTop
SetLike.coe_injective
AddEquivClass.instAddHomClass
AddEquiv.instAddEquivClass
Set.image_univ
Function.Surjective.range_eq
AddEquiv.surjective
map_iInf 📖mathematicalDFunLike.coe
AddHom
AddHom.funLike
map
iInf
AddSubsemigroup
instInfSet
SetLike.coe_injective
coe_iInf
Set.InjOn.image_iInter_eq
Set.injOn_of_injective
map_iInf_comap_of_surjective 📖mathematicalDFunLike.coe
AddHom
AddHom.funLike
map
iInf
AddSubsemigroup
instInfSet
comap
GaloisInsertion.l_iInf_u
map_iSup 📖mathematicalmap
iSup
AddSubsemigroup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
instCompleteLattice
GaloisConnection.l_iSup
gc_map_comap
map_iSup_comap_of_surjective 📖mathematicalDFunLike.coe
AddHom
AddHom.funLike
map
iSup
AddSubsemigroup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
instCompleteLattice
comap
GaloisInsertion.l_iSup_u
map_id 📖mathematicalmap
AddHom.id
ext
map_inf 📖mathematicalDFunLike.coe
AddHom
AddHom.funLike
map
AddSubsemigroup
instMin
SetLike.coe_injective
Set.image_inter
map_inf_comap_of_surjective 📖mathematicalDFunLike.coe
AddHom
AddHom.funLike
map
AddSubsemigroup
instMin
comap
GaloisInsertion.l_inf_u
map_injective_of_injective 📖mathematicalDFunLike.coe
AddHom
AddHom.funLike
AddSubsemigroup
map
GaloisCoinsertion.l_injective
map_le_iff_le_comap 📖mathematicalAddSubsemigroup
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
map
comap
Set.image_subset_iff
map_le_map_iff_of_injective 📖mathematicalDFunLike.coe
AddHom
AddHom.funLike
AddSubsemigroup
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
map
GaloisCoinsertion.l_le_l_iff
map_le_of_le_comap 📖mathematicalAddSubsemigroup
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
comap
mapGaloisConnection.l_le
gc_map_comap
map_map 📖mathematicalmap
AddHom.comp
SetLike.coe_injective
Set.image_image
map_strictMono_of_injective 📖mathematicalDFunLike.coe
AddHom
AddHom.funLike
StrictMono
AddSubsemigroup
PartialOrder.toPreorder
instPartialOrder
map
GaloisCoinsertion.strictMono_l
map_sup 📖mathematicalmap
AddSubsemigroup
SemilatticeSup.toMax
Lattice.toSemilatticeSup
CompleteLattice.toLattice
instCompleteLattice
GaloisConnection.l_sup
gc_map_comap
map_sup_comap_of_surjective 📖mathematicalDFunLike.coe
AddHom
AddHom.funLike
map
AddSubsemigroup
SemilatticeSup.toMax
Lattice.toSemilatticeSup
CompleteLattice.toLattice
instCompleteLattice
comap
GaloisInsertion.l_sup_u
map_surjective_of_surjective 📖mathematicalDFunLike.coe
AddHom
AddHom.funLike
AddSubsemigroup
map
GaloisInsertion.l_surjective
mem_comap 📖mathematicalAddSubsemigroup
SetLike.instMembership
instSetLike
comap
DFunLike.coe
AddHom
AddHom.funLike
mem_map 📖mathematicalAddSubsemigroup
SetLike.instMembership
instSetLike
map
DFunLike.coe
AddHom
AddHom.funLike
Set.mem_image
mem_map_equiv 📖mathematicalAddSubsemigroup
SetLike.instMembership
instSetLike
map
AddHomClass.toAddHom
AddEquiv
EquivLike.toFunLike
AddEquiv.instEquivLike
AddEquivClass.instAddHomClass
AddEquiv.instAddEquivClass
DFunLike.coe
AddEquiv.symm
Set.mem_image_equiv
mem_map_iff_mem 📖mathematicalDFunLike.coe
AddHom
AddHom.funLike
AddSubsemigroup
SetLike.instMembership
instSetLike
map
Function.Injective.mem_set_image
mem_map_of_mem 📖mathematicalAddSubsemigroup
SetLike.instMembership
instSetLike
map
DFunLike.coe
AddHom
AddHom.funLike
Set.mem_image_of_mem
