Documentation Verification Report

Operations

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

Statistics

MetricCount
DefinitionsaddSubmonoidCongr, addSubmonoidMap, ofLeftInverse', addSubmonoidComap, addSubmonoidMap, codRestrict, decidableMemMker, mker, mrange, mrangeRestrict, restrict, restrictHom, addUnitsTypeEquivIsAddUnitAddSubmonoid, comap, equivMapOfInjective, gciMapComap, giMapComap, inclusion, map, pi, prod, prodEquiv, toSubmonoid, toSubmonoid', topEquiv, range_copy_pattern, codRestrict, decidableMemMker, mker, mrange, mrangeRestrict, restrict, restrictHom, submonoidComap, submonoidMap, ofLeftInverse', submonoidCongr, submonoidMap, comap, equivMapOfInjective, gciMapComap, giMapComap, inclusion, map, pi, prod, prodEquiv, toAddSubmonoid, toAddSubmonoid', topEquiv, unitsTypeEquivIsUnitSubmonoid
51
TheoremsaddSubmonoidMap_symm_apply, add_submonoid_map_symm_apply, coe_addSubmonoidMap_apply, ofLeftInverse'_apply, ofLeftInverse'_symm_apply, addSubmonoidComap_apply_coe, addSubmonoidComap_surjective_of_surjective, addSubmonoidMap_apply_coe, addSubmonoidMap_surjective, codRestrict_apply, coe_mker, coe_mrange, coe_mrangeRestrict, comap_bot', comap_mker, injective_codRestrict, map_mclosure, map_mrange, mclosure_preimage_le, mclosure_range, mem_mker, mem_mrange, mker_fst, mker_inl, mker_inr, mker_prod_map, mker_snd, mker_zero, mrangeRestrict_mker, mrangeRestrict_surjective, mrange_comp, mrange_eq_map, mrange_eq_top, mrange_eq_top_of_surjective, mrange_id, prod_map_comap_prod', restrictHom_apply, restrict_apply, restrict_eq_zero_iff, restrict_mker, restrict_mrange, addUnitsTypeEquivIsAddUnitAddSubmonoid_apply_coe, apply_coe_mem_map, bot_or_exists_ne_zero, bot_or_nontrivial, bot_prod_bot, closure_closure_coe_preimage, closure_prod, closure_prod_zero, closure_zero_prod, codisjoint_map, coe_comap, coe_equivMapOfInjective_apply, coe_inclusion, coe_map, coe_pi, coe_prod, coe_toSubmonoid_apply, coe_toSubmonoid_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, disjoint_map, eq_bot_iff_forall, eq_bot_of_subsingleton, eq_top_iff', equivMapOfInjective_coe_addEquiv, faithfulVAdd, gc_map_comap, iSup_map_single_le, inclusion_inj, inclusion_injective, le_comap_map, le_comap_of_map_le, le_comap_single_pi, le_pi_iff, le_prod_iff, map_bot, map_coe_toAddEquiv, map_coe_toAddMonoidHom, map_comap_eq, map_comap_eq_of_surjective, map_comap_eq_self, map_comap_eq_self_of_surjective, 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_inl, map_inr, 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_pi, mem_prod, monotone_comap, monotone_map, mrange_fst, mrange_inl, mrange_inl', mrange_inl_sup_mrange_inr, mrange_inr, mrange_inr', mrange_snd, mrange_subtype, nontrivial_iff_exists_ne_zero, pi_bot, pi_empty, pi_eq_bot_iff, pi_top, prod_bot_sup_bot_prod, prod_eq_bot_iff, prod_eq_top_iff, prod_le_iff, prod_mono, prod_top, single_mem_pi, subtype_comp_inclusion, surjOn_iff_le_map, toSubmonoid'_closure, toSubmonoid_closure, topEquiv_apply, topEquiv_symm_apply_coe, topEquiv_toAddMonoidHom, top_prod, top_prod_top, val_addUnitsTypeEquivIsAddUnitAddSubmonoid_symm_apply, val_neg_addUnitsTypeEquivIsAddUnitAddSubmonoid_symm_apply, codRestrict_apply, coe_mker, coe_mrange, coe_mrangeRestrict, comap_bot', comap_mker, injective_codRestrict, map_mclosure, map_mrange, mclosure_preimage_le, mclosure_range, mem_mker, mem_mrange, mker_fst, mker_inl, mker_inr, mker_one, mker_prod_map, mker_snd, mrangeRestrict_mker, mrangeRestrict_surjective, mrange_comp, mrange_eq_map, mrange_eq_top, mrange_eq_top_of_surjective, mrange_id, prod_map_comap_prod', restrictHom_apply, restrict_apply, restrict_eq_one_iff, restrict_mker, restrict_mrange, submonoidComap_apply_coe, submonoidComap_surjective_of_surjective, submonoidMap_apply_coe, submonoidMap_surjective, coe_submonoidMap_apply, ofLeftInverse'_apply, ofLeftInverse'_symm_apply, submonoidMap_symm_apply, apply_coe_mem_map, bot_or_exists_ne_one, bot_or_nontrivial, bot_prod_bot, closure_closure_coe_preimage, closure_one_prod, closure_prod, closure_prod_one, codisjoint_map, coe_comap, coe_equivMapOfInjective_apply, coe_inclusion, coe_map, coe_pi, coe_prod, coe_toAddSubmonoid_apply, coe_toAddSubmonoid_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, disjoint_map, eq_bot_iff_forall, eq_bot_of_subsingleton, eq_top_iff', equivMapOfInjective_coe_mulEquiv, faithfulSMul, gc_map_comap, iSup_map_mulSingle_le, inclusion_inj, inclusion_injective, le_comap_map, le_comap_mulSingle_pi, le_comap_of_map_le, le_pi_iff, le_prod_iff, map_bot, map_coe_toMonoidHom, map_coe_toMulEquiv, map_comap_eq, map_comap_eq_of_surjective, map_comap_eq_self, map_comap_eq_self_of_surjective, 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_inl, map_inr, 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_pi, mem_prod, monotone_comap, monotone_map, mrange_fst, mrange_inl, mrange_inl', mrange_inl_sup_mrange_inr, mrange_inr, mrange_inr', mrange_snd, mrange_subtype, mulSingle_mem_pi, nontrivial_iff_exists_ne_one, pi_bot, pi_empty, pi_eq_bot_iff, pi_top, prod_bot_sup_bot_prod, prod_eq_bot_iff, prod_eq_top_iff, prod_le_iff, prod_mono, prod_top, subtype_comp_inclusion, surjOn_iff_le_map, toAddSubmonoid'_closure, toAddSubmonoid_closure, topEquiv_apply, topEquiv_symm_apply_coe, topEquiv_toMonoidHom, top_prod, top_prod_top, unitsTypeEquivIsUnitSubmonoid_apply_coe, val_inv_unitsTypeEquivIsUnitSubmonoid_symm_apply, val_unitsTypeEquivIsUnitSubmonoid_symm_apply
317
Total368

AddEquiv

Definitions

NameCategoryTheorems
addSubmonoidCongr 📖CompOp
1 mathmath: AddMonoid.IsTorsion.torsionAddEquiv_apply
addSubmonoidMap 📖CompOp
4 mathmath: coe_addSubmonoidMap_apply, add_submonoid_map_symm_apply, addSubmonoidMap_symm_apply, AddSubmonoid.equivMapOfInjective_coe_addEquiv
ofLeftInverse' 📖CompOp
2 mathmath: ofLeftInverse'_apply, ofLeftInverse'_symm_apply

Theorems

NameKindAssumesProvesValidatesDepends On
addSubmonoidMap_symm_apply 📖mathematicalDFunLike.coe
AddEquiv
AddSubmonoid
SetLike.instMembership
AddSubmonoid.instSetLike
AddSubmonoid.map
AddZero.toAdd
AddZeroClass.toAddZero
EquivLike.toFunLike
instEquivLike
AddEquivClass.instAddMonoidHomClass
instAddEquivClass
AddSubmonoid.add
symm
addSubmonoidMap
AddMonoidHom
AddMonoidHom.instFunLike
AddMonoidHom.instAddMonoidHomClass
AddMonoidHomClass.toAddMonoidHom
Set
Set.instMembership
SetLike.coe
SetLike.mem_coe
Set.image
Equiv
Equiv.instEquivLike
toEquiv
Equiv.symm
Set.mem_image_equiv
AddMonoidHom.instAddMonoidHomClass
AddEquivClass.instAddMonoidHomClass
instAddEquivClass
add_submonoid_map_symm_apply 📖mathematicalDFunLike.coe
AddEquiv
AddSubmonoid
SetLike.instMembership
AddSubmonoid.instSetLike
AddSubmonoid.map
AddZero.toAdd
AddZeroClass.toAddZero
EquivLike.toFunLike
instEquivLike
AddEquivClass.instAddMonoidHomClass
instAddEquivClass
AddSubmonoid.add
symm
addSubmonoidMap
AddMonoidHom
AddMonoidHom.instFunLike
AddMonoidHom.instAddMonoidHomClass
AddMonoidHomClass.toAddMonoidHom
Set
Set.instMembership
SetLike.coe
SetLike.mem_coe
Set.image
Equiv
Equiv.instEquivLike
toEquiv
Equiv.symm
Set.mem_image_equiv
addSubmonoidMap_symm_apply
coe_addSubmonoidMap_apply 📖mathematicalAddSubmonoid
SetLike.instMembership
AddSubmonoid.instSetLike
AddSubmonoid.map
AddEquiv
AddZero.toAdd
AddZeroClass.toAddZero
EquivLike.toFunLike
instEquivLike
AddEquivClass.instAddMonoidHomClass
instAddEquivClass
DFunLike.coe
AddSubmonoid.add
addSubmonoidMap
AddEquivClass.instAddMonoidHomClass
instAddEquivClass
ofLeftInverse'_apply 📖mathematicalDFunLike.coe
AddMonoidHom
AddZeroClass.toAddZero
AddMonoidHom.instFunLike
AddEquiv
AddSubmonoid
SetLike.instMembership
AddSubmonoid.instSetLike
AddMonoidHom.mrange
AddMonoidHom.instAddMonoidHomClass
AddZero.toAdd
AddSubmonoid.add
EquivLike.toFunLike
instEquivLike
ofLeftInverse'
AddSubmonoid.toAddZeroClass
AddMonoidHom.mrangeRestrict
AddMonoidHom.instAddMonoidHomClass
ofLeftInverse'_symm_apply 📖mathematicalDFunLike.coe
AddMonoidHom
AddZeroClass.toAddZero
AddMonoidHom.instFunLike
AddEquiv
AddSubmonoid
SetLike.instMembership
AddSubmonoid.instSetLike
AddMonoidHom.mrange
AddMonoidHom.instAddMonoidHomClass
AddSubmonoid.add
AddZero.toAdd
EquivLike.toFunLike
instEquivLike
symm
ofLeftInverse'
AddMonoidHom.instAddMonoidHomClass

AddMonoidHom

Definitions

NameCategoryTheorems
addSubmonoidComap 📖CompOp
2 mathmath: addSubmonoidComap_apply_coe, addSubmonoidComap_surjective_of_surjective
addSubmonoidMap 📖CompOp
2 mathmath: addSubmonoidMap_surjective, addSubmonoidMap_apply_coe
codRestrict 📖CompOp
4 mathmath: addSubgroupOf_range_eq_of_le, injective_codRestrict, ker_codRestrict, codRestrict_apply
decidableMemMker 📖CompOp
mker 📖CompOp
17 mathmath: DirectSum.mker_map, coe_mker, LinearMap.ker_toAddSubmonoid, mem_mker, restrict_mker, comap_bot', mker_fst, DFinsupp.mker_mapRangeAddMonoidHom, mker_zero, mker_prod_map, AddMonoid.Coprod.mker_swap, mrangeRestrict_mker, comap_mker, ker_toAddSubmonoid, mker_inr, mker_inl, mker_snd
mrange 📖CompOp
49 mathmath: mrange_eq_top_of_surjective, AddEquiv.ofLeftInverse'_apply, mgraph_eq_mrange_prod, DirectSum.mrange_map, LinearMap.range_toAddSubmonoid, AddMonoid.Coprod.mrange_lift, mrange_eq_top, map_mrange, AddSubmonoid.closure_singleton_eq, AddSubmonoid.mrange_subtype, AddSubmonoid.sup_eq_range, AddCon.mrange_mk', mem_mrange, AddMonoid.Coprod.codisjoint_mrange_inl_mrange_inr, AddSubmonoid.fg_iff_exists_fin_addMonoidHom, AddSubmonoid.iSup_eq_mrange_dfinsuppSumAddHom, AddCon.kerLift_range_eq, AddSubmonoid.mrange_inr', exists_addEquiv_mrange_eq_mgraph, noncommPiCoprod_mrange, mrange_eq_map, AddSubmonoid.mrange_inl_sup_mrange_inr, DFinsupp.mrange_mapRangeAddMonoidHom, AddSubmonoid.bsupr_eq_mrange_dfinsuppSumAddHom, AddMonoid.fg_range, restrict_mrange, AddSubmonoid.mrange_inr, FreeAddMonoid.mrange_lift, AddSubmonoid.one_eq_mrange, mclosure_range, AddSubmonoid.mrange_fst, AddSubmonoid.mrange_snd, AddSubmonoid.mrange_inl, AddCon.lift_range, AddEquiv.ofLeftInverse'_symm_apply, AddMonoid.Coprod.mrange_mk, AddMonoid.Coprod.mrange_inl_sup_mrange_inr, AddSubmonoid.map_comap_eq, mrangeRestrict_mker, AddMonoid.Coprod.mrange_swap, AddSubmonoid.mrange_inl', AddMonoid.Coprod.mrange_eq, exists_mrange_eq_mgraph, mrange_id, AddSubmonoid.closure_eq_mrange, mrangeRestrict_surjective, coe_mrange, coe_mrangeRestrict, mrange_comp
mrangeRestrict 📖CompOp
4 mathmath: AddEquiv.ofLeftInverse'_apply, mrangeRestrict_mker, mrangeRestrict_surjective, coe_mrangeRestrict
restrict 📖CompOp
13 mathmath: AddSubmonoid.LocalizationMap.add_neg_right, restrictHom_apply, restrict_eq_zero_iff, ker_restrict, AddSubmonoid.LocalizationMap.lift_apply, restrict_mker, AddSubmonoid.LocalizationMap.add_neg, AddSubmonoid.LocalizationMap.neg_unique, restrict_range, restrict_apply, restrict_mrange, AddSubmonoid.LocalizationMap.lift_mk', AddSubmonoid.LocalizationMap.add_neg_left
restrictHom 📖CompOp
1 mathmath: restrictHom_apply

