Documentation Verification Report

Units

πŸ“ Source: Mathlib/Algebra/Group/Submonoid/Units.lean

Statistics

MetricCount
DefinitionsaddUnit_of_mem_ofAddUnits, addUnitsEquivSelf, ofAddUnits, ofAddUnitsEquivType, ofAddUnitsTopEquiv, addUnits, addUnitsEquivAddUnitsType, addUnitsEquivIsAddUnitAddSubmonoid, ofUnits, ofUnitsEquivType, ofUnitsTopEquiv, unit_of_mem_ofUnits, unitsEquivSelf, units, unitsEquivIsUnitSubmonoid, unitsEquivUnitsType, ofAddUnits_addUnits_gci, ofUnits_units_gci
18
TheoremsaddUnit_eq_addUnit_of_mem_ofAddUnits, addUnit_mem_of_mem_ofAddUnits, addUnit_of_mem_ofAddUnits_spec_eq_of_val_mem, addUnit_of_mem_ofAddUnits_spec_mem, addUnit_of_mem_ofAddUnits_spec_val_eq_of_mem, addUnits_ofAddUnits_eq, exists_mem_ofAddUnits_val_eq, isAddUnit_of_mem_ofAddUnits, mem_addUnits_iff_val_mem, mem_iff_toAddUnits_mem_addUnits, mem_ofAddUnits, mem_ofAddUnits_iff, mem_ofAddUnits_iff_exists_isAddUnit, mem_ofAddUnits_iff_toAddUnits_mem, mem_ofAddUnits_of_isAddUnit_of_addUnit_mem, mem_of_mem_val_ofAddUnits, ofAddUnits_bot, ofAddUnits_iSup, ofAddUnits_iSupβ‚‚, ofAddUnits_inf, ofAddUnits_inf_addUnits, ofAddUnits_injective, ofAddUnits_mono, ofAddUnits_right_inverse, ofAddUnits_sSup, ofAddUnits_strictMono, ofAddUnits_sup_addUnits, val_mem_ofAddUnits_iff_mem, addUnits_bot, addUnits_iInf, addUnits_iInfβ‚‚, addUnits_inf, addUnits_left_inverse, addUnits_mono, addUnits_sInf, addUnits_surjective, addUnits_top, add_mem_addUnits, coe_neg_val_add_coe_val, coe_val_add_coe_neg_val, mem_addUnits_iff, mem_addUnits_of_val_mem_neg_val_mem, mk_add_mk_neg_eq_zero, mk_neg_add_mk_eq_zero, neg_mem_addUnits, neg_mem_addUnits_iff, neg_val_mem_of_mem_addUnits, ofAddUnits_addUnits_le, val_mem_of_mem_addUnits, exists_mem_ofUnits_val_eq, isUnit_of_mem_ofUnits, mem_iff_toUnits_mem_units, mem_ofUnits, mem_ofUnits_iff, mem_ofUnits_iff_exists_isUnit, mem_ofUnits_iff_toUnits_mem, mem_ofUnits_of_isUnit_of_unit_mem, mem_of_mem_val_ofUnits, mem_units_iff_val_mem, ofUnits_bot, ofUnits_iSup, ofUnits_iSupβ‚‚, ofUnits_inf, ofUnits_inf_units, ofUnits_injective, ofUnits_le_ofUnits_iff, ofUnits_mono, ofUnits_right_inverse, ofUnits_sSup, ofUnits_strictMono, ofUnits_sup_units, unit_eq_unit_of_mem_ofUnits, unit_mem_of_mem_ofUnits, unit_of_mem_ofUnits_spec_eq_of_val_mem, unit_of_mem_ofUnits_spec_mem, unit_of_mem_ofUnits_spec_val_eq_of_mem, units_ofUnits_eq, val_mem_ofUnits_iff_mem, coe_inv_val_mul_coe_val, coe_val_mul_coe_inv_val, instSubsingletonUnits, inv_mem_units, inv_mem_units_iff, inv_val_mem_of_mem_units, mem_units_iff, mem_units_of_val_mem_inv_val_mem, mk_inv_mul_mk_eq_one, mk_mul_mk_inv_eq_one, mul_mem_units, ofUnits_units_le, units_bot, units_iInf, units_iInfβ‚‚, units_inf, units_left_inverse, units_mono, units_sInf, units_surjective, units_top, val_mem_of_mem_units, ofAddUnits_addUnits_gc, ofAddUnits_le_iff_le_addUnits, ofUnits_le_iff_le_units, ofUnits_units_gc
104
Total122