mem_prod 📖mathematicalAddSubsemigroup
Prod.instAdd
SetLike.instMembership
instSetLike
prod
monotone_comap 📖mathematicalMonotone
AddSubsemigroup
PartialOrder.toPreorder
instPartialOrder
comap
GaloisConnection.monotone_u
gc_map_comap
monotone_map 📖mathematicalMonotone
AddSubsemigroup
PartialOrder.toPreorder
instPartialOrder
map
GaloisConnection.monotone_l
gc_map_comap
prod_eq_top_iff 📖mathematicalprod
Top.top
AddSubsemigroup
Prod.instAdd
instTop
eq_top_iff
le_prod_iff
AddHom.srange_eq_map
srange_fst
srange_snd
prod_mono 📖mathematicalAddSubsemigroup
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
Prod.instAdd
prod
Set.prod_mono
prod_top 📖mathematicalprod
Top.top
AddSubsemigroup
instTop
comap
Prod.instAdd
AddHom.fst
ext
mem_prod
mem_top
mem_comap
range_subtype 📖mathematicalAddHom.srange
AddSubsemigroup
SetLike.instMembership
instSetLike
AddMemClass.add
instAddMemClass
AddMemClass.subtype
SetLike.coe_injective
instAddMemClass
AddHom.coe_srange
Subtype.range_coe
srange_fst 📖mathematicalAddHom.srange
Prod.instAdd
AddHom.fst
Top.top
AddSubsemigroup
instTop
AddHom.srange_eq_top_of_surjective
Prod.fst_surjective
srange_snd 📖mathematicalAddHom.srange
Prod.instAdd
AddHom.snd
Top.top
AddSubsemigroup
instTop
AddHom.srange_eq_top_of_surjective
Prod.snd_surjective
toSubsemigroup'_closure 📖mathematicalDFunLike.coe
OrderIso
AddSubsemigroup
Additive
Additive.add
Subsemigroup
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
Subsemigroup.instPartialOrder
instFunLikeOrderIso
toSubsemigroup'
closure
Subsemigroup.closure
Set.preimage
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
Additive.ofMul
le_antisymm
OrderIso.le_symm_apply
closure_le
Subsemigroup.subset_closure
Subsemigroup.closure_le
subset_closure
toSubsemigroup_closure 📖mathematicalDFunLike.coe
OrderIso
AddSubsemigroup
Subsemigroup
Multiplicative
Multiplicative.mul
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
Subsemigroup.instPartialOrder
instFunLikeOrderIso
toSubsemigroup
closure
Subsemigroup.closure
Set.preimage
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
Multiplicative.toAdd
le_antisymm
GaloisConnection.l_le
OrderIso.to_galoisConnection
closure_le
Subsemigroup.subset_closure
Subsemigroup.closure_le
subset_closure
topEquiv_apply 📖mathematicalDFunLike.coe
AddEquiv
AddSubsemigroup
SetLike.instMembership
instSetLike
Top.top
instTop
AddMemClass.add
instAddMemClass
EquivLike.toFunLike
AddEquiv.instEquivLike
topEquiv
instAddMemClass
topEquiv_symm_apply_coe 📖mathematicalAddSubsemigroup
SetLike.instMembership
instSetLike
Top.top
instTop
DFunLike.coe
AddEquiv
AddMemClass.add
instAddMemClass
EquivLike.toFunLike
AddEquiv.instEquivLike
AddEquiv.symm
topEquiv
instAddMemClass
topEquiv_toAddHom 📖mathematicalAddHomClass.toAddHom
AddSubsemigroup
SetLike.instMembership
instSetLike
Top.top
instTop
AddEquiv
AddMemClass.add
instAddMemClass
EquivLike.toFunLike
AddEquiv.instEquivLike
AddEquivClass.instAddHomClass
AddEquiv.instAddEquivClass
topEquiv
AddMemClass.subtype
instAddMemClass
AddEquivClass.instAddHomClass
AddEquiv.instAddEquivClass
top_prod 📖mathematicalprod
Top.top
AddSubsemigroup
instTop
comap
Prod.instAdd
AddHom.snd
ext
mem_prod
mem_top
mem_comap
top_prod_top 📖mathematicalprod
Top.top
AddSubsemigroup
instTop
Prod.instAdd
top_prod
comap_top