Theorems

NameKindAssumesProvesValidatesDepends On
addSubmonoidComap_apply_coe 📖mathematicalAddSubmonoid
SetLike.instMembership
AddSubmonoid.instSetLike
DFunLike.coe
AddMonoidHom
AddSubmonoid.comap
AddZeroClass.toAddZero
instFunLike
instAddMonoidHomClass
AddSubmonoid.toAddZeroClass
addSubmonoidComap
instAddMonoidHomClass
addSubmonoidComap_surjective_of_surjective 📖mathematicalDFunLike.coe
AddMonoidHom
AddZeroClass.toAddZero
instFunLike
AddSubmonoid
SetLike.instMembership
AddSubmonoid.instSetLike
AddSubmonoid.comap
instAddMonoidHomClass
AddSubmonoid.toAddZeroClass
addSubmonoidComap
instAddMonoidHomClass
AddSubmonoid.mem_comap
Subtype.val_injective
addSubmonoidMap_apply_coe 📖mathematicalAddSubmonoid
SetLike.instMembership
AddSubmonoid.instSetLike
AddSubmonoid.map
AddMonoidHom
AddZeroClass.toAddZero
instFunLike
DFunLike.coe
instAddMonoidHomClass
AddSubmonoid.toAddZeroClass
addSubmonoidMap
instAddMonoidHomClass
addSubmonoidMap_surjective 📖mathematicalAddSubmonoid
SetLike.instMembership
AddSubmonoid.instSetLike
AddSubmonoid.map
AddMonoidHom
AddZeroClass.toAddZero
instFunLike
instAddMonoidHomClass
DFunLike.coe
AddSubmonoid.toAddZeroClass
addSubmonoidMap
instAddMonoidHomClass
codRestrict_apply 📖mathematicalSetLike.instMembership
DFunLike.coe
AddMonoidHom
AddZeroClass.toAddZero
instFunLike
AddSubmonoidClass.toAddZeroClass
codRestrict
coe_mker 📖mathematicalSetLike.coe
AddSubmonoid
AddSubmonoid.instSetLike
mker
Set.preimage
DFunLike.coe
Set
Set.instSingletonSet
AddZero.toZero
AddZeroClass.toAddZero
coe_mrange 📖mathematicalSetLike.coe
AddSubmonoid
AddSubmonoid.instSetLike
mrange
Set.range
DFunLike.coe
coe_mrangeRestrict 📖mathematicalAddSubmonoid
SetLike.instMembership
AddSubmonoid.instSetLike
mrange
AddMonoidHom
AddZeroClass.toAddZero
instFunLike
instAddMonoidHomClass
DFunLike.coe
AddSubmonoid.toAddZeroClass
mrangeRestrict
instAddMonoidHomClass
comap_bot' 📖mathematicalAddSubmonoid.comap
Bot.bot
AddSubmonoid
AddSubmonoid.instBot
mker
comap_mker 📖mathematicalAddSubmonoid.comap
AddMonoidHom
AddZeroClass.toAddZero
instFunLike
instAddMonoidHomClass
mker
comp
instAddMonoidHomClass
injective_codRestrict 📖mathematicalSetLike.instMembership
DFunLike.coe
AddMonoidHom
AddZeroClass.toAddZero
instFunLike
AddSubmonoidClass.toAddZeroClass
codRestrict
map_mclosure 📖mathematicalAddSubmonoid.map
AddSubmonoid.closure
Set.image
DFunLike.coe
GaloisConnection.l_comm_of_u_comm
Set.image_preimage
AddSubmonoid.gc_map_comap
GaloisInsertion.gc
map_mrange 📖mathematicalAddSubmonoid.map
AddMonoidHom
AddZeroClass.toAddZero
instFunLike
instAddMonoidHomClass
mrange
comp
instAddMonoidHomClass
AddSubmonoid.map.congr_simp
mrange_eq_map
AddSubmonoid.map_map
mclosure_preimage_le 📖mathematicalAddSubmonoid
Preorder.toLE
PartialOrder.toPreorder
AddSubmonoid.instPartialOrder
AddSubmonoid.closure
Set.preimage
DFunLike.coe
AddSubmonoid.comap
AddSubmonoid.closure_le
SetLike.mem_coe
AddSubmonoid.mem_comap
AddSubmonoid.subset_closure
mclosure_range 📖mathematicalAddSubmonoid.closure
Set.range
DFunLike.coe
mrange
Set.image_univ
map_mclosure
mrange_eq_map
AddSubmonoid.closure_univ
mem_mker 📖mathematicalAddSubmonoid
SetLike.instMembership
AddSubmonoid.instSetLike
mker
DFunLike.coe
AddZero.toZero
AddZeroClass.toAddZero
mem_mrange 📖mathematicalAddSubmonoid
SetLike.instMembership
AddSubmonoid.instSetLike
mrange
DFunLike.coe
mker_fst 📖mathematicalmker
Prod.instAddZeroClass
AddMonoidHom
AddZeroClass.toAddZero
instFunLike
instAddMonoidHomClass
fst
AddSubmonoid.prod
Bot.bot
AddSubmonoid
AddSubmonoid.instBot
Top.top
AddSubmonoid.instTop
SetLike.ext
instAddMonoidHomClass
mker_inl 📖mathematicalmker
Prod.instAddZeroClass
AddMonoidHom
AddZeroClass.toAddZero
instFunLike
instAddMonoidHomClass
inl
Bot.bot
AddSubmonoid
AddSubmonoid.instBot
AddSubmonoid.ext
instAddMonoidHomClass
mem_mker
Prod.mk_eq_zero
AddSubmonoid.mem_bot
mker_inr 📖mathematicalmker
Prod.instAddZeroClass
AddMonoidHom
AddZeroClass.toAddZero
instFunLike
instAddMonoidHomClass
inr
Bot.bot
AddSubmonoid
AddSubmonoid.instBot
AddSubmonoid.ext
instAddMonoidHomClass
mem_mker
Prod.mk_eq_zero
AddSubmonoid.mem_bot
mker_prod_map 📖mathematicalmker
Prod.instAddZeroClass
AddMonoidHom
AddZeroClass.toAddZero
instFunLike
instAddMonoidHomClass
prodMap
AddSubmonoid.prod
instAddMonoidHomClass
comap_bot'
prod_map_comap_prod'
AddSubmonoid.bot_prod_bot
mker_snd 📖mathematicalmker
Prod.instAddZeroClass
AddMonoidHom
AddZeroClass.toAddZero
instFunLike
instAddMonoidHomClass
snd
AddSubmonoid.prod
Top.top
AddSubmonoid
AddSubmonoid.instTop
Bot.bot
AddSubmonoid.instBot
SetLike.ext
instAddMonoidHomClass
mker_zero 📖mathematicalmker
AddMonoidHom
AddZeroClass.toAddZero
instFunLike
instAddMonoidHomClass
instZeroAddMonoidHom
Top.top
AddSubmonoid
AddSubmonoid.instTop
AddSubmonoid.ext
instAddMonoidHomClass
mem_mker
AddSubmonoid.mem_top
mrangeRestrict_mker 📖mathematicalmker
AddSubmonoid
SetLike.instMembership
AddSubmonoid.instSetLike
mrange
AddMonoidHom
AddZeroClass.toAddZero
instFunLike
instAddMonoidHomClass
AddSubmonoid.toAddZeroClass
mrangeRestrict
AddSubmonoid.ext
instAddMonoidHomClass
ZeroMemClass.zero_mem
AddSubmonoidClass.toZeroMemClass
AddSubmonoid.instAddSubmonoidClass
mrangeRestrict_surjective 📖mathematicalAddSubmonoid
SetLike.instMembership
AddSubmonoid.instSetLike
mrange
AddMonoidHom
AddZeroClass.toAddZero
instFunLike
instAddMonoidHomClass
DFunLike.coe
AddSubmonoid.toAddZeroClass
mrangeRestrict
instAddMonoidHomClass
mrange_comp 📖mathematicalmrange
AddMonoidHom
AddZeroClass.toAddZero
instFunLike
instAddMonoidHomClass
comp
AddSubmonoid.map
SetLike.coe_injective
instAddMonoidHomClass
Set.range_comp
mrange_eq_map 📖mathematicalmrange
AddSubmonoid.map
Top.top
AddSubmonoid
AddSubmonoid.instTop
AddSubmonoid.copy_eq
mrange_eq_top 📖mathematicalmrange
Top.top
AddSubmonoid
AddSubmonoid.instTop
DFunLike.coe
SetLike.ext'_iff
coe_mrange
AddSubmonoid.coe_top
Set.range_eq_univ
mrange_eq_top_of_surjective 📖mathematicalDFunLike.coemrange
Top.top
AddSubmonoid
AddSubmonoid.instTop
mrange_eq_top
mrange_id 📖mathematicalmrange
AddMonoidHom
AddZeroClass.toAddZero
instFunLike
instAddMonoidHomClass
id
Top.top
AddSubmonoid
AddSubmonoid.instTop
instAddMonoidHomClass
mrange_eq_map
AddSubmonoid.map_id
prod_map_comap_prod' 📖mathematicalAddSubmonoid.comap
Prod.instAddZeroClass
AddMonoidHom
AddZeroClass.toAddZero
instFunLike
instAddMonoidHomClass
prodMap
AddSubmonoid.prod
SetLike.coe_injective
instAddMonoidHomClass
Set.preimage_prod_map_prod
restrictHom_apply 📖mathematicalDFunLike.coe
AddMonoidHom
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
SetLike.instMembership
AddSubmonoidClass.toAddZeroClass
instAddCommMonoid
instFunLike
restrictHom
restrict
restrict_apply 📖mathematicalDFunLike.coe
AddMonoidHom
SetLike.instMembership
AddZeroClass.toAddZero
AddSubmonoidClass.toAddZeroClass
instFunLike
restrict
restrict_eq_zero_iff 📖mathematicalrestrict
AddMonoidHom
SetLike.instMembership
AddZeroClass.toAddZero
AddSubmonoidClass.toAddZeroClass
instZeroAddMonoidHom
DFunLike.coe
instFunLike
AddZero.toZero
ext_iff
restrict_mker 📖mathematicalmker
AddSubmonoid
SetLike.instMembership
AddSubmonoid.instSetLike
AddSubmonoid.toAddZeroClass
AddMonoidHom
AddZeroClass.toAddZero
AddSubmonoidClass.toAddZeroClass
AddSubmonoid.instAddSubmonoidClass
instFunLike
instAddMonoidHomClass
restrict
AddSubmonoid.comap
AddSubmonoid.subtype
AddSubmonoid.instAddSubmonoidClass
instAddMonoidHomClass
restrict_mrange 📖mathematicalmrange
AddSubmonoid
SetLike.instMembership
AddSubmonoid.instSetLike
AddSubmonoid.toAddZeroClass
AddMonoidHom
AddZeroClass.toAddZero
AddSubmonoidClass.toAddZeroClass
AddSubmonoid.instAddSubmonoidClass
instFunLike
instAddMonoidHomClass
restrict
AddSubmonoid.map
AddSubmonoid.instAddSubmonoidClass
instAddMonoidHomClass
SetLike.ext_iff
mem_mrange
AddSubmonoid.mem_map

AddSubmonoid

Definitions

NameCategoryTheorems
addUnitsTypeEquivIsAddUnitAddSubmonoid 📖CompOp
3 mathmath: addUnitsTypeEquivIsAddUnitAddSubmonoid_apply_coe, val_neg_addUnitsTypeEquivIsAddUnitAddSubmonoid_symm_apply, val_addUnitsTypeEquivIsAddUnitAddSubmonoid_symm_apply
comap 📖CompOp
56 mathmath: comap_top, DirectSum.mker_map, comap_le_comap_iff_of_surjective, DirectSum.mrange_map, comap_strictMono_of_surjective, prod_top, AddMonoidHom.prod_map_comap_prod', AddMonoidHom.addSubmonoidComap_apply_coe, comap_iInf, subPairs_comap, comap_map_comap, map_comap_eq_self_of_surjective, AddMonoidHom.mclosure_preimage_le, mk_add_mk_neg_eq_zero, le_comap_single_pi, comap_equiv_eq_map_symm, gc_map_comap, comap_inf, AddMonoidHom.addSubgroupComap_apply_coe, le_comap_map, AddMonoidHom.restrict_mker, le_pi_iff, AddMonoidHom.comap_bot', map_comap_eq_of_surjective, DFinsupp.mker_mapRangeAddMonoidHom, AddSubgroup.comap_toAddSubmonoid, mrange_inr', map_comap_eq_self, map_inf_comap_of_surjective, DFinsupp.mrange_mapRangeAddMonoidHom, mk_neg_add_mk_eq_zero, le_comap_of_map_le, top_prod, mem_comap, map_iInf_comap_of_surjective, comap_inf_map_of_injective, comap_surjective_of_injective, map_comap_eq, map_sup_comap_of_surjective, mrange_inl', AddMonoidHom.addSubmonoidComap_surjective_of_surjective, comap_iInf_map_of_injective, AddMonoidHom.comap_mker, comap_injective_of_surjective, comap_id, map_equiv_eq_comap_symm, comap_comap, comap_map_eq_of_injective, map_comap_map, map_comap_le, coe_comap, monotone_comap, map_iSup_comap_of_surjective, comap_iSup_map_of_injective, map_le_iff_le_comap, comap_sup_map_of_injective
equivMapOfInjective 📖CompOp
2 mathmath: coe_equivMapOfInjective_apply, equivMapOfInjective_coe_addEquiv
gciMapComap 📖CompOp
giMapComap 📖CompOp
inclusion 📖CompOp
4 mathmath: subtype_comp_inclusion, inclusion_inj, inclusion_injective, coe_inclusion
map 📖CompOp
71 mathmath: AddSubgroup.map_toAddSubmonoid, prod_le_iff, LocalizationMap.map_surjective_of_surjective, coe_equivMapOfInjective_apply, iSup_map_single, pi_le_iff, coe_map, AddMonoidHom.addSubgroupMap_apply_coe, comap_map_comap, AddMonoidHom.map_mrange, map_comap_eq_self_of_surjective, mem_map, map_equiv_top, mem_map_of_mem, AddMonoidHom.map_mclosure, le_prod_iff, AddEquiv.coe_addSubmonoidMap_apply, comap_equiv_eq_map_symm, AddMonoidHom.addSubmonoidMap_surjective, iSup_map_single_le, map_inl, map_coe_toAddMonoidHom, map_id, gc_map_comap, AddEquiv.add_submonoid_map_symm_apply, map_coe_toAddEquiv, le_comap_map, map_comap_eq_of_surjective, FG.map, map_comap_eq_self, AddMonoidHom.mrange_eq_map, map_inf_comap_of_surjective, AddMonoidHom.addSubmonoidMap_apply_coe, map_inf, AddMonoidHom.restrict_mrange, surjOn_iff_le_map, AddEquiv.addSubmonoidMap_symm_apply, LocalizationMap.map_injective_of_injective, map_iInf_comap_of_surjective, comap_inf_map_of_injective, mem_map_iff_mem, map_comap_eq, map_le_map_iff_of_injective, codisjoint_map, map_iSup, map_sup_comap_of_surjective, map_inr, apply_coe_mem_map, map_strictMono_of_injective, comap_iInf_map_of_injective, map_iInf, map_le_of_le_comap, map_bot, map_equiv_eq_comap_symm, comap_map_eq_of_injective, map_sup, map_comap_map, map_comap_le, Submodule.map_toAddSubmonoid', map_iSup_comap_of_surjective, comap_iSup_map_of_injective, mem_map_equiv, Submodule.map_toAddSubmonoid, monotone_map, map_surjective_of_surjective, map_le_iff_le_comap, comap_sup_map_of_injective, map_map, AddMonoidHom.mrange_comp, disjoint_map, map_injective_of_injective
pi 📖CompOp
19 mathmath: DirectSum.mker_map, IsLocalizationMap.pi, DirectSum.mrange_map, FG.pi, iSup_map_single, pi_le_iff, closure_pi, single_mem_pi, pi_eq_bot_iff, pi_bot, le_comap_single_pi, iSup_map_single_le, le_pi_iff, DFinsupp.mker_mapRangeAddMonoidHom, pi_empty, DFinsupp.mrange_mapRangeAddMonoidHom, coe_pi, pi_top, mem_pi
prod 📖CompOp
25 mathmath: prod_eq_bot_iff, bot_prod_bot, prod_le_iff, prod_top, AddMonoidHom.prod_map_comap_prod', prod_mono, closure_prod, le_prod_iff, closure_zero_prod, mem_prod, map_inl, AddMonoidHom.mker_fst, coe_prod, FG.sum, AddMonoidHom.mker_prod_map, mrange_inr, prod_eq_top_iff, top_prod, closure_prod_zero, mrange_inl, top_prod_top, map_inr, FG.prod, prod_bot_sup_bot_prod, AddMonoidHom.mker_snd
prodEquiv 📖CompOp
toSubmonoid 📖CompOp
4 mathmath: coe_toSubmonoid_apply, toSubmonoid_closure, coe_toSubmonoid_symm_apply, fg_iff_mul_fg
toSubmonoid' 📖CompOp
1 mathmath: toSubmonoid'_closure
topEquiv 📖CompOp
4 mathmath: AddMonoid.IsTorsion.torsionAddEquiv_symm_apply_coe, topEquiv_symm_apply_coe, topEquiv_apply, topEquiv_toAddMonoidHom