AddSubgroup

Definitions

NameCategoryTheorems
addUnit_of_mem_ofAddUnits πŸ“–CompOp
4 mathmath: addUnit_eq_addUnit_of_mem_ofAddUnits, addUnit_of_mem_ofAddUnits_spec_eq_of_val_mem, addUnit_of_mem_ofAddUnits_spec_mem, addUnit_of_mem_ofAddUnits_spec_val_eq_of_mem
addUnitsEquivSelf πŸ“–CompOpβ€”
ofAddUnits πŸ“–CompOp
22 mathmath: ofAddUnits_right_inverse, ofAddUnits_bot, ofAddUnits_addUnits_gc, ofAddUnits_le_iff_le_addUnits, mem_ofAddUnits_iff_toAddUnits_mem, ofAddUnits_injective, ofAddUnits_sSup, ofAddUnits_inf, mem_ofAddUnits, ofAddUnits_mono, mem_ofAddUnits_iff_exists_isAddUnit, mem_ofAddUnits_of_isAddUnit_of_addUnit_mem, ofAddUnits_iSupβ‚‚, ofAddUnits_inf_addUnits, ofAddUnits_strictMono, val_mem_ofAddUnits_iff_mem, AddSubmonoid.addUnits_left_inverse, ofAddUnits_sup_addUnits, mem_ofAddUnits_iff, AddSubmonoid.ofAddUnits_addUnits_le, ofAddUnits_iSup, addUnits_ofAddUnits_eq
ofAddUnitsEquivType πŸ“–CompOpβ€”
ofAddUnitsTopEquiv πŸ“–CompOpβ€”