MulEquiv

Definitions

NameCategoryTheorems
ofLeftInverse 📖CompOp
2 mathmath: ofLeftInverse_symm_apply, ofLeftInverse_apply
subsemigroupCongr 📖CompOp
1 mathmath: strictMono_subsemigroupCongr
subsemigroupMap 📖CompOp
2 mathmath: subsemigroupMap_apply_coe, subsemigroupMap_symm_apply_coe

Theorems

NameKindAssumesProvesValidatesDepends On
ofLeftInverse_apply 📖mathematicalDFunLike.coe
MulHom
MulHom.funLike
MulEquiv
Subsemigroup
SetLike.instMembership
Subsemigroup.instSetLike
MulHom.srange
MulMemClass.mul
Subsemigroup.instMulMemClass
EquivLike.toFunLike
instEquivLike
ofLeftInverse
MulHom.srangeRestrict
Subsemigroup.instMulMemClass
ofLeftInverse_symm_apply 📖mathematicalDFunLike.coe
MulHom
MulHom.funLike
MulEquiv
Subsemigroup
SetLike.instMembership
Subsemigroup.instSetLike
MulHom.srange
MulMemClass.mul
Subsemigroup.instMulMemClass
EquivLike.toFunLike
instEquivLike
symm
ofLeftInverse
Subsemigroup.instMulMemClass
subsemigroupMap_apply_coe 📖mathematicalSubsemigroup
SetLike.instMembership
Subsemigroup.instSetLike
Subsemigroup.map
MulHomClass.toMulHom
MulEquiv
EquivLike.toFunLike
instEquivLike
DFunLike.coe
MulEquivClass.instMulHomClass
instMulEquivClass
MulMemClass.mul
Subsemigroup.instMulMemClass
subsemigroupMap
MulEquivClass.instMulHomClass
instMulEquivClass
Subsemigroup.instMulMemClass
subsemigroupMap_symm_apply_coe 📖mathematicalSubsemigroup
SetLike.instMembership
Subsemigroup.instSetLike
DFunLike.coe
MulEquiv
Subsemigroup.map
MulHomClass.toMulHom
EquivLike.toFunLike
instEquivLike
MulEquivClass.instMulHomClass
instMulEquivClass
MulMemClass.mul
Subsemigroup.instMulMemClass
symm
subsemigroupMap
MulEquivClass.instMulHomClass
instMulEquivClass
Subsemigroup.instMulMemClass

MulHom

Definitions

NameCategoryTheorems
codRestrict 📖CompOp
1 mathmath: codRestrict_apply_coe
restrict 📖CompOp
1 mathmath: restrict_apply
srange 📖CompOp
15 mathmath: Subsemigroup.srange_snd, coe_srange, coe_srangeRestrict, MulEquiv.ofLeftInverse_symm_apply, srange_eq_top_iff_surjective, Subsemigroup.map_comap_eq, MulEquiv.ofLeftInverse_apply, map_srange, Subsemigroup.range_subtype, Subsemigroup.srange_fst, mem_srange, srange_eq_top_of_surjective, srange_eq_map, srangeRestrict_surjective, srange_mk
srangeRestrict 📖CompOp
3 mathmath: coe_srangeRestrict, MulEquiv.ofLeftInverse_apply, srangeRestrict_surjective
subsemigroupComap 📖CompOp
1 mathmath: subsemigroupComap_apply_coe
subsemigroupMap 📖CompOp
2 mathmath: subsemigroupMap_surjective, subsemigroupMap_apply_coe