Theorems

NameKindAssumesProvesValidatesDepends On
addUnitsTypeEquivIsAddUnitAddSubmonoid_apply_coe 📖mathematicalAddSubmonoid
AddMonoid.toAddZeroClass
SetLike.instMembership
instSetLike
IsAddUnit.addSubmonoid
DFunLike.coe
AddEquiv
AddUnits
AddUnits.instAdd
add
EquivLike.toFunLike
AddEquiv.instEquivLike
addUnitsTypeEquivIsAddUnitAddSubmonoid
AddUnits.val
apply_coe_mem_map 📖mathematicalAddSubmonoid
SetLike.instMembership
instSetLike
map
DFunLike.coe
mem_map_of_mem
bot_or_exists_ne_zero 📖mathematicalBot.bot
AddSubmonoid
instBot
SetLike.instMembership
instSetLike
nontrivial_iff_exists_ne_zero
bot_or_nontrivial
bot_or_nontrivial 📖mathematicalBot.bot
AddSubmonoid
instBot
Nontrivial
SetLike.instMembership
instSetLike
eq_bot_iff_forall
nontrivial_iff_exists_ne_zero
bot_prod_bot 📖mathematicalprod
Bot.bot
AddSubmonoid
instBot
Prod.instAddZeroClass
SetLike.coe_injective
Set.singleton_prod_singleton
Set.singleton_eq_singleton_iff
Prod.mk_eq_zero
closure_closure_coe_preimage 📖mathematicalclosure
AddSubmonoid
SetLike.instMembership
instSetLike
toAddZeroClass
Set.preimage
Top.top
instTop
eq_top_iff
closure_induction
subset_closure
ZeroMemClass.zero_mem
AddSubmonoidClass.toZeroMemClass
instAddSubmonoidClass
AddMemClass.add_mem
AddSubmonoidClass.toAddMemClass
closure_prod 📖mathematicalSet
Set.instMembership
AddZero.toZero
AddZeroClass.toAddZero
closure
Prod.instAddZeroClass
SProd.sprod
Set.instSProd
prod
le_antisymm
closure_le
Set.prod_subset_prod_iff
subset_closure
AddMonoidHom.instAddMonoidHomClass
prod_le_iff
map_le_of_le_comap
closure_prod_zero 📖mathematicalclosure
Prod.instAddZeroClass
SProd.sprod
Set
Set.instSProd
Set.instSingletonSet
AddZero.toZero
AddZeroClass.toAddZero
prod
Bot.bot
AddSubmonoid
instBot
le_antisymm
closure_le
Set.prod_subset_prod_iff
subset_closure
Set.Subset.rfl
AddMonoidHom.instAddMonoidHomClass
prod_le_iff
map_le_of_le_comap
map_bot
bot_le
closure_zero_prod 📖mathematicalclosure
Prod.instAddZeroClass
SProd.sprod
Set
Set.instSProd
Set.instSingletonSet
AddZero.toZero
AddZeroClass.toAddZero
prod
Bot.bot
AddSubmonoid
instBot
le_antisymm
closure_le
Set.prod_subset_prod_iff
Set.Subset.rfl
subset_closure
AddMonoidHom.instAddMonoidHomClass
prod_le_iff
map_bot
bot_le
map_le_of_le_comap
codisjoint_map 📖mathematicalDFunLike.coe
Codisjoint
AddSubmonoid
instPartialOrder
BoundedOrder.toOrderTop
Preorder.toLE
PartialOrder.toPreorder
CompleteLattice.toBoundedOrder
instCompleteLattice
mapcodisjoint_iff
map_sup
AddMonoidHom.mrange_eq_map
AddMonoidHom.mrange_eq_top_of_surjective
coe_comap 📖mathematicalSetLike.coe
AddSubmonoid
instSetLike
comap
Set.preimage
DFunLike.coe
coe_equivMapOfInjective_apply 📖mathematicalDFunLike.coe
AddMonoidHom
AddZeroClass.toAddZero
AddMonoidHom.instFunLike
AddSubmonoid
SetLike.instMembership
instSetLike
map
AddMonoidHom.instAddMonoidHomClass
AddEquiv
add
EquivLike.toFunLike
AddEquiv.instEquivLike
equivMapOfInjective
AddMonoidHom.instAddMonoidHomClass
coe_inclusion 📖mathematicalAddSubmonoid
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
SetLike.instMembership
instSetLike
DFunLike.coe
AddMonoidHom
AddZeroClass.toAddZero
toAddZeroClass
AddMonoidHom.instFunLike
inclusion
Set.coe_inclusion
coe_map 📖mathematicalSetLike.coe
AddSubmonoid
instSetLike
map
Set.image
DFunLike.coe
coe_pi 📖mathematicalSetLike.coe
AddSubmonoid
Pi.addZeroClass
instSetLike
pi
Set.pi
coe_prod 📖mathematicalSetLike.coe
AddSubmonoid
Prod.instAddZeroClass
instSetLike
prod
SProd.sprod
Set
Set.instSProd
coe_toSubmonoid_apply 📖mathematicalSetLike.coe
Submonoid
Multiplicative
Multiplicative.mulOneClass
Submonoid.instSetLike
DFunLike.coe
RelIso
AddSubmonoid
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
Submonoid.instPartialOrder
RelIso.instFunLike
toSubmonoid
Set.preimage
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
Multiplicative.toAdd
instSetLike
coe_toSubmonoid_symm_apply 📖mathematicalSetLike.coe
AddSubmonoid
instSetLike
DFunLike.coe
RelIso
Submonoid
Multiplicative
Multiplicative.mulOneClass
Preorder.toLE
PartialOrder.toPreorder
Submonoid.instPartialOrder
instPartialOrder
RelIso.instFunLike
RelIso.symm
toSubmonoid
Set.preimage
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
Multiplicative.ofAdd
Submonoid.instSetLike
comap_comap 📖mathematicalcomap
AddMonoidHom
AddZeroClass.toAddZero
AddMonoidHom.instFunLike
AddMonoidHom.instAddMonoidHomClass
AddMonoidHom.comp
AddMonoidHom.instAddMonoidHomClass
comap_equiv_eq_map_symm 📖mathematicalcomap
AddEquiv
AddZero.toAdd
AddZeroClass.toAddZero
EquivLike.toFunLike
AddEquiv.instEquivLike
AddEquivClass.instAddMonoidHomClass
AddEquiv.instAddEquivClass
map
AddEquiv.symm
AddEquivClass.instAddMonoidHomClass
AddEquiv.instAddEquivClass
map_equiv_eq_comap_symm
comap_iInf 📖mathematicalcomap
iInf
AddSubmonoid
instInfSet
GaloisConnection.u_iInf
gc_map_comap
comap_iInf_map_of_injective 📖mathematicalDFunLike.coecomap
iInf
AddSubmonoid
instInfSet
map
GaloisCoinsertion.u_iInf_l
comap_iSup_map_of_injective 📖mathematicalDFunLike.coecomap
iSup
AddSubmonoid
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
instCompleteLattice
map
GaloisCoinsertion.u_iSup_l
comap_id 📖mathematicalcomap
AddMonoidHom
AddZeroClass.toAddZero
AddMonoidHom.instFunLike
AddMonoidHom.instAddMonoidHomClass
AddMonoidHom.id
ext
AddMonoidHom.instAddMonoidHomClass
mem_comap
comap_inf 📖mathematicalcomap
AddSubmonoid
instMin
GaloisConnection.u_inf
gc_map_comap
comap_inf_map_of_injective 📖mathematicalDFunLike.coecomap
AddSubmonoid
instMin
map
GaloisCoinsertion.u_inf_l
comap_injective_of_surjective 📖mathematicalDFunLike.coeAddSubmonoid
comap
GaloisInsertion.u_injective
comap_le_comap_iff_of_surjective 📖mathematicalDFunLike.coeAddSubmonoid
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.coecomap
map
GaloisCoinsertion.u_l_eq
comap_strictMono_of_surjective 📖mathematicalDFunLike.coeStrictMono
AddSubmonoid
PartialOrder.toPreorder
instPartialOrder
comap
GaloisInsertion.strictMono_u
comap_sup_map_of_injective 📖mathematicalDFunLike.coecomap
AddSubmonoid
SemilatticeSup.toMax
Lattice.toSemilatticeSup
CompleteLattice.toLattice
instCompleteLattice
map
GaloisCoinsertion.u_sup_l
comap_surjective_of_injective 📖mathematicalDFunLike.coeAddSubmonoid
comap
GaloisCoinsertion.u_surjective
comap_top 📖mathematicalcomap
Top.top
AddSubmonoid
instTop
GaloisConnection.u_top
gc_map_comap
disjoint_map 📖mathematicalDFunLike.coe
Disjoint
AddSubmonoid
instPartialOrder
BoundedOrder.toOrderBot
Preorder.toLE
PartialOrder.toPreorder
CompleteLattice.toBoundedOrder
instCompleteLattice
mapdisjoint_iff
map_inf
map_bot
eq_bot_iff_forall 📖mathematicalBot.bot
AddSubmonoid
instBot
AddZero.toZero
AddZeroClass.toAddZero
SetLike.ext_iff
mem_bot
zero_mem
eq_bot_of_subsingleton 📖mathematicalBot.bot
AddSubmonoid
instBot
eq_bot_iff_forall
eq_top_iff' 📖mathematicalTop.top
AddSubmonoid
instTop
SetLike.instMembership
instSetLike
eq_top_iff
mem_top
equivMapOfInjective_coe_addEquiv 📖mathematicalequivMapOfInjective
AddMonoidHomClass.toAddMonoidHom
AddEquiv
AddZero.toAdd
AddZeroClass.toAddZero
EquivLike.toFunLike
AddEquiv.instEquivLike
AddEquivClass.instAddMonoidHomClass
AddEquiv.instAddEquivClass
EquivLike.injective
AddEquiv.addSubmonoidMap
AddEquiv.ext
AddMonoidHom.instAddMonoidHomClass
AddEquivClass.instAddMonoidHomClass
AddEquiv.instAddEquivClass
EquivLike.injective
faithfulVAdd 📖mathematicalFaithfulVAdd
AddSubmonoid
SetLike.instMembership
instSetLike
vadd
FaithfulVAdd.eq_of_vadd_eq_vadd
gc_map_comap 📖mathematicalGaloisConnection
AddSubmonoid
PartialOrder.toPreorder
instPartialOrder
map
comap
map_le_iff_le_comap
iSup_map_single_le 📖mathematicalAddSubmonoid
Pi.addZeroClass
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
iSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
instCompleteLattice
map
AddMonoidHom
AddZeroClass.toAddZero
AddMonoidHom.instFunLike
AddMonoidHom.instAddMonoidHomClass
AddMonoidHom.single
pi
iSup_le
AddMonoidHom.instAddMonoidHomClass
map_le_iff_le_comap
le_comap_single_pi
inclusion_inj 📖mathematicalAddSubmonoid
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
DFunLike.coe
AddMonoidHom
SetLike.instMembership
instSetLike
AddZeroClass.toAddZero
toAddZeroClass
AddMonoidHom.instFunLike
inclusion
inclusion_injective
inclusion_injective 📖mathematicalAddSubmonoid
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
SetLike.instMembership
instSetLike
DFunLike.coe
AddMonoidHom
AddZeroClass.toAddZero
toAddZeroClass
AddMonoidHom.instFunLike
inclusion
Set.inclusion_injective
le_comap_map 📖mathematicalAddSubmonoid
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
comap
map
GaloisConnection.le_u_l
gc_map_comap
le_comap_of_map_le 📖mathematicalAddSubmonoid
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
map
comapGaloisConnection.le_u
gc_map_comap
le_comap_single_pi 📖mathematicalAddSubmonoid
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
comap
Pi.addZeroClass
AddMonoidHom
AddZeroClass.toAddZero
AddMonoidHom.instFunLike
AddMonoidHom.instAddMonoidHomClass
AddMonoidHom.single
pi
AddMonoidHom.instAddMonoidHomClass
mem_comap
single_mem_pi
le_pi_iff 📖mathematicalAddSubmonoid
Pi.addZeroClass
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
pi
comap
AddMonoidHom
AddZeroClass.toAddZero
AddMonoidHom.instFunLike
AddMonoidHom.instAddMonoidHomClass
Pi.evalAddMonoidHom
Set.subset_pi_iff
le_prod_iff 📖mathematicalAddSubmonoid
Prod.instAddZeroClass
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
prod
map
AddMonoidHom
AddZeroClass.toAddZero
AddMonoidHom.instFunLike
AddMonoidHom.instAddMonoidHomClass
AddMonoidHom.fst
AddMonoidHom.snd
AddMonoidHom.instAddMonoidHomClass
map_bot 📖mathematicalmap
Bot.bot
AddSubmonoid
instBot
GaloisConnection.l_bot
gc_map_comap
map_coe_toAddEquiv 📖mathematicalmap
AddEquiv
AddZero.toAdd
AddZeroClass.toAddZero
EquivLike.toFunLike
AddEquiv.instEquivLike
AddEquivClass.instAddMonoidHomClass
AddEquiv.instAddEquivClass
AddEquivClass.toAddEquiv
AddEquivClass.instAddMonoidHomClass
AddEquiv.instAddEquivClass
map_coe_toAddMonoidHom 📖mathematicalmap
AddMonoidHom
AddZeroClass.toAddZero
AddMonoidHom.instFunLike
AddMonoidHom.instAddMonoidHomClass
AddMonoidHomClass.toAddMonoidHom
AddMonoidHom.instAddMonoidHomClass
map_comap_eq 📖mathematicalmap
comap
AddSubmonoid
instMin
AddMonoidHom.mrange
SetLike.coe_injective
Set.image_preimage_eq_inter_range
map_comap_eq_of_surjective 📖mathematicalDFunLike.coemap
comap
GaloisInsertion.l_u_eq
map_comap_eq_self 📖mathematicalAddSubmonoid
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
AddMonoidHom.mrange
map
comap
inf_of_le_left
map_comap_eq
map_comap_eq_self_of_surjective 📖mathematicalDFunLike.coemap
comap
map_comap_eq_self
le_top
AddMonoidHom.mrange_eq_top_of_surjective
map_comap_le 📖mathematicalAddSubmonoid
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
AddEquiv
AddZero.toAdd
AddZeroClass.toAddZero
EquivLike.toFunLike
AddEquiv.instEquivLike
AddEquivClass.instAddMonoidHomClass
AddEquiv.instAddEquivClass
comap
AddEquiv.symm
SetLike.coe_injective
AddEquivClass.instAddMonoidHomClass
AddEquiv.instAddEquivClass
Equiv.image_eq_preimage_symm
map_equiv_top 📖mathematicalmap
AddEquiv
AddZero.toAdd
AddZeroClass.toAddZero
EquivLike.toFunLike
AddEquiv.instEquivLike
AddEquivClass.instAddMonoidHomClass
AddEquiv.instAddEquivClass
Top.top
AddSubmonoid
instTop
SetLike.coe_injective
AddEquivClass.instAddMonoidHomClass
AddEquiv.instAddEquivClass
Set.image_univ
Function.Surjective.range_eq
AddEquiv.surjective
map_iInf 📖mathematicalDFunLike.coemap
iInf
AddSubmonoid
instInfSet
SetLike.coe_injective
coe_iInf
Set.InjOn.image_iInter_eq
Set.injOn_of_injective
map_iInf_comap_of_surjective 📖mathematicalDFunLike.coemap
iInf
AddSubmonoid
instInfSet
comap
GaloisInsertion.l_iInf_u
map_iSup 📖mathematicalmap
iSup
AddSubmonoid
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
instCompleteLattice
GaloisConnection.l_iSup
gc_map_comap
map_iSup_comap_of_surjective 📖mathematicalDFunLike.coemap