Theorems

NameKindAssumesProvesValidatesDepends On
addUnit_eq_addUnit_of_mem_ofAddUnits πŸ“–mathematicalIsAddUnit
AddSubmonoid
AddMonoid.toAddZeroClass
SetLike.instMembership
AddSubmonoid.instSetLike
ofAddUnits
IsAddUnit.addUnit
addUnit_of_mem_ofAddUnits
β€”AddUnits.ext
addUnit_mem_of_mem_ofAddUnits πŸ“–mathematicalIsAddUnit
AddSubmonoid
AddMonoid.toAddZeroClass
SetLike.instMembership
AddSubmonoid.instSetLike
ofAddUnits
AddUnits
AddSubgroup
AddUnits.instAddGroup
instSetLike
IsAddUnit.addUnit
β€”addUnit_of_mem_ofAddUnits_spec_mem
addUnit_eq_addUnit_of_mem_ofAddUnits
addUnit_of_mem_ofAddUnits_spec_eq_of_val_mem πŸ“–mathematicalAddSubmonoid
AddMonoid.toAddZeroClass
SetLike.instMembership
AddSubmonoid.instSetLike
ofAddUnits
AddUnits.val
addUnit_of_mem_ofAddUnitsβ€”AddUnits.ext
addUnit_of_mem_ofAddUnits_spec_mem πŸ“–mathematicalAddSubmonoid
AddMonoid.toAddZeroClass
SetLike.instMembership
AddSubmonoid.instSetLike
ofAddUnits
AddUnits
AddSubgroup
AddUnits.instAddGroup
instSetLike
addUnit_of_mem_ofAddUnits
β€”mem_of_mem_val_ofAddUnits
addUnit_of_mem_ofAddUnits_spec_val_eq_of_mem πŸ“–mathematicalAddSubmonoid
AddMonoid.toAddZeroClass
SetLike.instMembership
AddSubmonoid.instSetLike
ofAddUnits
AddUnits.val
addUnit_of_mem_ofAddUnits
β€”β€”
addUnits_ofAddUnits_eq πŸ“–mathematicalβ€”AddSubmonoid.addUnits
ofAddUnits
β€”ext
AddUnits.ext
neg_mem
exists_mem_ofAddUnits_val_eq πŸ“–mathematicalAddSubmonoid
AddMonoid.toAddZeroClass
SetLike.instMembership
AddSubmonoid.instSetLike
ofAddUnits
AddUnits
AddSubgroup
AddUnits.instAddGroup
instSetLike
AddUnits.val
β€”β€”
isAddUnit_of_mem_ofAddUnits πŸ“–mathematicalAddSubmonoid
AddMonoid.toAddZeroClass
SetLike.instMembership
AddSubmonoid.instSetLike
ofAddUnits
IsAddUnitβ€”β€”
mem_addUnits_iff_val_mem πŸ“–mathematicalβ€”AddUnits
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddSubgroup
AddUnits.instAddGroup
SetLike.instMembership
instSetLike
AddSubmonoid.addUnits
toAddSubmonoid
AddUnits.val
β€”AddSubmonoid.mem_addUnits_iff
mem_toAddSubmonoid
AddUnits.val_neg_eq_neg_val
neg_mem_iff
AddSubgroupClass.toNegMemClass
instAddSubgroupClass
mem_iff_toAddUnits_mem_addUnits πŸ“–mathematicalβ€”AddUnits
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddSubgroup
AddUnits.instAddGroup
SetLike.instMembership
instSetLike
AddSubmonoid.addUnits
toAddSubmonoid
DFunLike.coe
AddEquiv
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddUnits.instAdd
EquivLike.toFunLike
AddEquiv.instEquivLike
toAddUnits
β€”mem_addUnits_iff_val_mem
mem_ofAddUnits πŸ“–mathematicalAddUnits
AddSubgroup