Theorems

NameKindAssumesProvesValidatesDepends On
codRestrict_apply_coe 📖mathematicalSetLike.instMembership
DFunLike.coe
MulHom
funLike
MulMemClass.mul
codRestrict
coe_srange 📖mathematicalSetLike.coe
Subsemigroup
Subsemigroup.instSetLike
srange
Set.range
DFunLike.coe
MulHom
funLike
coe_srangeRestrict 📖mathematicalSubsemigroup
SetLike.instMembership
Subsemigroup.instSetLike
srange
DFunLike.coe
MulHom
MulMemClass.mul
Subsemigroup.instMulMemClass
funLike
srangeRestrict
Subsemigroup.instMulMemClass
map_mclosure 📖mathematicalSubsemigroup.map
Subsemigroup.closure
Set.image
DFunLike.coe
MulHom
funLike
GaloisConnection.l_comm_of_u_comm
Set.image_preimage
Subsemigroup.gc_map_comap
GaloisInsertion.gc
map_srange 📖mathematicalSubsemigroup.map
srange
comp
srange_eq_map
Subsemigroup.map_map
mclosure_preimage_le 📖mathematicalSubsemigroup
Preorder.toLE
PartialOrder.toPreorder
Subsemigroup.instPartialOrder
Subsemigroup.closure
Set.preimage
DFunLike.coe
MulHom
funLike
Subsemigroup.comap
Subsemigroup.closure_le
SetLike.mem_coe
Subsemigroup.mem_comap
Subsemigroup.subset_closure
mem_srange 📖mathematicalSubsemigroup
SetLike.instMembership
Subsemigroup.instSetLike
srange
DFunLike.coe
MulHom
funLike
prod_map_comap_prod' 📖mathematicalSubsemigroup.comap
Prod.instMul
prodMap
Subsemigroup.prod
SetLike.coe_injective
Set.preimage_prod_map_prod
restrict_apply 📖mathematicalDFunLike.coe
MulHom
SetLike.instMembership
MulMemClass.mul
funLike
restrict
srangeRestrict_surjective 📖mathematicalSubsemigroup
SetLike.instMembership
Subsemigroup.instSetLike
srange
DFunLike.coe
MulHom
MulMemClass.mul
Subsemigroup.instMulMemClass
funLike
srangeRestrict
Subsemigroup.instMulMemClass
srange_eq_map 📖mathematicalsrange
Subsemigroup.map
Top.top
Subsemigroup
Subsemigroup.instTop
Subsemigroup.copy_eq
srange_eq_top_iff_surjective 📖mathematicalsrange
Top.top
Subsemigroup
Subsemigroup.instTop
DFunLike.coe
MulHom
funLike
SetLike.ext'_iff
coe_srange
Subsemigroup.coe_top
Set.range_eq_univ
srange_eq_top_of_surjective 📖mathematicalDFunLike.coe
MulHom
funLike
srange
Top.top
Subsemigroup
Subsemigroup.instTop
srange_eq_top_iff_surjective
srange_mk 📖mathematicalsrange
Set.range
subsemigroupComap_apply_coe 📖mathematicalSubsemigroup
SetLike.instMembership
Subsemigroup.instSetLike
DFunLike.coe
MulHom
Subsemigroup.comap
MulMemClass.mul
Subsemigroup.instMulMemClass
funLike
subsemigroupComap
Subsemigroup.instMulMemClass
subsemigroupMap_apply_coe 📖mathematicalSubsemigroup
SetLike.instMembership
Subsemigroup.instSetLike
Subsemigroup.map
DFunLike.coe
MulHom
MulMemClass.mul
Subsemigroup.instMulMemClass
funLike
subsemigroupMap
Subsemigroup.instMulMemClass
subsemigroupMap_surjective 📖mathematicalSubsemigroup
SetLike.instMembership
Subsemigroup.instSetLike
Subsemigroup.map
DFunLike.coe
MulHom
MulMemClass.mul
Subsemigroup.instMulMemClass
funLike
subsemigroupMap
Subsemigroup.instMulMemClass