iSup
AddSubmonoid
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
instCompleteLattice
comap
GaloisInsertion.l_iSup_u
map_id 📖mathematicalmap
AddMonoidHom
AddZeroClass.toAddZero
AddMonoidHom.instFunLike
AddMonoidHom.instAddMonoidHomClass
AddMonoidHom.id
ext
AddMonoidHom.instAddMonoidHomClass
map_inf 📖mathematicalDFunLike.coemap
AddSubmonoid
instMin
SetLike.coe_injective
Set.image_inter
map_inf_comap_of_surjective 📖mathematicalDFunLike.coemap
AddSubmonoid
instMin
comap
GaloisInsertion.l_inf_u
map_injective_of_injective 📖mathematicalDFunLike.coeAddSubmonoid
map
GaloisCoinsertion.l_injective
map_inl 📖mathematicalmap
Prod.instAddZeroClass
AddMonoidHom
AddZeroClass.toAddZero
AddMonoidHom.instFunLike
AddMonoidHom.instAddMonoidHomClass
AddMonoidHom.inl
prod
Bot.bot
AddSubmonoid
instBot
ext
AddMonoidHom.instAddMonoidHomClass
Set.mem_singleton
Set.eq_of_mem_singleton
map_inr 📖mathematicalmap
Prod.instAddZeroClass
AddMonoidHom
AddZeroClass.toAddZero
AddMonoidHom.instFunLike
AddMonoidHom.instAddMonoidHomClass
AddMonoidHom.inr
prod
Bot.bot
AddSubmonoid
instBot
ext
AddMonoidHom.instAddMonoidHomClass
Set.mem_singleton
Set.eq_of_mem_singleton
map_le_iff_le_comap 📖mathematicalAddSubmonoid
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
map
comap
Set.image_subset_iff
map_le_map_iff_of_injective 📖mathematicalDFunLike.coeAddSubmonoid
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
map
GaloisCoinsertion.l_le_l_iff
map_le_of_le_comap 📖mathematicalAddSubmonoid
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
comap
mapGaloisConnection.l_le
gc_map_comap
map_map 📖mathematicalmap
AddMonoidHom
AddZeroClass.toAddZero
AddMonoidHom.instFunLike
AddMonoidHom.instAddMonoidHomClass
AddMonoidHom.comp
SetLike.coe_injective
AddMonoidHom.instAddMonoidHomClass
Set.image_image
map_strictMono_of_injective 📖mathematicalDFunLike.coeStrictMono
AddSubmonoid
PartialOrder.toPreorder
instPartialOrder
map
GaloisCoinsertion.strictMono_l
map_sup 📖mathematicalmap
AddSubmonoid
SemilatticeSup.toMax
Lattice.toSemilatticeSup
CompleteLattice.toLattice
instCompleteLattice
GaloisConnection.l_sup
gc_map_comap
map_sup_comap_of_surjective 📖mathematicalDFunLike.coemap
AddSubmonoid
SemilatticeSup.toMax
Lattice.toSemilatticeSup
CompleteLattice.toLattice
instCompleteLattice
comap
GaloisInsertion.l_sup_u
map_surjective_of_surjective 📖mathematicalDFunLike.coeAddSubmonoid
map
GaloisInsertion.l_surjective
mem_comap 📖mathematicalAddSubmonoid
SetLike.instMembership
instSetLike
comap
DFunLike.coe
mem_map 📖mathematicalAddSubmonoid
SetLike.instMembership
instSetLike
map
DFunLike.coe
mem_map_equiv 📖mathematicalAddSubmonoid
SetLike.instMembership
instSetLike
map
AddMonoidHom
AddZeroClass.toAddZero
AddMonoidHom.instFunLike
AddMonoidHom.instAddMonoidHomClass
AddEquiv.toAddMonoidHom
DFunLike.coe
AddEquiv
AddZero.toAdd
EquivLike.toFunLike
AddEquiv.instEquivLike
AddEquiv.symm
Set.mem_image_equiv
mem_map_iff_mem 📖mathematicalDFunLike.coeAddSubmonoid
SetLike.instMembership
instSetLike
map
Function.Injective.mem_set_image
mem_map_of_mem 📖mathematicalAddSubmonoid
SetLike.instMembership
instSetLike
map
DFunLike.coe
Set.mem_image_of_mem
mem_pi 📖mathematicalAddSubmonoid
Pi.addZeroClass
SetLike.instMembership
instSetLike
pi
mem_prod 📖mathematicalAddSubmonoid
Prod.instAddZeroClass
SetLike.instMembership
instSetLike
prod
monotone_comap 📖mathematicalMonotone
AddSubmonoid
PartialOrder.toPreorder
instPartialOrder
comap
GaloisConnection.monotone_u
gc_map_comap
monotone_map 📖mathematicalMonotone
AddSubmonoid
PartialOrder.toPreorder
instPartialOrder
map
GaloisConnection.monotone_l
gc_map_comap
mrange_fst 📖mathematicalAddMonoidHom.mrange
Prod.instAddZeroClass
AddMonoidHom
AddZeroClass.toAddZero
AddMonoidHom.instFunLike
AddMonoidHom.instAddMonoidHomClass
AddMonoidHom.fst
Top.top
AddSubmonoid
instTop
AddMonoidHom.mrange_eq_top_of_surjective
AddMonoidHom.instAddMonoidHomClass
Prod.fst_surjective
mrange_inl 📖mathematicalAddMonoidHom.mrange
Prod.instAddZeroClass
AddMonoidHom
AddZeroClass.toAddZero
AddMonoidHom.instFunLike
AddMonoidHom.instAddMonoidHomClass
AddMonoidHom.inl
prod
Top.top
AddSubmonoid
instTop
Bot.bot
instBot
AddMonoidHom.instAddMonoidHomClass
AddMonoidHom.mrange_eq_map
map_inl
mrange_inl' 📖mathematicalAddMonoidHom.mrange
Prod.instAddZeroClass
AddMonoidHom
AddZeroClass.toAddZero
AddMonoidHom.instFunLike
AddMonoidHom.instAddMonoidHomClass
AddMonoidHom.inl
comap
AddMonoidHom.snd
Bot.bot
AddSubmonoid
instBot
AddMonoidHom.instAddMonoidHomClass
mrange_inl
top_prod
mrange_inl_sup_mrange_inr 📖mathematicalAddSubmonoid
Prod.instAddZeroClass
SemilatticeSup.toMax
Lattice.toSemilatticeSup
CompleteLattice.toLattice
instCompleteLattice
AddMonoidHom.mrange
AddMonoidHom
AddZeroClass.toAddZero
AddMonoidHom.instFunLike
AddMonoidHom.instAddMonoidHomClass
AddMonoidHom.inl
AddMonoidHom.inr
Top.top
instTop
AddMonoidHom.instAddMonoidHomClass
mrange_inl
mrange_inr
prod_bot_sup_bot_prod
top_prod_top
mrange_inr 📖mathematicalAddMonoidHom.mrange
Prod.instAddZeroClass
AddMonoidHom
AddZeroClass.toAddZero
AddMonoidHom.instFunLike
AddMonoidHom.instAddMonoidHomClass
AddMonoidHom.inr
prod
Bot.bot
AddSubmonoid
instBot
Top.top
instTop
AddMonoidHom.instAddMonoidHomClass
AddMonoidHom.mrange_eq_map
map_inr
mrange_inr' 📖mathematicalAddMonoidHom.mrange
Prod.instAddZeroClass
AddMonoidHom
AddZeroClass.toAddZero
AddMonoidHom.instFunLike
AddMonoidHom.instAddMonoidHomClass
AddMonoidHom.inr
comap
AddMonoidHom.fst
Bot.bot
AddSubmonoid
instBot
AddMonoidHom.instAddMonoidHomClass
mrange_inr
prod_top
mrange_snd 📖mathematicalAddMonoidHom.mrange
Prod.instAddZeroClass
AddMonoidHom
AddZeroClass.toAddZero
AddMonoidHom.instFunLike
AddMonoidHom.instAddMonoidHomClass
AddMonoidHom.snd
Top.top
AddSubmonoid
instTop
AddMonoidHom.mrange_eq_top_of_surjective
AddMonoidHom.instAddMonoidHomClass
Prod.snd_surjective
mrange_subtype 📖mathematicalAddMonoidHom.mrange
AddSubmonoid
SetLike.instMembership
instSetLike
toAddZeroClass
AddMonoidHom
AddZeroClass.toAddZero
AddMonoidHom.instFunLike
AddMonoidHom.instAddMonoidHomClass
subtype
SetLike.coe_injective
AddMonoidHom.instAddMonoidHomClass
AddMonoidHom.coe_mrange
Subtype.range_coe
nontrivial_iff_exists_ne_zero 📖mathematicalNontrivial
AddSubmonoid
SetLike.instMembership
instSetLike
zero_mem
nontrivial_iff_exists_ne
pi_bot 📖mathematicalpi
Set.univ
Bot.bot
AddSubmonoid
instBot
Pi.addZeroClass
ext
mem_pi
Set.mem_univ
mem_bot
pi_empty 📖mathematicalpi
Set
Set.instEmptyCollection
Top.top
AddSubmonoid
Pi.addZeroClass
instTop
ext
mem_pi
Set.mem_empty_iff_false
IsEmpty.forall_iff
instIsEmptyFalse
mem_top
pi_eq_bot_iff 📖mathematicalpi
Set.univ
Bot.bot
AddSubmonoid
Pi.addZeroClass
instBot
SetLike.ext'_iff
Set.univ_pi_eq_singleton_iff
pi_top 📖mathematicalpi
Top.top
AddSubmonoid
instTop
Pi.addZeroClass
ext
mem_pi
mem_top
prod_bot_sup_bot_prod 📖mathematicalAddSubmonoid
Prod.instAddZeroClass
SemilatticeSup.toMax
Lattice.toSemilatticeSup
CompleteLattice.toLattice
instCompleteLattice
prod
Bot.bot
instBot
le_antisymm
sup_le
prod_mono
le_refl
bot_le
AddMemClass.add_mem
AddSubmonoidClass.toAddMemClass
instAddSubmonoidClass
le_sup_left
Set.mem_singleton
le_sup_right
Prod.fst_add_snd
prod_eq_bot_iff 📖mathematicalprod
Bot.bot
AddSubmonoid
Prod.instAddZeroClass
instBot
eq_bot_iff
AddMonoidHom.instAddMonoidHomClass
prod_le_iff
GaloisConnection.le_iff_le
gc_map_comap
AddMonoidHom.mker_inl
AddMonoidHom.mker_inr
prod_eq_top_iff 📖mathematicalprod
Top.top
AddSubmonoid
Prod.instAddZeroClass
instTop
eq_top_iff
AddMonoidHom.instAddMonoidHomClass
le_prod_iff
AddMonoidHom.mrange_eq_map
mrange_fst
mrange_snd
prod_le_iff 📖mathematicalAddSubmonoid
Prod.instAddZeroClass
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
prod
map
AddMonoidHom
AddZeroClass.toAddZero
AddMonoidHom.instFunLike
AddMonoidHom.instAddMonoidHomClass
AddMonoidHom.inl
AddMonoidHom.inr
AddMonoidHom.instAddMonoidHomClass
zero_mem
mem_map
SetLike.mem_coe
add_zero
zero_add
add_mem
prod_mono 📖mathematicalAddSubmonoid
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
Prod.instAddZeroClass
prod
Set.prod_mono
prod_top 📖mathematicalprod
Top.top
AddSubmonoid
instTop
comap
Prod.instAddZeroClass
AddMonoidHom
AddZeroClass.toAddZero
AddMonoidHom.instFunLike
AddMonoidHom.instAddMonoidHomClass
AddMonoidHom.fst
ext
AddMonoidHom.instAddMonoidHomClass
mem_prod
mem_top
mem_comap
single_mem_pi 📖mathematicalAddSubmonoid
Pi.addZeroClass
SetLike.instMembership
instSetLike
pi
Pi.single
AddZero.toZero
AddZeroClass.toAddZero
Set.update_mem_pi_iff_of_mem
ZeroMemClass.zero_mem
AddSubmonoidClass.toZeroMemClass
instAddSubmonoidClass
subtype_comp_inclusion 📖mathematicalAddSubmonoid
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
AddMonoidHom.comp
SetLike.instMembership
instSetLike
AddZeroClass.toAddZero
toAddZeroClass
subtype
inclusion
surjOn_iff_le_map 📖mathematicalSet.SurjOn
DFunLike.coe
AddMonoidHom
AddZeroClass.toAddZero
AddMonoidHom.instFunLike
SetLike.coe
AddSubmonoid
instSetLike
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
map
AddMonoidHom.instAddMonoidHomClass
toSubmonoid'_closure 📖mathematicalDFunLike.coe
OrderIso
AddSubmonoid
Additive
Additive.addZeroClass
Submonoid
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
Submonoid.instPartialOrder
instFunLikeOrderIso
toSubmonoid'
closure
Submonoid.closure
Set.preimage
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
Additive.ofMul
le_antisymm
OrderIso.le_symm_apply
closure_le
Submonoid.subset_closure
Submonoid.closure_le
subset_closure
toSubmonoid_closure 📖mathematicalDFunLike.coe
OrderIso
AddSubmonoid
Submonoid
Multiplicative
Multiplicative.mulOneClass
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
Submonoid.instPartialOrder
instFunLikeOrderIso
toSubmonoid
closure
Submonoid.closure
Set.preimage
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
Multiplicative.toAdd
le_antisymm
GaloisConnection.l_le
OrderIso.to_galoisConnection
closure_le
Submonoid.subset_closure
Submonoid.closure_le
subset_closure
topEquiv_apply 📖mathematicalDFunLike.coe
AddEquiv
AddSubmonoid
SetLike.instMembership
instSetLike
Top.top
instTop
add
AddZero.toAdd
AddZeroClass.toAddZero
EquivLike.toFunLike
AddEquiv.instEquivLike
topEquiv
topEquiv_symm_apply_coe 📖mathematicalAddSubmonoid
SetLike.instMembership
instSetLike
Top.top
instTop
DFunLike.coe
AddEquiv
AddZero.toAdd
AddZeroClass.toAddZero
add
EquivLike.toFunLike
AddEquiv.instEquivLike
AddEquiv.symm
topEquiv
topEquiv_toAddMonoidHom 📖mathematicalAddMonoidHomClass.toAddMonoidHom
AddSubmonoid
SetLike.instMembership
instSetLike
Top.top
instTop
AddEquiv
add
AddZero.toAdd
AddZeroClass.toAddZero
toAddZeroClass
EquivLike.toFunLike
AddEquiv.instEquivLike
AddEquivClass.instAddMonoidHomClass
AddEquiv.instAddEquivClass
topEquiv
subtype
AddEquivClass.instAddMonoidHomClass
AddEquiv.instAddEquivClass
top_prod 📖mathematicalprod
Top.top
AddSubmonoid
instTop
comap
Prod.instAddZeroClass
AddMonoidHom
AddZeroClass.toAddZero
AddMonoidHom.instFunLike
AddMonoidHom.instAddMonoidHomClass
AddMonoidHom.snd
ext
AddMonoidHom.instAddMonoidHomClass
mem_prod
mem_top
mem_comap
top_prod_top 📖mathematicalprod
Top.top
AddSubmonoid
instTop
Prod.instAddZeroClass
AddMonoidHom.instAddMonoidHomClass
top_prod
comap_top
val_addUnitsTypeEquivIsAddUnitAddSubmonoid_symm_apply 📖mathematicalAddUnits.val
DFunLike.coe
AddEquiv
AddSubmonoid
AddMonoid.toAddZeroClass
SetLike.instMembership
instSetLike
IsAddUnit.addSubmonoid
AddUnits
add
AddUnits.instAdd
EquivLike.toFunLike
AddEquiv.instEquivLike
AddEquiv.symm
addUnitsTypeEquivIsAddUnitAddSubmonoid
val_neg_addUnitsTypeEquivIsAddUnitAddSubmonoid_symm_apply 📖mathematicalAddUnits.val
AddUnits
AddUnits.instNeg
DFunLike.coe
AddEquiv
AddSubmonoid
AddMonoid.toAddZeroClass
SetLike.instMembership
instSetLike
IsAddUnit.addSubmonoid
add
AddUnits.instAdd
EquivLike.toFunLike
AddEquiv.instEquivLike
AddEquiv.symm
addUnitsTypeEquivIsAddUnitAddSubmonoid