AddUnits.instAddGroup
SetLike.instMembership
instSetLike
AddUnits.val
AddSubmonoid
AddMonoid.toAddZeroClass
AddSubmonoid.instSetLike
ofAddUnits
β€”β€”
mem_ofAddUnits_iff πŸ“–mathematicalβ€”AddSubmonoid
AddMonoid.toAddZeroClass
SetLike.instMembership
AddSubmonoid.instSetLike
ofAddUnits
AddUnits
AddSubgroup
AddUnits.instAddGroup
instSetLike
AddUnits.val
β€”β€”
mem_ofAddUnits_iff_exists_isAddUnit πŸ“–mathematicalβ€”AddSubmonoid
AddMonoid.toAddZeroClass
SetLike.instMembership
AddSubmonoid.instSetLike
ofAddUnits
AddUnits
AddSubgroup
AddUnits.instAddGroup
instSetLike
IsAddUnit.addUnit
β€”isAddUnit_of_mem_ofAddUnits
addUnit_mem_of_mem_ofAddUnits
mem_ofAddUnits_of_isAddUnit_of_addUnit_mem
mem_ofAddUnits_iff_toAddUnits_mem πŸ“–mathematicalβ€”AddSubmonoid
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
SetLike.instMembership
AddSubmonoid.instSetLike
ofAddUnits
AddUnits
AddSubgroup
AddUnits.instAddGroup
instSetLike
DFunLike.coe
AddEquiv
AddZero.toAdd
AddZeroClass.toAddZero
AddUnits.instAdd
EquivLike.toFunLike
AddEquiv.instEquivLike
toAddUnits
β€”mem_ofAddUnits_iff
Function.Surjective.exists
AddEquiv.surjective
mem_ofAddUnits_of_isAddUnit_of_addUnit_mem πŸ“–mathematicalIsAddUnit
AddUnits
AddSubgroup
AddUnits.instAddGroup
SetLike.instMembership
instSetLike
IsAddUnit.addUnit
AddSubmonoid
AddMonoid.toAddZeroClass
AddSubmonoid.instSetLike
ofAddUnits
β€”mem_ofAddUnits
IsAddUnit.addUnit_spec
mem_of_mem_val_ofAddUnits πŸ“–mathematicalAddSubmonoid
AddMonoid.toAddZeroClass
SetLike.instMembership
AddSubmonoid.instSetLike
ofAddUnits
AddUnits.val
AddUnits
AddSubgroup
AddUnits.instAddGroup
instSetLike
β€”AddUnits.ext
ofAddUnits_bot πŸ“–mathematicalβ€”ofAddUnits
Bot.bot
AddSubgroup
AddUnits
AddUnits.instAddGroup
instBot
AddSubmonoid
AddMonoid.toAddZeroClass
AddSubmonoid.instBot
β€”GaloisConnection.l_bot
ofAddUnits_addUnits_gc
ofAddUnits_iSup πŸ“–mathematicalβ€”ofAddUnits
iSup
AddSubgroup
AddUnits
AddUnits.instAddGroup
ConditionallyCompletePartialOrderSup.toSupSet
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
CompleteLattice.toConditionallyCompleteLattice
instCompleteLattice
AddSubmonoid
AddMonoid.toAddZeroClass
AddSubmonoid.instCompleteLattice
β€”GaloisConnection.l_iSup
ofAddUnits_addUnits_gc
ofAddUnits_iSupβ‚‚ πŸ“–mathematicalβ€”ofAddUnits
iSup
AddSubgroup
AddUnits
AddUnits.instAddGroup
ConditionallyCompletePartialOrderSup.toSupSet
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
CompleteLattice.toConditionallyCompleteLattice
instCompleteLattice
AddSubmonoid
AddMonoid.toAddZeroClass
AddSubmonoid.instCompleteLattice