Subsemigroup

Definitions

NameCategoryTheorems
comap 📖CompOp
38 mathmath: map_iInf_comap_of_surjective, MulHom.subsemigroupComap_apply_coe, map_le_iff_le_comap, comap_le_comap_iff_of_surjective, comap_injective_of_surjective, map_comap_eq_self, MulHom.mclosure_preimage_le, comap_id, le_comap_of_map_le, gc_map_comap, comap_map_comap, map_comap_eq, comap_sup_map_of_injective, comap_iSup_map_of_injective, prod_top, coe_comap, comap_inf_map_of_injective, comap_iInf_map_of_injective, monotone_comap, mem_comap, map_comap_eq_of_surjective, top_prod, map_inf_comap_of_surjective, map_comap_map, map_equiv_eq_comap_symm, le_comap_map, MulHom.prod_map_comap_prod', comap_top, map_comap_le, map_iSup_comap_of_surjective, comap_inf, comap_surjective_of_injective, comap_comap, map_sup_comap_of_surjective, comap_strictMono_of_surjective, comap_map_eq_of_injective, comap_equiv_eq_map_symm, comap_iInf
equivMapOfInjective 📖CompOp
1 mathmath: coe_equivMapOfInjective_apply
gciMapComap 📖CompOp
giMapComap 📖CompOp
inclusion 📖CompOp
map 📖CompOp
50 mathmath: map_iInf_comap_of_surjective, map_id, map_le_iff_le_comap, map_comap_eq_self, mem_map, mem_map_of_mem, gc_map_comap, map_sup, comap_map_comap, MulHom.subsemigroupMap_surjective, mem_map_iff_mem, map_comap_eq, comap_sup_map_of_injective, comap_iSup_map_of_injective, map_inf, MulHom.map_srange, comap_inf_map_of_injective, comap_iInf_map_of_injective, MulHom.map_mclosure, monotone_map, map_comap_eq_of_surjective, map_inf_comap_of_surjective, Matrix.subsemigroupCenter_eq_scalar_map, map_map, map_iInf, MulHom.srange_eq_map, map_le_of_le_comap, mem_map_equiv, map_comap_map, map_bot, map_equiv_eq_comap_symm, le_comap_map, map_strictMono_of_injective, map_surjective_of_surjective, map_comap_le, map_iSup, map_injective_of_injective, map_iSup_comap_of_surjective, apply_coe_mem_map, map_equiv_top, MulHom.subsemigroupMap_apply_coe, MulEquiv.subsemigroupMap_apply_coe, MulEquiv.subsemigroupMap_symm_apply_coe, map_sup_comap_of_surjective, le_prod_iff, coe_equivMapOfInjective_apply, comap_map_eq_of_injective, coe_map, comap_equiv_eq_map_symm, map_le_map_iff_of_injective
prod 📖CompOp
10 mathmath: coe_prod, mem_prod, prod_top, top_prod, MulHom.prod_map_comap_prod', bot_prod_bot, prod_eq_top_iff, prod_mono, top_prod_top, le_prod_iff
prodEquiv 📖CompOp
toAddSubsemigroup 📖CompOp
3 mathmath: toAddSubsemigroup_closure, coe_toAddSubsemigroup_symm_apply, coe_toAddSubsemigroup_apply
toAddSubsemigroup' 📖CompOp
1 mathmath: toAddSubsemigroup'_closure
topEquiv 📖CompOp
4 mathmath: topEquiv_symm_apply_coe, topEquiv_toMulHom, strictMono_topEquiv, topEquiv_apply