LibraryNote

Definitions

NameCategoryTheorems
range_copy_pattern 📖CompOp

MonoidHom

Definitions

NameCategoryTheorems
codRestrict 📖CompOp
4 mathmath: subgroupOf_range_eq_of_le, injective_codRestrict, codRestrict_apply, ker_codRestrict
decidableMemMker 📖CompOp
mker 📖CompOp
17 mathmath: mker_snd, Zsqrtd.mker_norm_eq_unitary, mker_inl, mem_mker, comap_bot', coe_mker, mker_inr, QuadraticAlgebra.mker_norm_eq_unitary, restrict_mker, Submodule.mker_spanSingleton, Monoid.Coprod.mker_swap, mker_fst, mker_one, mrangeRestrict_mker, mker_prod_map, ker_toSubmonoid, comap_mker
mrange 📖CompOp
53 mathmath: Submonoid.mrange_inr', coe_mrange, Valuation.val_mrange_zero, Fintype.card_coeSort_mrange, Submonoid.mrange_inl', MonoidWithZeroHom.mrange_nontrivial, Submonoid.map_comap_eq, Submonoid.mrange_inl_sup_mrange_inr, mrange_eq_map, Monoid.Coprod.mrange_swap, Monoid.CoprodI.mrange_eq_iSup, Monoid.Coprod.mrange_eq, Submonoid.closure_singleton_eq, mrange_eq_top, Submonoid.mrange_inr, mrange_comp, Monoid.CoprodI.lift_mrange_le, Submonoid.mrange_subtype, Monoid.fg_range, MulEquiv.ofLeftInverse'_apply, mrange_id, mrangeRestrict_surjective, Valued.integer.mulArchimedean_mrange_of_isCompact_integer, Monoid.Coprod.mrange_lift, Con.kerLift_range_eq, mgraph_eq_mrange_prod, noncommPiCoprod_mrange, FreeMonoid.mrange_lift, map_mrange, Monoid.CoprodI.iSup_mrange_of, Monoid.Coprod.mrange_mk, Valued.integer.locallyFiniteOrder_units_mrange_of_isCompact_integer, MonoidWithZeroHom.val_mrange_zero, MulEquiv.ofLeftInverse'_symm_apply, Submonoid.mrange_snd, Valuation.Integers.wellFounded_gt_on_v_iff_discrete_mrange, Submonoid.mrange_inl, mrange_eq_top_of_surjective, Submonoid.mrange_fst, coe_mrangeRestrict, Con.lift_range, exists_mrange_eq_mgraph, restrict_mrange, mclosure_range, Submonoid.sup_eq_range, mrangeRestrict_mker, Con.mrange_mk', Monoid.Coprod.mrange_inl_sup_mrange_inr, Monoid.Coprod.codisjoint_mrange_inl_mrange_inr, Valuation.Integers.isPrincipalIdealRing_iff_not_denselyOrdered_mrange, Submonoid.closure_eq_mrange, exists_mulEquiv_mrange_eq_mgraph, mem_mrange
mrangeRestrict 📖CompOp
4 mathmath: MulEquiv.ofLeftInverse'_apply, mrangeRestrict_surjective, coe_mrangeRestrict, mrangeRestrict_mker
restrict 📖CompOp
19 mathmath: IsLocalization.mul_add_inv_left, RootPairing.range_weylGroup_coweightHom, transferSylow_restrict_eq_pow, restrict_range, Submonoid.LocalizationMap.inv_unique, IsLocalization.lift_mk', restrict_apply, Submonoid.LocalizationMap.lift_mk', restrict_eq_one_iff, restrict_mker, Submonoid.LocalizationMap.lift_apply, restrictHom_apply, Submonoid.LocalizationMap.mul_inv_right, Submonoid.LocalizationMap.mul_inv_left, Submonoid.LocalizationMap.mul_inv, Submonoid.LocalizationMap.lift₀_apply, restrict_mrange, RootPairing.range_weylGroup_weightHom, ker_restrict
restrictHom 📖CompOp
4 mathmath: restrictHomKerEquiv_apply_coe, restrictHomKerEquiv_symm_coe_apply, restrictHom_apply, restrict_surjective
submonoidComap 📖CompOp
2 mathmath: submonoidComap_apply_coe, submonoidComap_surjective_of_surjective
submonoidMap 📖CompOp
2 mathmath: submonoidMap_apply_coe, submonoidMap_surjective

Theorems

NameKindAssumesProvesValidatesDepends On
codRestrict_apply 📖mathematicalSetLike.instMembership
DFunLike.coe
MonoidHom
MulOneClass.toMulOne
instFunLike
SubmonoidClass.toMulOneClass
codRestrict
coe_mker 📖mathematicalSetLike.coe
Submonoid
Submonoid.instSetLike
mker
Set.preimage
DFunLike.coe
Set
Set.instSingletonSet
MulOne.toOne
MulOneClass.toMulOne
coe_mrange 📖mathematicalSetLike.coe
Submonoid
Submonoid.instSetLike
mrange
Set.range
DFunLike.coe
coe_mrangeRestrict 📖mathematicalSubmonoid
SetLike.instMembership
Submonoid.instSetLike
mrange
MonoidHom
MulOneClass.toMulOne
instFunLike
instMonoidHomClass
DFunLike.coe
Submonoid.toMulOneClass
mrangeRestrict
instMonoidHomClass
comap_bot' 📖mathematicalSubmonoid.comap
Bot.bot
Submonoid
Submonoid.instBot
mker
comap_mker 📖mathematicalSubmonoid.comap
MonoidHom
MulOneClass.toMulOne
instFunLike
instMonoidHomClass
mker
comp
instMonoidHomClass
injective_codRestrict 📖mathematicalSetLike.instMembership
DFunLike.coe
MonoidHom
MulOneClass.toMulOne
instFunLike
SubmonoidClass.toMulOneClass
codRestrict
map_mclosure 📖mathematicalSubmonoid.map
Submonoid.closure
Set.image
DFunLike.coe
GaloisConnection.l_comm_of_u_comm
Set.image_preimage
Submonoid.gc_map_comap
GaloisInsertion.gc
map_mrange 📖mathematicalSubmonoid.map
MonoidHom
MulOneClass.toMulOne
instFunLike
instMonoidHomClass
mrange
comp
instMonoidHomClass
Submonoid.map.congr_simp
mrange_eq_map
Submonoid.map_map
mclosure_preimage_le 📖mathematicalSubmonoid
Preorder.toLE
PartialOrder.toPreorder
Submonoid.instPartialOrder
Submonoid.closure
Set.preimage
DFunLike.coe
Submonoid.comap
Submonoid.closure_le
SetLike.mem_coe
Submonoid.mem_comap
Submonoid.subset_closure
mclosure_range 📖mathematicalSubmonoid.closure
Set.range
DFunLike.coe
mrange
Set.image_univ
map_mclosure
mrange_eq_map
Submonoid.closure_univ
mem_mker 📖mathematicalSubmonoid
SetLike.instMembership
Submonoid.instSetLike
mker
DFunLike.coe
MulOne.toOne
MulOneClass.toMulOne
mem_mrange 📖mathematicalSubmonoid
SetLike.instMembership
Submonoid.instSetLike
mrange
DFunLike.coe
mker_fst 📖mathematicalmker
Prod.instMulOneClass
MonoidHom
MulOneClass.toMulOne
instFunLike
instMonoidHomClass
fst
Submonoid.prod
Bot.bot
Submonoid
Submonoid.instBot
Top.top
Submonoid.instTop
SetLike.ext
instMonoidHomClass
mker_inl 📖mathematicalmker
Prod.instMulOneClass
MonoidHom
MulOneClass.toMulOne
instFunLike
instMonoidHomClass
inl
Bot.bot
Submonoid
Submonoid.instBot
Submonoid.ext
instMonoidHomClass
mker_inr 📖mathematicalmker
Prod.instMulOneClass
MonoidHom
MulOneClass.toMulOne
instFunLike
instMonoidHomClass
inr
Bot.bot
Submonoid
Submonoid.instBot
Submonoid.ext
instMonoidHomClass
mker_one 📖mathematicalmker
MonoidHom
MulOneClass.toMulOne
instFunLike
instMonoidHomClass
instOneMonoidHom
Top.top
Submonoid
Submonoid.instTop
Submonoid.ext
instMonoidHomClass
mker_prod_map 📖mathematicalmker
Prod.instMulOneClass
MonoidHom
MulOneClass.toMulOne
instFunLike
instMonoidHomClass
prodMap
Submonoid.prod
instMonoidHomClass
comap_bot'
prod_map_comap_prod'
Submonoid.bot_prod_bot
mker_snd 📖mathematicalmker
Prod.instMulOneClass
MonoidHom
MulOneClass.toMulOne
instFunLike
instMonoidHomClass
snd
Submonoid.prod
Top.top
Submonoid
Submonoid.instTop
Bot.bot
Submonoid.instBot
SetLike.ext
instMonoidHomClass
mrangeRestrict_mker 📖mathematicalmker
Submonoid
SetLike.instMembership
Submonoid.instSetLike
mrange
MonoidHom
MulOneClass.toMulOne
instFunLike
instMonoidHomClass
Submonoid.toMulOneClass
mrangeRestrict
Submonoid.ext
instMonoidHomClass
OneMemClass.one_mem
SubmonoidClass.toOneMemClass
Submonoid.instSubmonoidClass
mrangeRestrict_surjective 📖mathematicalSubmonoid
SetLike.instMembership
Submonoid.instSetLike
mrange
MonoidHom
MulOneClass.toMulOne
instFunLike
instMonoidHomClass
DFunLike.coe
Submonoid.toMulOneClass
mrangeRestrict
instMonoidHomClass
mrange_comp 📖mathematicalmrange
MonoidHom
MulOneClass.toMulOne
instFunLike
instMonoidHomClass
comp
Submonoid.map
SetLike.coe_injective
instMonoidHomClass
Set.range_comp
mrange_eq_map 📖mathematicalmrange
Submonoid.map
Top.top
Submonoid
Submonoid.instTop
Submonoid.copy_eq
mrange_eq_top 📖mathematicalmrange
Top.top
Submonoid
Submonoid.instTop
DFunLike.coe
SetLike.ext'_iff
coe_mrange
Submonoid.coe_top
Set.range_eq_univ
mrange_eq_top_of_surjective 📖mathematicalDFunLike.coemrange
Top.top
Submonoid
Submonoid.instTop
mrange_eq_top
mrange_id 📖mathematicalmrange
MonoidHom
MulOneClass.toMulOne
instFunLike
instMonoidHomClass
id
Top.top
Submonoid
Submonoid.instTop
instMonoidHomClass
mrange_eq_map
Submonoid.map_id
prod_map_comap_prod' 📖mathematicalSubmonoid.comap
Prod.instMulOneClass
MonoidHom
MulOneClass.toMulOne
instFunLike
instMonoidHomClass
prodMap
Submonoid.prod
SetLike.coe_injective
instMonoidHomClass
Set.preimage_prod_map_prod
restrictHom_apply 📖mathematicalDFunLike.coe
MonoidHom
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
SetLike.instMembership
SubmonoidClass.toMulOneClass
instCommMonoid
instFunLike
restrictHom
restrict
restrict_apply 📖mathematicalDFunLike.coe
MonoidHom
SetLike.instMembership
MulOneClass.toMulOne
SubmonoidClass.toMulOneClass
instFunLike
restrict
restrict_eq_one_iff 📖mathematicalrestrict
MonoidHom
SetLike.instMembership
MulOneClass.toMulOne
SubmonoidClass.toMulOneClass
instOneMonoidHom
DFunLike.coe
instFunLike
MulOne.toOne
restrict_mker 📖mathematicalmker
Submonoid
SetLike.instMembership
Submonoid.instSetLike
Submonoid.toMulOneClass
MonoidHom
MulOneClass.toMulOne
SubmonoidClass.toMulOneClass
Submonoid.instSubmonoidClass
instFunLike
instMonoidHomClass
restrict
Submonoid.comap
Submonoid.subtype
Submonoid.instSubmonoidClass
instMonoidHomClass
restrict_mrange 📖mathematicalmrange
Submonoid
SetLike.instMembership
Submonoid.instSetLike
Submonoid.toMulOneClass
MonoidHom
MulOneClass.toMulOne
SubmonoidClass.toMulOneClass
Submonoid.instSubmonoidClass
instFunLike
instMonoidHomClass
restrict
Submonoid.map
Submonoid.instSubmonoidClass
instMonoidHomClass
submonoidComap_apply_coe 📖mathematicalSubmonoid
SetLike.instMembership
Submonoid.instSetLike
DFunLike.coe
MonoidHom
Submonoid.comap
MulOneClass.toMulOne
instFunLike
instMonoidHomClass
Submonoid.toMulOneClass
submonoidComap
instMonoidHomClass
submonoidComap_surjective_of_surjective 📖mathematicalDFunLike.coe
MonoidHom
MulOneClass.toMulOne
instFunLike
Submonoid
SetLike.instMembership
Submonoid.instSetLike
Submonoid.comap
instMonoidHomClass
Submonoid.toMulOneClass
submonoidComap
instMonoidHomClass
Submonoid.mem_comap
Subtype.val_injective
submonoidMap_apply_coe 📖mathematicalSubmonoid
SetLike.instMembership
Submonoid.instSetLike
Submonoid.map
MonoidHom
MulOneClass.toMulOne
instFunLike
DFunLike.coe
instMonoidHomClass
Submonoid.toMulOneClass
submonoidMap
instMonoidHomClass
submonoidMap_surjective 📖mathematicalSubmonoid
SetLike.instMembership
Submonoid.instSetLike
Submonoid.map
MonoidHom
MulOneClass.toMulOne
instFunLike
instMonoidHomClass
DFunLike.coe
Submonoid.toMulOneClass
submonoidMap
instMonoidHomClass