β€”GaloisConnection.l_iSupβ‚‚
ofAddUnits_addUnits_gc
ofAddUnits_inf πŸ“–mathematicalβ€”ofAddUnits
AddSubgroup
AddUnits
AddUnits.instAddGroup
SemilatticeSup.toMax
Lattice.toSemilatticeSup
ConditionallyCompleteLattice.toLattice
CompleteLattice.toConditionallyCompleteLattice
instCompleteLattice
AddSubmonoid
AddMonoid.toAddZeroClass
AddSubmonoid.instCompleteLattice
β€”GaloisConnection.l_sup
ofAddUnits_addUnits_gc
ofAddUnits_inf_addUnits πŸ“–mathematicalβ€”AddSubmonoid.addUnits
AddSubmonoid
AddMonoid.toAddZeroClass
AddSubmonoid.instMin
ofAddUnits
AddSubgroup
AddUnits
AddUnits.instAddGroup
instMin
β€”GaloisCoinsertion.u_inf_l
ofAddUnits_injective πŸ“–mathematicalβ€”AddSubgroup
AddUnits
AddUnits.instAddGroup
AddSubmonoid
AddMonoid.toAddZeroClass
ofAddUnits
β€”GaloisCoinsertion.l_injective
ofAddUnits_mono πŸ“–mathematicalβ€”Monotone
AddSubgroup
AddUnits
AddUnits.instAddGroup
AddSubmonoid
AddMonoid.toAddZeroClass
PartialOrder.toPreorder
instPartialOrder
AddSubmonoid.instPartialOrder
ofAddUnits
β€”β€”
ofAddUnits_right_inverse πŸ“–mathematicalβ€”AddSubmonoid
AddMonoid.toAddZeroClass
AddSubgroup
AddUnits
AddUnits.instAddGroup
ofAddUnits
AddSubmonoid.addUnits
β€”GaloisCoinsertion.u_l_leftInverse
ofAddUnits_sSup πŸ“–mathematicalβ€”ofAddUnits
SupSet.sSup
AddSubgroup
AddUnits
AddUnits.instAddGroup
ConditionallyCompletePartialOrderSup.toSupSet
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
CompleteLattice.toConditionallyCompleteLattice
instCompleteLattice
iSup
AddSubmonoid
AddMonoid.toAddZeroClass
AddSubmonoid.instCompleteLattice
Set
Set.instMembership
β€”GaloisConnection.l_sSup
ofAddUnits_addUnits_gc
ofAddUnits_strictMono πŸ“–mathematicalβ€”StrictMono
AddSubgroup
AddUnits
AddUnits.instAddGroup
AddSubmonoid
AddMonoid.toAddZeroClass
PartialOrder.toPreorder
instPartialOrder
AddSubmonoid.instPartialOrder
ofAddUnits
β€”GaloisCoinsertion.strictMono_l
ofAddUnits_sup_addUnits πŸ“–mathematicalβ€”AddSubmonoid.addUnits
AddSubmonoid
AddMonoid.toAddZeroClass
SemilatticeSup.toMax
Lattice.toSemilatticeSup
ConditionallyCompleteLattice.toLattice
CompleteLattice.toConditionallyCompleteLattice
AddSubmonoid.instCompleteLattice
ofAddUnits
AddSubgroup
AddUnits
AddUnits.instAddGroup
instCompleteLattice
β€”GaloisCoinsertion.u_sup_l
val_mem_ofAddUnits_iff_mem πŸ“–mathematicalβ€”AddSubmonoid
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
SetLike.instMembership
AddSubmonoid.instSetLike
ofAddUnits
AddUnits.val
AddUnits
AddSubgroup
AddUnits.instAddGroup
instSetLike
β€”mem_ofAddUnits_iff_toAddUnits_mem
toAddUnits_val_apply