Theorems

NameKindAssumesProvesValidatesDepends On
apply_coe_mem_map 📖mathematicalSubsemigroup
SetLike.instMembership
instSetLike
map
DFunLike.coe
MulHom
MulHom.funLike
mem_map_of_mem
Subtype.prop
bot_prod_bot 📖mathematicalprod
Bot.bot
Subsemigroup
instBot
Prod.instMul
SetLike.coe_injective
Set.prod_empty
closure_closure_coe_preimage 📖mathematicalclosure
Subsemigroup
SetLike.instMembership
instSetLike
MulMemClass.mul
instMulMemClass
Set.preimage
Top.top
instTop
instMulMemClass
eq_top_iff
closure_induction
subset_closure
MulMemClass.mul_mem
coe_comap 📖mathematicalSetLike.coe
Subsemigroup
instSetLike
comap
Set.preimage
DFunLike.coe
MulHom
MulHom.funLike
coe_equivMapOfInjective_apply 📖mathematicalDFunLike.coe
MulHom
MulHom.funLike
Subsemigroup
SetLike.instMembership
instSetLike
map
MulEquiv
MulMemClass.mul
instMulMemClass
EquivLike.toFunLike
MulEquiv.instEquivLike
equivMapOfInjective
instMulMemClass
coe_map 📖mathematicalSetLike.coe
Subsemigroup
instSetLike
map
Set.image
DFunLike.coe
MulHom
MulHom.funLike
coe_prod 📖mathematicalSetLike.coe
Subsemigroup
Prod.instMul
instSetLike
prod
SProd.sprod
Set
Set.instSProd
coe_toAddSubsemigroup_apply 📖mathematicalSetLike.coe
AddSubsemigroup
Additive
Additive.add
AddSubsemigroup.instSetLike
DFunLike.coe
RelIso
Subsemigroup
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
AddSubsemigroup.instPartialOrder
RelIso.instFunLike
toAddSubsemigroup
Set.preimage
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
Additive.toMul
instSetLike
coe_toAddSubsemigroup_symm_apply 📖mathematicalSetLike.coe
Subsemigroup
instSetLike
DFunLike.coe
RelIso
AddSubsemigroup
Additive
Additive.add
Preorder.toLE
PartialOrder.toPreorder
AddSubsemigroup.instPartialOrder
instPartialOrder
RelIso.instFunLike
RelIso.symm
toAddSubsemigroup
Set.preimage
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
Additive.ofMul
AddSubsemigroup.instSetLike
comap_comap 📖mathematicalcomap
MulHom.comp
comap_equiv_eq_map_symm 📖mathematicalcomap
MulHomClass.toMulHom
MulEquiv
EquivLike.toFunLike
MulEquiv.instEquivLike
MulEquivClass.instMulHomClass
MulEquiv.instMulEquivClass
map
MulEquiv.symm
MulEquivClass.instMulHomClass
MulEquiv.instMulEquivClass
map_equiv_eq_comap_symm
comap_iInf 📖mathematicalcomap
iInf
Subsemigroup
instInfSet
GaloisConnection.u_iInf
gc_map_comap
comap_iInf_map_of_injective 📖mathematicalDFunLike.coe
MulHom
MulHom.funLike
comap
iInf
Subsemigroup
instInfSet
map
GaloisCoinsertion.u_iInf_l
comap_iSup_map_of_injective 📖mathematicalDFunLike.coe
MulHom
MulHom.funLike
comap
iSup
Subsemigroup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
instCompleteLattice
map
GaloisCoinsertion.u_iSup_l
comap_id 📖mathematicalcomap
MulHom.id
ext
comap_inf 📖mathematicalcomap
Subsemigroup
instMin
GaloisConnection.u_inf
gc_map_comap
comap_inf_map_of_injective 📖mathematicalDFunLike.coe
MulHom
MulHom.funLike
comap
Subsemigroup
instMin
map
GaloisCoinsertion.u_inf_l
comap_injective_of_surjective 📖mathematicalDFunLike.coe
MulHom
MulHom.funLike
Subsemigroup
comap
GaloisInsertion.u_injective
comap_le_comap_iff_of_surjective 📖mathematicalDFunLike.coe
MulHom
MulHom.funLike
Subsemigroup
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
comap
GaloisInsertion.u_le_u_iff
comap_map_comap 📖mathematicalcomap
map
GaloisConnection.u_l_u_eq_u
gc_map_comap
comap_map_eq_of_injective 📖mathematicalDFunLike.coe
MulHom
MulHom.funLike
comap
map
GaloisCoinsertion.u_l_eq
comap_strictMono_of_surjective 📖mathematicalDFunLike.coe
MulHom
MulHom.funLike
StrictMono
Subsemigroup
PartialOrder.toPreorder
instPartialOrder
comap
GaloisInsertion.strictMono_u
comap_sup_map_of_injective 📖mathematicalDFunLike.coe
MulHom
MulHom.funLike
comap
Subsemigroup
SemilatticeSup.toMax
Lattice.toSemilatticeSup
CompleteLattice.toLattice
instCompleteLattice
map
GaloisCoinsertion.u_sup_l
comap_surjective_of_injective 📖mathematicalDFunLike.coe
MulHom
MulHom.funLike
Subsemigroup
comap
GaloisCoinsertion.u_surjective
comap_top 📖mathematicalcomap
Top.top
Subsemigroup
instTop
GaloisConnection.u_top
gc_map_comap
eq_top_iff' 📖mathematicalTop.top
Subsemigroup
instTop
SetLike.instMembership