MulEquiv

Definitions

NameCategoryTheorems
ofLeftInverse' 📖CompOp
2 mathmath: ofLeftInverse'_apply, ofLeftInverse'_symm_apply
submonoidCongr 📖CompOp
1 mathmath: Monoid.IsTorsion.torsionMulEquiv_apply
submonoidMap 📖CompOp
3 mathmath: coe_submonoidMap_apply, Submonoid.equivMapOfInjective_coe_mulEquiv, submonoidMap_symm_apply

Theorems

NameKindAssumesProvesValidatesDepends On
coe_submonoidMap_apply 📖mathematicalSubmonoid
SetLike.instMembership
Submonoid.instSetLike
Submonoid.map
MulEquiv
MulOne.toMul
MulOneClass.toMulOne
EquivLike.toFunLike
instEquivLike
MulEquivClass.instMonoidHomClass
instMulEquivClass
DFunLike.coe
Submonoid.mul
submonoidMap
MulEquivClass.instMonoidHomClass
instMulEquivClass
ofLeftInverse'_apply 📖mathematicalDFunLike.coe
MonoidHom
MulOneClass.toMulOne
MonoidHom.instFunLike
MulEquiv
Submonoid
SetLike.instMembership
Submonoid.instSetLike
MonoidHom.mrange
MonoidHom.instMonoidHomClass
MulOne.toMul
Submonoid.mul
EquivLike.toFunLike
instEquivLike
ofLeftInverse'
Submonoid.toMulOneClass
MonoidHom.mrangeRestrict
MonoidHom.instMonoidHomClass
ofLeftInverse'_symm_apply 📖mathematicalDFunLike.coe
MonoidHom
MulOneClass.toMulOne
MonoidHom.instFunLike
MulEquiv
Submonoid
SetLike.instMembership
Submonoid.instSetLike
MonoidHom.mrange
MonoidHom.instMonoidHomClass
Submonoid.mul
MulOne.toMul
EquivLike.toFunLike
instEquivLike
symm
ofLeftInverse'
MonoidHom.instMonoidHomClass
submonoidMap_symm_apply 📖mathematicalDFunLike.coe
MulEquiv
Submonoid
SetLike.instMembership
Submonoid.instSetLike
Submonoid.map
MulOne.toMul
MulOneClass.toMulOne
EquivLike.toFunLike
instEquivLike
MulEquivClass.instMonoidHomClass
instMulEquivClass
Submonoid.mul
symm
submonoidMap
MonoidHom
MonoidHom.instFunLike
MonoidHom.instMonoidHomClass
MonoidHomClass.toMonoidHom
Set
Set.instMembership
SetLike.coe
SetLike.mem_coe
Set.image
Equiv
Equiv.instEquivLike
toEquiv
Equiv.symm
Set.mem_image_equiv
MonoidHom.instMonoidHomClass
MulEquivClass.instMonoidHomClass
instMulEquivClass

Submonoid

Definitions

NameCategoryTheorems
comap 📖CompOp
70 mathmath: IsLocalization.localization_localization_isLocalization_of_has_all_units, nonZeroDivisors_le_comap_nonZeroDivisors_of_injective, monotone_comap, mrange_inr', comap_iInf, AlgebraicGeometry.ProjectiveSpectrum.Proj.awayToSection_apply, mrange_inl', prod_top, comap_sup_map_of_injective, le_pi_iff, Subgroup.comap_toSubmonoid, Localization.localRingHom_mk', comap_surjective_of_injective, map_comap_eq, le_comap_map, comap_strictMono_of_surjective, map_sup_comap_of_surjective, top_prod, comap_iInf_map_of_injective, comap_top, map_le_iff_le_comap, mem_comap, Algebra.essFiniteType_cond_iff, LocalizationMap.nonZeroDivisors_le_comap, MonoidHom.prod_map_comap_prod', mk_mul_mk_inv_eq_one, mk_inv_mul_mk_eq_one, Localization.mapPiEvalRingHom_bijective, map_comap_le, le_comap_mulSingle_pi, Units.unitary_eq, MonoidHom.comap_bot', TopCat.Presheaf.SubmonoidPresheaf.map, map_comap_eq_self_of_surjective, Algebra.algebraMapSubmonoid_le_comap, map_iSup_comap_of_surjective, comap_iSup_map_of_injective, MonoidHom.submonoidComap_apply_coe, coe_comap, map_inf_comap_of_surjective, IsLocalization.nonZeroDivisors_le_comap, map_equiv_eq_comap_symm, MonoidHom.submonoidComap_surjective_of_surjective, MonoidHom.mclosure_preimage_le, comap_inf, comap_le_comap_iff_of_surjective, MonoidHom.restrict_mker, comap_inf_map_of_injective, comap_comap, gc_map_comap, IsLocalization.ker_map, map_comap_map, comap_map_eq_of_injective, le_comap_of_map_le, comap_id, comap_equiv_eq_map_symm, Localization.le_comap_primeCompl_iff, AlgebraicGeometry.StructureSheaf.comap_basicOpen, divPairs_comap, map_comap_eq_self, MonoidHom.subgroupComap_apply_coe, comap_nonZeroDivisors_le_of_injective, Algebra.EssFiniteType.cond, map_iInf_comap_of_surjective, TopCat.Presheaf.submonoidPresheafOfStalk_obj, RingHom.toKerIsLocalization_isLocalizedModule, MonoidHom.comap_mker, comap_injective_of_surjective, map_comap_eq_of_surjective, comap_map_comap
equivMapOfInjective 📖CompOp
2 mathmath: equivMapOfInjective_coe_mulEquiv, coe_equivMapOfInjective_apply
gciMapComap 📖CompOp
giMapComap 📖CompOp
inclusion 📖CompOp
4 mathmath: inclusion_inj, subtype_comp_inclusion, inclusion_injective, coe_inclusion
map 📖CompOp
99 mathmath: mem_map_iff_mem, mem_map_equiv, map_inr, IsLocalization.smul_mem_finsetIntegerMultiple_span, IsLocalization.map_surjective_of_surjective, comap_sup_map_of_injective, coe_map, mem_map, IsLocalization.lift_mem_adjoin_finsetIntegerMultiple, map_comap_eq, le_comap_map, LocalizationMap.map_injective_of_injective, map_sup_comap_of_surjective, MulEquiv.coe_submonoidMap_apply, IsLocalization.isLocalization_iff_of_base_ringEquiv, comap_iInf_map_of_injective, MonoidHom.mrange_eq_map, map_le_of_le_comap, iSup_map_mulSingle_le, IsLocalization.of_surjective, map_coe_toMulEquiv, LocalizationMap.map_surjective_of_surjective, IsLocalization.Away.instMapRingHomPowersOfCoe, MonoidHom.submonoidMap_apply_coe, map_le_iff_le_comap, Ideal.disjoint_map_primeCompl_iff_comap_le, isIntegral_localization', MonoidHom.mrange_comp, map_iSup, map_inf, iSup_map_mulSingle, pi_le_iff, map_sup, IsLocalization.iff_map_piEvalRingHom, map_comap_le, map_le_map_iff_of_injective, map_map, map_id, apply_coe_mem_map, map_le_nonZeroDivisors_of_injective, map_comap_eq_self_of_surjective, Algebra.algebraMapSubmonoid_map_eq, Subgroup.map_toSubmonoid, map_iSup_comap_of_surjective, Matrix.submonoidCenter_eq_scalar_map, IsLocalization.isLocalization_of_submonoid_le, comap_iSup_map_of_injective, map_inf_comap_of_surjective, LocalizationMap.map_nonZeroDivisors_le, MulEquivClass.map_nonZeroDivisors, le_prod_iff, map_equiv_eq_comap_symm, MulEquiv.submonoidMap_symm_apply, IsLocalization.isLocalization_of_base_ringEquiv, IsLocalization.map_injective_of_injective, pinGroup.mem_lipschitzGroup, Submodule.mker_spanSingleton, MonoidHom.map_mrange, comap_inf_map_of_injective, Polynomial.isLocalization, map_surjective_of_surjective, gc_map_comap, map_injective_of_injective, monotone_map, map_comap_map, IsLocalization.submonoid_map_le_is_unit, pinGroup.mem_iff, FG.map, RingHom.IsStableUnderBaseChange.isLocalization_map, RingHom.isIntegralElem_localization_at_leadingCoeff, disjoint_map, lipschitzGroup.coe_mem_iff_mem, coe_equivMapOfInjective_apply, comap_map_eq_of_injective, MvPolynomial.isLocalization_C_mk', MvPolynomial.isLocalization, map_iInf, codisjoint_map, map_bot, comap_equiv_eq_map_symm, IsLocalization.isLocalization_algebraMapSubmonoid_map_algHom, map_equiv_top, prod_le_iff, map_powers, MonoidHom.map_mclosure, map_inl, map_comap_eq_self, MonoidHom.restrict_mrange, surjOn_iff_le_map, map_iInf_comap_of_surjective, map_strictMono_of_injective, MonoidHom.subgroupMap_apply_coe, mem_map_of_mem, MonoidHom.submonoidMap_surjective, map_comap_eq_of_surjective, comap_map_comap, Polynomial.isIntegral_isLocalization_polynomial_quotient, IsLocalization.map_nonZeroDivisors_le, map_coe_toMonoidHom
pi 📖CompOp
17 mathmath: coe_pi, mem_pi, pi_top, le_pi_iff, closure_pi, iSup_map_mulSingle_le, IsLocalization.instForallPiUniv, iSup_map_mulSingle, pi_le_iff, IsLocalization.iff_map_piEvalRingHom, le_comap_mulSingle_pi, IsLocalizationMap.pi, FG.pi, pi_bot, mulSingle_mem_pi, pi_eq_bot_iff, pi_empty
prod 📖CompOp
24 mathmath: map_inr, MonoidHom.mker_snd, prod_top, top_prod, prod_bot_sup_bot_prod, mrange_inr, coe_prod, MonoidHom.prod_map_comap_prod', FG.prod, prod_mono, mem_prod, top_prod_top, closure_prod_one, prod_eq_bot_iff, bot_prod_bot, le_prod_iff, MonoidHom.mker_fst, prod_eq_top_iff, closure_prod, mrange_inl, prod_le_iff, map_inl, MonoidHom.mker_prod_map, closure_one_prod
prodEquiv 📖CompOp
toAddSubmonoid 📖CompOp
4 mathmath: fg_iff_add_fg, toAddSubmonoid_closure, coe_toAddSubmonoid_symm_apply, coe_toAddSubmonoid_apply
toAddSubmonoid' 📖CompOp
1 mathmath: toAddSubmonoid'_closure
topEquiv 📖CompOp
4 mathmath: topEquiv_symm_apply_coe, Monoid.IsTorsion.torsionMulEquiv_symm_apply_coe, topEquiv_toMonoidHom, topEquiv_apply
unitsTypeEquivIsUnitSubmonoid 📖CompOp
3 mathmath: val_inv_unitsTypeEquivIsUnitSubmonoid_symm_apply, unitsTypeEquivIsUnitSubmonoid_apply_coe, val_unitsTypeEquivIsUnitSubmonoid_symm_apply