AddSubmonoid

Definitions

NameCategoryTheorems
addUnits πŸ“–CompOp
22 mathmath: AddSubgroup.ofAddUnits_right_inverse, ofAddUnits_addUnits_gc, addUnits_iInfβ‚‚, addUnits_sInf, AddSubgroup.mem_iff_toAddUnits_mem_addUnits, ofAddUnits_le_iff_le_addUnits, addUnits_iInf, neg_mem_addUnits_iff, addUnits_mono, addUnits_bot, addUnits_inf, mem_addUnits_of_val_mem_neg_val_mem, AddSubgroup.ofAddUnits_inf_addUnits, isOpen_addUnits, addUnits_left_inverse, AddSubgroup.ofAddUnits_sup_addUnits, AddSubgroup.mem_addUnits_iff_val_mem, mem_addUnits_iff, ofAddUnits_addUnits_le, addUnits_surjective, addUnits_top, AddSubgroup.addUnits_ofAddUnits_eq
addUnitsEquivAddUnitsType πŸ“–CompOpβ€”
addUnitsEquivIsAddUnitAddSubmonoid πŸ“–CompOpβ€”

Theorems

NameKindAssumesProvesValidatesDepends On
addUnits_bot πŸ“–mathematicalβ€”addUnits
Bot.bot
AddSubmonoid
AddMonoid.toAddZeroClass
instBot
AddSubgroup
AddUnits
AddUnits.instAddGroup
AddSubgroup.instBot
β€”GaloisCoinsertion.u_bot
addUnits_iInf πŸ“–mathematicalβ€”addUnits
iInf
AddSubmonoid
AddMonoid.toAddZeroClass
instInfSet
AddSubgroup
AddUnits
AddUnits.instAddGroup
AddSubgroup.instInfSet
β€”GaloisConnection.u_iInf
ofAddUnits_addUnits_gc
addUnits_iInfβ‚‚ πŸ“–mathematicalβ€”addUnits
iInf
AddSubmonoid
AddMonoid.toAddZeroClass
instInfSet
AddSubgroup
AddUnits
AddUnits.instAddGroup
AddSubgroup.instInfSet
β€”GaloisConnection.u_iInfβ‚‚
ofAddUnits_addUnits_gc
addUnits_inf πŸ“–mathematicalβ€”addUnits
AddSubmonoid
AddMonoid.toAddZeroClass
instMin
AddSubgroup
AddUnits
AddUnits.instAddGroup
AddSubgroup.instMin
β€”GaloisConnection.u_inf
ofAddUnits_addUnits_gc
addUnits_left_inverse πŸ“–mathematicalβ€”AddSubgroup
AddUnits
AddUnits.instAddGroup
AddSubmonoid
AddMonoid.toAddZeroClass
addUnits
AddSubgroup.ofAddUnits
β€”GaloisCoinsertion.u_l_leftInverse
addUnits_mono πŸ“–mathematicalβ€”Monotone
AddSubmonoid
AddMonoid.toAddZeroClass
AddSubgroup
AddUnits
AddUnits.instAddGroup
PartialOrder.toPreorder
instPartialOrder
AddSubgroup.instPartialOrder
addUnits
β€”β€”
addUnits_sInf πŸ“–mathematicalβ€”addUnits
InfSet.sInf
AddSubmonoid
AddMonoid.toAddZeroClass
instInfSet
iInf
AddSubgroup
AddUnits
AddUnits.instAddGroup
AddSubgroup.instInfSet
Set
Set.instMembership
β€”GaloisConnection.u_sInf
ofAddUnits_addUnits_gc
addUnits_surjective πŸ“–mathematicalβ€”AddSubmonoid
AddMonoid.toAddZeroClass
AddSubgroup
AddUnits
AddUnits.instAddGroup
addUnits
β€”GaloisCoinsertion.u_surjective
addUnits_top πŸ“–mathematicalβ€”addUnits
Top.top
AddSubmonoid
AddMonoid.toAddZeroClass
instTop
AddSubgroup
AddUnits
AddUnits.instAddGroup
AddSubgroup.instTop
β€”GaloisConnection.u_top
ofAddUnits_addUnits_gc
add_mem_addUnits πŸ“–mathematicalAddUnits
AddSubgroup
AddUnits.instAddGroup
SetLike.instMembership
AddSubgroup.instSetLike
addUnits
AddUnits.instAddβ€”AddMemClass.add_mem
AddSubmonoidClass.toAddMemClass
AddSubgroupClass.toAddSubmonoidClass
AddSubgroup.instAddSubgroupClass
coe_neg_val_add_coe_val πŸ“–mathematicalβ€”AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddSubmonoid
SetLike.instMembership
instSetLike
AddUnits.val
toAddMonoid
AddUnits
AddUnits.instNeg
AddZero.toZero
β€”DFunLike.congr_arg
AddUnits.neg_add
coe_val_add_coe_neg_val πŸ“–mathematicalβ€”AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddSubmonoid
SetLike.instMembership
instSetLike
AddUnits.val
toAddMonoid
AddUnits