instSetLike
eq_top_iff
mem_top
gc_map_comap 📖mathematicalGaloisConnection
Subsemigroup
PartialOrder.toPreorder
instPartialOrder
map
comap
map_le_iff_le_comap
le_comap_map 📖mathematicalSubsemigroup
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
comap
map
GaloisConnection.le_u_l
gc_map_comap
le_comap_of_map_le 📖mathematicalSubsemigroup
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
map
comapGaloisConnection.le_u
gc_map_comap
le_prod_iff 📖mathematicalSubsemigroup
Prod.instMul
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
prod
map
MulHom.fst
MulHom.snd
map_bot 📖mathematicalmap
Bot.bot
Subsemigroup
instBot
GaloisConnection.l_bot
gc_map_comap
map_comap_eq 📖mathematicalmap
comap
Subsemigroup
instMin
MulHom.srange
SetLike.coe_injective
Set.image_preimage_eq_inter_range
map_comap_eq_of_surjective 📖mathematicalDFunLike.coe
MulHom
MulHom.funLike
map
comap
GaloisInsertion.l_u_eq
map_comap_eq_self 📖mathematicalSubsemigroup
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
MulHom.srange
map
comap
inf_of_le_left
map_comap_eq
map_comap_le 📖mathematicalSubsemigroup
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
map
comap
GaloisConnection.l_u_le
gc_map_comap
map_comap_map 📖mathematicalmap
comap
GaloisConnection.l_u_l_eq_l
gc_map_comap
map_equiv_eq_comap_symm 📖mathematicalmap
MulHomClass.toMulHom
MulEquiv
EquivLike.toFunLike
MulEquiv.instEquivLike
MulEquivClass.instMulHomClass
MulEquiv.instMulEquivClass
comap
MulEquiv.symm
SetLike.coe_injective
MulEquivClass.instMulHomClass
MulEquiv.instMulEquivClass
Equiv.image_eq_preimage_symm
map_equiv_top 📖mathematicalmap
MulHomClass.toMulHom
MulEquiv
EquivLike.toFunLike
MulEquiv.instEquivLike
MulEquivClass.instMulHomClass
MulEquiv.instMulEquivClass
Top.top
Subsemigroup
instTop
SetLike.coe_injective
MulEquivClass.instMulHomClass
MulEquiv.instMulEquivClass
Set.image_univ
Function.Surjective.range_eq
MulEquiv.surjective
map_iInf 📖mathematicalDFunLike.coe
MulHom
MulHom.funLike
map
iInf
Subsemigroup
instInfSet
SetLike.coe_injective
coe_iInf
Set.InjOn.image_iInter_eq
Set.injOn_of_injective
map_iInf_comap_of_surjective 📖mathematicalDFunLike.coe
MulHom
MulHom.funLike
map
iInf
Subsemigroup
instInfSet
comap
GaloisInsertion.l_iInf_u
map_iSup 📖mathematicalmap
iSup
Subsemigroup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
instCompleteLattice
GaloisConnection.l_iSup
gc_map_comap
map_iSup_comap_of_surjective 📖mathematicalDFunLike.coe
MulHom
MulHom.funLike
map
iSup
Subsemigroup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
instCompleteLattice
comap
GaloisInsertion.l_iSup_u
map_id 📖mathematicalmap
MulHom.id
ext
map_inf 📖mathematicalDFunLike.coe
MulHom
MulHom.funLike
map
Subsemigroup
instMin
SetLike.coe_injective
Set.image_inter
map_inf_comap_of_surjective 📖mathematicalDFunLike.coe
MulHom
MulHom.funLike
map
Subsemigroup
instMin
comap
GaloisInsertion.l_inf_u
map_injective_of_injective 📖mathematicalDFunLike.coe
MulHom
MulHom.funLike
Subsemigroup
map
GaloisCoinsertion.l_injective
map_le_iff_le_comap 📖mathematicalSubsemigroup
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
map
comap
Set.image_subset_iff
map_le_map_iff_of_injective 📖mathematicalDFunLike.coe
MulHom
MulHom.funLike
Subsemigroup
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
map
GaloisCoinsertion.l_le_l_iff
map_le_of_le_comap 📖mathematicalSubsemigroup
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
comap
mapGaloisConnection.l_le
gc_map_comap
map_map 📖mathematicalmap
MulHom.comp
SetLike.coe_injective
Set.image_image
map_strictMono_of_injective 📖mathematicalDFunLike.coe
MulHom
MulHom.funLike
StrictMono
Subsemigroup
PartialOrder.toPreorder
instPartialOrder
map
GaloisCoinsertion.strictMono_l
map_sup 📖mathematicalmap
Subsemigroup
SemilatticeSup.toMax
Lattice.toSemilatticeSup
CompleteLattice.toLattice
instCompleteLattice
GaloisConnection.l_sup
gc_map_comap
map_sup_comap_of_surjective 📖mathematicalDFunLike.coe
MulHom
MulHom.funLike
map
Subsemigroup
SemilatticeSup.toMax
Lattice.toSemilatticeSup
CompleteLattice.toLattice
instCompleteLattice
comap
GaloisInsertion.l_sup_u