Theorems

NameKindAssumesProvesValidatesDepends On
apply_coe_mem_map 📖mathematicalSubmonoid
SetLike.instMembership
instSetLike
map
DFunLike.coe
mem_map_of_mem
bot_or_exists_ne_one 📖mathematicalBot.bot
Submonoid
instBot
SetLike.instMembership
instSetLike
nontrivial_iff_exists_ne_one
bot_or_nontrivial
bot_or_nontrivial 📖mathematicalBot.bot
Submonoid
instBot
Nontrivial
SetLike.instMembership
instSetLike
bot_prod_bot 📖mathematicalprod
Bot.bot
Submonoid
instBot
Prod.instMulOneClass
SetLike.coe_injective
Set.singleton_prod_singleton
closure_closure_coe_preimage 📖mathematicalclosure
Submonoid
SetLike.instMembership
instSetLike
toMulOneClass
Set.preimage
Top.top
instTop
eq_top_iff
closure_induction
subset_closure
OneMemClass.one_mem
SubmonoidClass.toOneMemClass
instSubmonoidClass
MulMemClass.mul_mem
SubmonoidClass.toMulMemClass
closure_one_prod 📖mathematicalclosure
Prod.instMulOneClass
SProd.sprod
Set
Set.instSProd
Set.instSingletonSet
MulOne.toOne
MulOneClass.toMulOne
prod
Bot.bot
Submonoid
instBot
le_antisymm
closure_le
Set.prod_subset_prod_iff
Set.Subset.rfl
subset_closure
MonoidHom.instMonoidHomClass
prod_le_iff
map_bot
map_le_of_le_comap
closure_prod 📖mathematicalSet
Set.instMembership
MulOne.toOne
MulOneClass.toMulOne
closure
Prod.instMulOneClass
SProd.sprod
Set.instSProd
prod
le_antisymm
closure_le
Set.prod_subset_prod_iff
subset_closure
MonoidHom.instMonoidHomClass
prod_le_iff
map_le_of_le_comap
closure_prod_one 📖mathematicalclosure
Prod.instMulOneClass
SProd.sprod
Set
Set.instSProd
Set.instSingletonSet
MulOne.toOne
MulOneClass.toMulOne
prod
Bot.bot
Submonoid
instBot
le_antisymm
closure_le
Set.prod_subset_prod_iff
subset_closure
Set.Subset.rfl
MonoidHom.instMonoidHomClass
prod_le_iff
map_le_of_le_comap
map_bot
codisjoint_map 📖mathematicalDFunLike.coe
Codisjoint
Submonoid
instPartialOrder
BoundedOrder.toOrderTop
Preorder.toLE
PartialOrder.toPreorder
CompleteLattice.toBoundedOrder
instCompleteLattice
mapcodisjoint_iff
map_sup
MonoidHom.mrange_eq_map
MonoidHom.mrange_eq_top_of_surjective
coe_comap 📖mathematicalSetLike.coe
Submonoid
instSetLike
comap
Set.preimage
DFunLike.coe
coe_equivMapOfInjective_apply 📖mathematicalDFunLike.coe
MonoidHom
MulOneClass.toMulOne
MonoidHom.instFunLike
Submonoid
SetLike.instMembership
instSetLike
map
MonoidHom.instMonoidHomClass
MulEquiv
mul
EquivLike.toFunLike
MulEquiv.instEquivLike
equivMapOfInjective
MonoidHom.instMonoidHomClass
coe_inclusion 📖mathematicalSubmonoid
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
SetLike.instMembership
instSetLike
DFunLike.coe
MonoidHom
MulOneClass.toMulOne
toMulOneClass
MonoidHom.instFunLike
inclusion
Set.coe_inclusion
coe_map 📖mathematicalSetLike.coe
Submonoid
instSetLike
map
Set.image
DFunLike.coe
coe_pi 📖mathematicalSetLike.coe
Submonoid
Pi.mulOneClass
instSetLike
pi
Set.pi
coe_prod 📖mathematicalSetLike.coe
Submonoid
Prod.instMulOneClass
instSetLike
prod
SProd.sprod
Set
Set.instSProd
coe_toAddSubmonoid_apply 📖mathematicalSetLike.coe
AddSubmonoid
Additive
Additive.addZeroClass
AddSubmonoid.instSetLike
DFunLike.coe
RelIso
Submonoid
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
AddSubmonoid.instPartialOrder
RelIso.instFunLike
toAddSubmonoid
Set.preimage
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
Additive.toMul
instSetLike
coe_toAddSubmonoid_symm_apply 📖mathematicalSetLike.coe
Submonoid
instSetLike
DFunLike.coe
RelIso
AddSubmonoid
Additive
Additive.addZeroClass
Preorder.toLE
PartialOrder.toPreorder
AddSubmonoid.instPartialOrder
instPartialOrder
RelIso.instFunLike
RelIso.symm
toAddSubmonoid
Set.preimage
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
Additive.ofMul
AddSubmonoid.instSetLike
comap_comap 📖mathematicalcomap
MonoidHom
MulOneClass.toMulOne
MonoidHom.instFunLike
MonoidHom.instMonoidHomClass
MonoidHom.comp
MonoidHom.instMonoidHomClass
comap_equiv_eq_map_symm 📖mathematicalcomap
MulEquiv
MulOne.toMul
MulOneClass.toMulOne
EquivLike.toFunLike
MulEquiv.instEquivLike
MulEquivClass.instMonoidHomClass
MulEquiv.instMulEquivClass
map
MulEquiv.symm
MulEquivClass.instMonoidHomClass
MulEquiv.instMulEquivClass
map_equiv_eq_comap_symm
comap_iInf 📖mathematicalcomap
iInf
Submonoid
instInfSet
GaloisConnection.u_iInf
gc_map_comap
comap_iInf_map_of_injective 📖mathematicalDFunLike.coecomap
iInf
Submonoid
instInfSet
map
GaloisCoinsertion.u_iInf_l
comap_iSup_map_of_injective 📖mathematicalDFunLike.coecomap
iSup
Submonoid
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
instCompleteLattice
map
GaloisCoinsertion.u_iSup_l
comap_id 📖mathematicalcomap
MonoidHom
MulOneClass.toMulOne
MonoidHom.instFunLike
MonoidHom.instMonoidHomClass
MonoidHom.id
ext
MonoidHom.instMonoidHomClass
comap_inf 📖mathematicalcomap
Submonoid
instMin
GaloisConnection.u_inf
gc_map_comap
comap_inf_map_of_injective 📖mathematicalDFunLike.coecomap
Submonoid
instMin
map
GaloisCoinsertion.u_inf_l
comap_injective_of_surjective 📖mathematicalDFunLike.coeSubmonoid
comap
GaloisInsertion.u_injective
comap_le_comap_iff_of_surjective 📖mathematicalDFunLike.coeSubmonoid
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.coecomap
map
GaloisCoinsertion.u_l_eq
comap_strictMono_of_surjective 📖mathematicalDFunLike.coeStrictMono
Submonoid
PartialOrder.toPreorder
instPartialOrder
comap
GaloisInsertion.strictMono_u
comap_sup_map_of_injective 📖mathematicalDFunLike.coecomap
Submonoid
SemilatticeSup.toMax
Lattice.toSemilatticeSup
CompleteLattice.toLattice
instCompleteLattice
map
GaloisCoinsertion.u_sup_l
comap_surjective_of_injective 📖mathematicalDFunLike.coeSubmonoid
comap
GaloisCoinsertion.u_surjective
comap_top 📖mathematicalcomap
Top.top
Submonoid
instTop
GaloisConnection.u_top
gc_map_comap
disjoint_map 📖mathematicalDFunLike.coe
Disjoint
Submonoid
instPartialOrder
BoundedOrder.toOrderBot
Preorder.toLE
PartialOrder.toPreorder
CompleteLattice.toBoundedOrder
instCompleteLattice
mapdisjoint_iff
map_inf
map_bot
eq_bot_iff_forall 📖mathematicalBot.bot
Submonoid
instBot
MulOne.toOne
MulOneClass.toMulOne
SetLike.ext_iff
one_mem
eq_bot_of_subsingleton 📖mathematicalBot.bot
Submonoid
instBot
eq_bot_iff_forall
eq_top_iff' 📖mathematicalTop.top
Submonoid
instTop
SetLike.instMembership
instSetLike
eq_top_iff
mem_top
equivMapOfInjective_coe_mulEquiv 📖mathematicalequivMapOfInjective
MonoidHomClass.toMonoidHom
MulEquiv
MulOne.toMul
MulOneClass.toMulOne
EquivLike.toFunLike
MulEquiv.instEquivLike
MulEquivClass.instMonoidHomClass
MulEquiv.instMulEquivClass
EquivLike.injective
MulEquiv.submonoidMap
MulEquiv.ext
MonoidHom.instMonoidHomClass
MulEquivClass.instMonoidHomClass
MulEquiv.instMulEquivClass
EquivLike.injective
faithfulSMul 📖mathematicalFaithfulSMul
Submonoid
SetLike.instMembership
instSetLike
smul
FaithfulSMul.eq_of_smul_eq_smul
gc_map_comap 📖mathematicalGaloisConnection
Submonoid
PartialOrder.toPreorder
instPartialOrder
map
comap
map_le_iff_le_comap
iSup_map_mulSingle_le 📖mathematicalSubmonoid
Pi.mulOneClass
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
iSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
instCompleteLattice
map
MonoidHom
MulOneClass.toMulOne
MonoidHom.instFunLike
MonoidHom.instMonoidHomClass
MonoidHom.mulSingle
pi
iSup_le
MonoidHom.instMonoidHomClass
map_le_iff_le_comap
le_comap_mulSingle_pi
inclusion_inj 📖mathematicalSubmonoid
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
DFunLike.coe
MonoidHom
SetLike.instMembership
instSetLike
MulOneClass.toMulOne
toMulOneClass
MonoidHom.instFunLike
inclusion
inclusion_injective
inclusion_injective 📖mathematicalSubmonoid
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
SetLike.instMembership
instSetLike
DFunLike.coe
MonoidHom
MulOneClass.toMulOne
toMulOneClass
MonoidHom.instFunLike
inclusion
Set.inclusion_injective
le_comap_map 📖mathematicalSubmonoid
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
comap
map
GaloisConnection.le_u_l
gc_map_comap
le_comap_mulSingle_pi 📖mathematicalSubmonoid
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
comap
Pi.mulOneClass
MonoidHom
MulOneClass.toMulOne
MonoidHom.instFunLike
MonoidHom.instMonoidHomClass
MonoidHom.mulSingle
pi
MonoidHom.instMonoidHomClass
le_comap_of_map_le 📖mathematicalSubmonoid
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
map
comapGaloisConnection.le_u
gc_map_comap
le_pi_iff 📖mathematicalSubmonoid
Pi.mulOneClass
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
pi
comap
MonoidHom
MulOneClass.toMulOne
MonoidHom.instFunLike
MonoidHom.instMonoidHomClass
Pi.evalMonoidHom
Set.subset_pi_iff
le_prod_iff 📖mathematicalSubmonoid
Prod.instMulOneClass
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
prod
map
MonoidHom
MulOneClass.toMulOne
MonoidHom.instFunLike
MonoidHom.instMonoidHomClass
MonoidHom.fst
MonoidHom.snd
MonoidHom.instMonoidHomClass
map_bot 📖mathematicalmap
Bot.bot
Submonoid
instBot
GaloisConnection.l_bot
gc_map_comap
map_coe_toMonoidHom 📖mathematicalmap
MonoidHom
MulOneClass.toMulOne
MonoidHom.instFunLike
MonoidHom.instMonoidHomClass
MonoidHomClass.toMonoidHom
MonoidHom.instMonoidHomClass
map_coe_toMulEquiv 📖mathematicalmap
MulEquiv
MulOne.toMul
MulOneClass.toMulOne
EquivLike.toFunLike
MulEquiv.instEquivLike
MulEquivClass.instMonoidHomClass
MulEquiv.instMulEquivClass
MulEquivClass.toMulEquiv
MulEquivClass.instMonoidHomClass
MulEquiv.instMulEquivClass
map_comap_eq 📖mathematicalmap
comap
Submonoid
instMin
MonoidHom.mrange
SetLike.coe_injective
Set.image_preimage_eq_inter_range
map_comap_eq_of_surjective 📖mathematicalDFunLike.coemap
comap
GaloisInsertion.l_u_eq
map_comap_eq_self 📖mathematicalSubmonoid
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
MonoidHom.mrange
map
comap
inf_of_le_left
map_comap_eq
map_comap_eq_self_of_surjective 📖mathematicalDFunLike.coemap
comap
map_comap_eq_self
le_top
MonoidHom.mrange_eq_top_of_surjective
map_comap_le 📖mathematicalSubmonoid
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
MulEquiv
MulOne.toMul
MulOneClass.toMulOne
EquivLike.toFunLike
MulEquiv.instEquivLike
MulEquivClass.instMonoidHomClass
MulEquiv.instMulEquivClass
comap
MulEquiv.symm
SetLike.coe_injective
MulEquivClass.instMonoidHomClass
MulEquiv.instMulEquivClass
Equiv.image_eq_preimage_symm
map_equiv_top 📖mathematicalmap
MulEquiv
MulOne.toMul
MulOneClass.toMulOne
EquivLike.toFunLike
MulEquiv.instEquivLike
MulEquivClass.instMonoidHomClass
MulEquiv.instMulEquivClass
Top.top
Submonoid
instTop
SetLike.coe_injective
MulEquivClass.instMonoidHomClass
MulEquiv.instMulEquivClass
Set.image_univ
Function.Surjective.range_eq
MulEquiv.surjective
map_iInf 📖mathematicalDFunLike.coemap
iInf
Submonoid
instInfSet
SetLike.coe_injective
coe_iInf
Set.InjOn.image_iInter_eq
Set.injOn_of_injective
map_iInf_comap_of_surjective 📖mathematicalDFunLike.coemap
iInf
Submonoid
instInfSet
comap
GaloisInsertion.l_iInf_u
map_iSup 📖mathematicalmap
iSup
Submonoid
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
instCompleteLattice
GaloisConnection.l_iSup
gc_map_comap
map_iSup_comap_of_surjective 📖mathematicalDFunLike.coemap
iSup
Submonoid
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
instCompleteLattice
comap
GaloisInsertion.l_iSup_u