map_surjective_of_surjective 📖mathematicalDFunLike.coe
MulHom
MulHom.funLike
Subsemigroup
map
GaloisInsertion.l_surjective
mem_comap 📖mathematicalSubsemigroup
SetLike.instMembership
instSetLike
comap
DFunLike.coe
MulHom
MulHom.funLike
mem_map 📖mathematicalSubsemigroup
SetLike.instMembership
instSetLike
map
DFunLike.coe
MulHom
MulHom.funLike
Set.mem_image
mem_map_equiv 📖mathematicalSubsemigroup
SetLike.instMembership
instSetLike
map
MulHomClass.toMulHom
MulEquiv
EquivLike.toFunLike
MulEquiv.instEquivLike
MulEquivClass.instMulHomClass
MulEquiv.instMulEquivClass
DFunLike.coe
MulEquiv.symm
Set.mem_image_equiv
mem_map_iff_mem 📖mathematicalDFunLike.coe
MulHom
MulHom.funLike
Subsemigroup
SetLike.instMembership
instSetLike
map
Function.Injective.mem_set_image
mem_map_of_mem 📖mathematicalSubsemigroup
SetLike.instMembership
instSetLike
map
DFunLike.coe
MulHom
MulHom.funLike
Set.mem_image_of_mem
mem_prod 📖mathematicalSubsemigroup
Prod.instMul
SetLike.instMembership
instSetLike
prod
monotone_comap 📖mathematicalMonotone
Subsemigroup
PartialOrder.toPreorder
instPartialOrder
comap
GaloisConnection.monotone_u
gc_map_comap
monotone_map 📖mathematicalMonotone
Subsemigroup
PartialOrder.toPreorder
instPartialOrder
map
GaloisConnection.monotone_l
gc_map_comap
prod_eq_top_iff 📖mathematicalprod
Top.top
Subsemigroup
Prod.instMul
instTop
srange_fst
srange_snd
prod_mono 📖mathematicalSubsemigroup
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
Prod.instMul
prod
Set.prod_mono
prod_top 📖mathematicalprod
Top.top
Subsemigroup
instTop
comap
Prod.instMul
MulHom.fst
ext
range_subtype 📖mathematicalMulHom.srange
Subsemigroup
SetLike.instMembership
instSetLike
MulMemClass.mul
instMulMemClass
MulMemClass.subtype
SetLike.coe_injective
instMulMemClass
MulHom.coe_srange
Subtype.range_coe
srange_fst 📖mathematicalMulHom.srange
Prod.instMul
MulHom.fst
Top.top
Subsemigroup
instTop
MulHom.srange_eq_top_of_surjective
Prod.fst_surjective
srange_snd 📖mathematicalMulHom.srange
Prod.instMul
MulHom.snd
Top.top
Subsemigroup
instTop
MulHom.srange_eq_top_of_surjective
Prod.snd_surjective
toAddSubsemigroup'_closure 📖mathematicalDFunLike.coe
OrderIso
Subsemigroup
Multiplicative
Multiplicative.mul
AddSubsemigroup
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
AddSubsemigroup.instPartialOrder
instFunLikeOrderIso
toAddSubsemigroup'
closure
AddSubsemigroup.closure
Set.preimage
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
Multiplicative.ofAdd
le_antisymm
GaloisConnection.l_le
OrderIso.to_galoisConnection
closure_le
AddSubsemigroup.subset_closure
AddSubsemigroup.closure_le
subset_closure
toAddSubsemigroup_closure 📖mathematicalDFunLike.coe
OrderIso
Subsemigroup
AddSubsemigroup
Additive
Additive.add
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
AddSubsemigroup.instPartialOrder
instFunLikeOrderIso
toAddSubsemigroup
closure
AddSubsemigroup.closure
Set.preimage
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
Additive.toMul
le_antisymm
OrderIso.le_symm_apply
closure_le
AddSubsemigroup.subset_closure
AddSubsemigroup.closure_le
subset_closure
topEquiv_apply 📖mathematicalDFunLike.coe
MulEquiv
Subsemigroup
SetLike.instMembership
instSetLike
Top.top
instTop
MulMemClass.mul
instMulMemClass
EquivLike.toFunLike
MulEquiv.instEquivLike
topEquiv
instMulMemClass
topEquiv_symm_apply_coe 📖mathematicalSubsemigroup
SetLike.instMembership
instSetLike
Top.top
instTop
DFunLike.coe
MulEquiv
MulMemClass.mul
instMulMemClass
EquivLike.toFunLike
MulEquiv.instEquivLike
MulEquiv.symm
topEquiv
instMulMemClass
topEquiv_toMulHom 📖mathematicalMulHomClass.toMulHom
Subsemigroup
SetLike.instMembership
instSetLike
Top.top
instTop
MulEquiv
MulMemClass.mul
instMulMemClass
EquivLike.toFunLike
MulEquiv.instEquivLike
MulEquivClass.instMulHomClass
MulEquiv.instMulEquivClass
topEquiv
MulMemClass.subtype
instMulMemClass
MulEquivClass.instMulHomClass
MulEquiv.instMulEquivClass
top_prod 📖mathematicalprod
Top.top
Subsemigroup
instTop
comap
Prod.instMul
MulHom.snd
ext
top_prod_top 📖mathematicalprod
Top.top
Subsemigroup
instTop
Prod.instMul
top_prod
comap_top

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