map_id 📖mathematicalmap
MonoidHom
MulOneClass.toMulOne
MonoidHom.instFunLike
MonoidHom.instMonoidHomClass
MonoidHom.id
ext
MonoidHom.instMonoidHomClass
map_inf 📖mathematicalDFunLike.coemap
Submonoid
instMin
SetLike.coe_injective
Set.image_inter
map_inf_comap_of_surjective 📖mathematicalDFunLike.coemap
Submonoid
instMin
comap
GaloisInsertion.l_inf_u
map_injective_of_injective 📖mathematicalDFunLike.coeSubmonoid
map
GaloisCoinsertion.l_injective
map_inl 📖mathematicalmap
Prod.instMulOneClass
MonoidHom
MulOneClass.toMulOne
MonoidHom.instFunLike
MonoidHom.instMonoidHomClass
MonoidHom.inl
prod
Bot.bot
Submonoid
instBot
ext
MonoidHom.instMonoidHomClass
Set.mem_singleton
Set.eq_of_mem_singleton
map_inr 📖mathematicalmap
Prod.instMulOneClass
MonoidHom
MulOneClass.toMulOne
MonoidHom.instFunLike
MonoidHom.instMonoidHomClass
MonoidHom.inr
prod
Bot.bot
Submonoid
instBot
ext
MonoidHom.instMonoidHomClass
Set.mem_singleton
Set.eq_of_mem_singleton
map_le_iff_le_comap 📖mathematicalSubmonoid
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
map
comap
Set.image_subset_iff
map_le_map_iff_of_injective 📖mathematicalDFunLike.coeSubmonoid
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
map
GaloisCoinsertion.l_le_l_iff
map_le_of_le_comap 📖mathematicalSubmonoid
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
comap
mapGaloisConnection.l_le
gc_map_comap
map_map 📖mathematicalmap
MonoidHom
MulOneClass.toMulOne
MonoidHom.instFunLike
MonoidHom.instMonoidHomClass
MonoidHom.comp
SetLike.coe_injective
MonoidHom.instMonoidHomClass
Set.image_image
map_strictMono_of_injective 📖mathematicalDFunLike.coeStrictMono
Submonoid
PartialOrder.toPreorder
instPartialOrder
map
GaloisCoinsertion.strictMono_l
map_sup 📖mathematicalmap
Submonoid
SemilatticeSup.toMax
Lattice.toSemilatticeSup
CompleteLattice.toLattice
instCompleteLattice
GaloisConnection.l_sup
gc_map_comap
map_sup_comap_of_surjective 📖mathematicalDFunLike.coemap
Submonoid
SemilatticeSup.toMax
Lattice.toSemilatticeSup
CompleteLattice.toLattice
instCompleteLattice
comap
GaloisInsertion.l_sup_u
map_surjective_of_surjective 📖mathematicalDFunLike.coeSubmonoid
map
GaloisInsertion.l_surjective
mem_comap 📖mathematicalSubmonoid
SetLike.instMembership
instSetLike
comap
DFunLike.coe
mem_map 📖mathematicalSubmonoid
SetLike.instMembership
instSetLike
map
DFunLike.coe
mem_map_equiv 📖mathematicalSubmonoid
SetLike.instMembership
instSetLike
map
MonoidHom
MulOneClass.toMulOne
MonoidHom.instFunLike
MonoidHom.instMonoidHomClass
MulEquiv.toMonoidHom
DFunLike.coe
MulEquiv
MulOne.toMul
EquivLike.toFunLike
MulEquiv.instEquivLike
MulEquiv.symm
Set.mem_image_equiv
mem_map_iff_mem 📖mathematicalDFunLike.coeSubmonoid
SetLike.instMembership
instSetLike
map
Function.Injective.mem_set_image
mem_map_of_mem 📖mathematicalSubmonoid
SetLike.instMembership
instSetLike
map
DFunLike.coe
Set.mem_image_of_mem
mem_pi 📖mathematicalSubmonoid
Pi.mulOneClass
SetLike.instMembership
instSetLike
pi
mem_prod 📖mathematicalSubmonoid
Prod.instMulOneClass
SetLike.instMembership
instSetLike
prod
monotone_comap 📖mathematicalMonotone
Submonoid
PartialOrder.toPreorder
instPartialOrder
comap
GaloisConnection.monotone_u
gc_map_comap
monotone_map 📖mathematicalMonotone
Submonoid
PartialOrder.toPreorder
instPartialOrder
map
GaloisConnection.monotone_l
gc_map_comap
mrange_fst 📖mathematicalMonoidHom.mrange
Prod.instMulOneClass
MonoidHom
MulOneClass.toMulOne
MonoidHom.instFunLike
MonoidHom.instMonoidHomClass
MonoidHom.fst
Top.top
Submonoid
instTop
MonoidHom.mrange_eq_top_of_surjective
MonoidHom.instMonoidHomClass
Prod.fst_surjective
mrange_inl 📖mathematicalMonoidHom.mrange
Prod.instMulOneClass
MonoidHom
MulOneClass.toMulOne
MonoidHom.instFunLike
MonoidHom.instMonoidHomClass
MonoidHom.inl
prod
Top.top
Submonoid
instTop
Bot.bot
instBot
MonoidHom.instMonoidHomClass
MonoidHom.mrange_eq_map
map_inl
mrange_inl' 📖mathematicalMonoidHom.mrange
Prod.instMulOneClass
MonoidHom
MulOneClass.toMulOne
MonoidHom.instFunLike
MonoidHom.instMonoidHomClass
MonoidHom.inl
comap
MonoidHom.snd
Bot.bot
Submonoid
instBot
MonoidHom.instMonoidHomClass
mrange_inl
top_prod
mrange_inl_sup_mrange_inr 📖mathematicalSubmonoid
Prod.instMulOneClass
SemilatticeSup.toMax
Lattice.toSemilatticeSup
CompleteLattice.toLattice
instCompleteLattice
MonoidHom.mrange
MonoidHom
MulOneClass.toMulOne
MonoidHom.instFunLike
MonoidHom.instMonoidHomClass
MonoidHom.inl
MonoidHom.inr
Top.top
instTop
MonoidHom.instMonoidHomClass
mrange_inl
mrange_inr
prod_bot_sup_bot_prod
top_prod_top
mrange_inr 📖mathematicalMonoidHom.mrange
Prod.instMulOneClass
MonoidHom
MulOneClass.toMulOne
MonoidHom.instFunLike
MonoidHom.instMonoidHomClass
MonoidHom.inr
prod
Bot.bot
Submonoid
instBot
Top.top
instTop
MonoidHom.instMonoidHomClass
MonoidHom.mrange_eq_map
map_inr
mrange_inr' 📖mathematicalMonoidHom.mrange
Prod.instMulOneClass
MonoidHom
MulOneClass.toMulOne
MonoidHom.instFunLike
MonoidHom.instMonoidHomClass
MonoidHom.inr
comap
MonoidHom.fst
Bot.bot
Submonoid
instBot
MonoidHom.instMonoidHomClass
mrange_inr
prod_top
mrange_snd 📖mathematicalMonoidHom.mrange
Prod.instMulOneClass
MonoidHom
MulOneClass.toMulOne
MonoidHom.instFunLike
MonoidHom.instMonoidHomClass
MonoidHom.snd
Top.top
Submonoid
instTop
MonoidHom.mrange_eq_top_of_surjective
MonoidHom.instMonoidHomClass
Prod.snd_surjective
mrange_subtype 📖mathematicalMonoidHom.mrange
Submonoid
SetLike.instMembership
instSetLike
toMulOneClass
MonoidHom
MulOneClass.toMulOne
MonoidHom.instFunLike
MonoidHom.instMonoidHomClass
subtype
SetLike.coe_injective
MonoidHom.instMonoidHomClass
MonoidHom.coe_mrange
Subtype.range_coe
mulSingle_mem_pi 📖mathematicalSubmonoid
Pi.mulOneClass
SetLike.instMembership
instSetLike
pi
Pi.mulSingle
MulOne.toOne
MulOneClass.toMulOne
Set.update_mem_pi_iff_of_mem
OneMemClass.one_mem
SubmonoidClass.toOneMemClass
instSubmonoidClass
nontrivial_iff_exists_ne_one 📖mathematicalNontrivial
Submonoid
SetLike.instMembership
instSetLike
one_mem
nontrivial_iff_exists_ne
pi_bot 📖mathematicalpi
Set.univ
Bot.bot
Submonoid
instBot
Pi.mulOneClass
ext
pi_empty 📖mathematicalpi
Set
Set.instEmptyCollection
Top.top
Submonoid
Pi.mulOneClass
instTop
ext
instIsEmptyFalse
pi_eq_bot_iff 📖mathematicalpi
Set.univ
Bot.bot
Submonoid
Pi.mulOneClass
instBot
Set.univ_pi_eq_singleton_iff
pi_top 📖mathematicalpi
Top.top
Submonoid
instTop
Pi.mulOneClass
ext
prod_bot_sup_bot_prod 📖mathematicalSubmonoid
Prod.instMulOneClass
SemilatticeSup.toMax
Lattice.toSemilatticeSup
CompleteLattice.toLattice
instCompleteLattice
prod
Bot.bot
instBot
le_antisymm
sup_le
prod_mono
le_refl
bot_le
MulMemClass.mul_mem
SubmonoidClass.toMulMemClass
instSubmonoidClass
le_sup_left
Set.mem_singleton
le_sup_right
Prod.fst_mul_snd
prod_eq_bot_iff 📖mathematicalprod
Bot.bot
Submonoid
Prod.instMulOneClass
instBot
MonoidHom.instMonoidHomClass
GaloisConnection.le_iff_le
gc_map_comap
MonoidHom.mker_inl
MonoidHom.mker_inr
prod_eq_top_iff 📖mathematicalprod
Top.top
Submonoid
Prod.instMulOneClass
instTop
MonoidHom.instMonoidHomClass
mrange_fst
mrange_snd
prod_le_iff 📖mathematicalSubmonoid
Prod.instMulOneClass
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
prod
map
MonoidHom
MulOneClass.toMulOne
MonoidHom.instFunLike
MonoidHom.instMonoidHomClass
MonoidHom.inl
MonoidHom.inr
MonoidHom.instMonoidHomClass
one_mem
mul_one
one_mul
mul_mem
prod_mono 📖mathematicalSubmonoid
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
Prod.instMulOneClass
prod
Set.prod_mono
prod_top 📖mathematicalprod
Top.top
Submonoid
instTop
comap
Prod.instMulOneClass
MonoidHom
MulOneClass.toMulOne
MonoidHom.instFunLike
MonoidHom.instMonoidHomClass
MonoidHom.fst
ext
MonoidHom.instMonoidHomClass
subtype_comp_inclusion 📖mathematicalSubmonoid
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
MonoidHom.comp
SetLike.instMembership
instSetLike
MulOneClass.toMulOne
toMulOneClass
subtype
inclusion
surjOn_iff_le_map 📖mathematicalSet.SurjOn
DFunLike.coe
MonoidHom
MulOneClass.toMulOne
MonoidHom.instFunLike
SetLike.coe
Submonoid
instSetLike
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
map
MonoidHom.instMonoidHomClass
toAddSubmonoid'_closure 📖mathematicalDFunLike.coe
OrderIso
Submonoid
Multiplicative
Multiplicative.mulOneClass
AddSubmonoid
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
AddSubmonoid.instPartialOrder
instFunLikeOrderIso
toAddSubmonoid'
closure
AddSubmonoid.closure
Set.preimage
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
Multiplicative.ofAdd
le_antisymm
GaloisConnection.l_le
OrderIso.to_galoisConnection
closure_le
AddSubmonoid.subset_closure
AddSubmonoid.closure_le
subset_closure
toAddSubmonoid_closure 📖mathematicalDFunLike.coe
OrderIso
Submonoid
AddSubmonoid
Additive
Additive.addZeroClass
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
AddSubmonoid.instPartialOrder
instFunLikeOrderIso
toAddSubmonoid
closure
AddSubmonoid.closure
Set.preimage
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
Additive.toMul
le_antisymm
OrderIso.le_symm_apply
closure_le
AddSubmonoid.subset_closure
AddSubmonoid.closure_le
subset_closure
topEquiv_apply 📖mathematicalDFunLike.coe
MulEquiv
Submonoid
SetLike.instMembership
instSetLike
Top.top
instTop
mul
MulOne.toMul
MulOneClass.toMulOne
EquivLike.toFunLike
MulEquiv.instEquivLike
topEquiv
topEquiv_symm_apply_coe 📖mathematicalSubmonoid
SetLike.instMembership
instSetLike
Top.top
instTop
DFunLike.coe
MulEquiv
MulOne.toMul
MulOneClass.toMulOne
mul
EquivLike.toFunLike
MulEquiv.instEquivLike
MulEquiv.symm
topEquiv
topEquiv_toMonoidHom 📖mathematicalMonoidHomClass.toMonoidHom
Submonoid
SetLike.instMembership
instSetLike
Top.top
instTop
MulEquiv
mul
MulOne.toMul
MulOneClass.toMulOne
toMulOneClass
EquivLike.toFunLike
MulEquiv.instEquivLike
MulEquivClass.instMonoidHomClass
MulEquiv.instMulEquivClass
topEquiv
subtype
MulEquivClass.instMonoidHomClass
MulEquiv.instMulEquivClass
top_prod 📖mathematicalprod
Top.top
Submonoid
instTop
comap
Prod.instMulOneClass
MonoidHom
MulOneClass.toMulOne
MonoidHom.instFunLike
MonoidHom.instMonoidHomClass
MonoidHom.snd
ext
MonoidHom.instMonoidHomClass
top_prod_top 📖mathematicalprod
Top.top
Submonoid
instTop
Prod.instMulOneClass
MonoidHom.instMonoidHomClass
top_prod
comap_top
unitsTypeEquivIsUnitSubmonoid_apply_coe 📖mathematicalSubmonoid
Monoid.toMulOneClass
SetLike.instMembership
instSetLike
IsUnit.submonoid
DFunLike.coe
MulEquiv
Units
Units.instMul
mul
EquivLike.toFunLike
MulEquiv.instEquivLike
unitsTypeEquivIsUnitSubmonoid
Units.val
val_inv_unitsTypeEquivIsUnitSubmonoid_symm_apply 📖mathematicalUnits.val
Units
Units.instInv
DFunLike.coe
MulEquiv
Submonoid
Monoid.toMulOneClass
SetLike.instMembership
instSetLike
IsUnit.submonoid
mul
Units.instMul
EquivLike.toFunLike
MulEquiv.instEquivLike
MulEquiv.symm
unitsTypeEquivIsUnitSubmonoid
val_unitsTypeEquivIsUnitSubmonoid_symm_apply 📖mathematicalUnits.val
DFunLike.coe
MulEquiv
Submonoid
Monoid.toMulOneClass
SetLike.instMembership
instSetLike
IsUnit.submonoid
Units
mul
Units.instMul
EquivLike.toFunLike
MulEquiv.instEquivLike
MulEquiv.symm
unitsTypeEquivIsUnitSubmonoid

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