AddUnits.instNeg
AddZero.toZero
β€”DFunLike.congr_arg
AddUnits.add_neg
mem_addUnits_iff πŸ“–mathematicalβ€”AddUnits
AddSubgroup
AddUnits.instAddGroup
SetLike.instMembership
AddSubgroup.instSetLike
addUnits
AddSubmonoid
AddMonoid.toAddZeroClass
instSetLike
AddUnits.val
AddUnits.instNeg
β€”β€”
mem_addUnits_of_val_mem_neg_val_mem πŸ“–mathematicalAddSubmonoid
AddMonoid.toAddZeroClass
SetLike.instMembership
instSetLike
AddUnits.val
AddUnits
AddUnits.instNeg
AddSubgroup
AddUnits.instAddGroup
AddSubgroup.instSetLike
addUnits
β€”β€”
mk_add_mk_neg_eq_zero πŸ“–mathematicalAddUnits
AddSubgroup
AddUnits.instAddGroup
SetLike.instMembership
AddSubgroup.instSetLike
addUnits
AddSubmonoid
AddMonoid.toAddZeroClass
instSetLike
add
DFunLike.coe
AddMonoidHom
AddZeroClass.toAddZero
AddUnits.instAddZeroClass
AddMonoidHom.instFunLike
AddUnits.coeHom
Set
Set.instMembership
SetLike.coe
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
comap
neg
NegZeroClass.toNeg
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
AddGroup.toSubtractionMonoid
zero
β€”AddUnits.add_neg
mk_neg_add_mk_eq_zero πŸ“–mathematicalAddUnits
AddSubgroup
AddUnits.instAddGroup
SetLike.instMembership
AddSubgroup.instSetLike
addUnits
AddSubmonoid
AddMonoid.toAddZeroClass
instSetLike
add
DFunLike.coe
AddMonoidHom
AddZeroClass.toAddZero
AddUnits.instAddZeroClass
AddMonoidHom.instFunLike
AddUnits.coeHom
NegZeroClass.toNeg
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
AddGroup.toSubtractionMonoid
Set
Set.instMembership
SetLike.coe
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
comap
neg
zero
β€”AddUnits.neg_add
neg_mem_addUnits πŸ“–mathematicalAddUnits
AddSubgroup
AddUnits.instAddGroup
SetLike.instMembership
AddSubgroup.instSetLike
addUnits
AddUnits.instNegβ€”NegMemClass.neg_mem
AddSubgroupClass.toNegMemClass
AddSubgroup.instAddSubgroupClass
neg_mem_addUnits_iff πŸ“–mathematicalβ€”AddUnits
AddSubgroup
AddUnits.instAddGroup
SetLike.instMembership
AddSubgroup.instSetLike
addUnits
AddUnits.instNeg
β€”neg_mem_iff
AddSubgroupClass.toNegMemClass
AddSubgroup.instAddSubgroupClass
neg_val_mem_of_mem_addUnits πŸ“–mathematicalAddUnits
AddSubgroup
AddUnits.instAddGroup
SetLike.instMembership
AddSubgroup.instSetLike
addUnits
AddSubmonoid
AddMonoid.toAddZeroClass
instSetLike
AddUnits.val
AddUnits.instNeg
β€”β€”
ofAddUnits_addUnits_le πŸ“–mathematicalβ€”AddSubmonoid
AddMonoid.toAddZeroClass
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
AddSubgroup.ofAddUnits
addUnits
β€”β€”
val_mem_of_mem_addUnits πŸ“–mathematicalAddUnits
AddSubgroup
AddUnits.instAddGroup
SetLike.instMembership
AddSubgroup.instSetLike
addUnits
AddSubmonoid
AddMonoid.toAddZeroClass
instSetLike
AddUnits.val
β€”β€”

Subgroup

Definitions

NameCategoryTheorems
ofUnits πŸ“–CompOp
23 mathmath: ofUnits_bot, ofUnits_le_iff_le_units, mem_ofUnits_iff_exists_isUnit, ofUnits_strictMono, Submonoid.ofUnits_units_le, mem_ofUnits_iff, ofUnits_le_ofUnits_iff, mem_ofUnits_of_isUnit_of_unit_mem, Submonoid.units_left_inverse, mem_ofUnits_iff_toUnits_mem, ofUnits_inf, ofUnits_units_gc, ofUnits_mono, ofUnits_inf_units, mem_ofUnits, val_mem_ofUnits_iff_mem, ofUnits_injective, ofUnits_iSupβ‚‚, ofUnits_sSup, ofUnits_right_inverse, ofUnits_iSup, units_ofUnits_eq, ofUnits_sup_units
ofUnitsEquivType πŸ“–CompOpβ€”
ofUnitsTopEquiv πŸ“–CompOpβ€”
unit_of_mem_ofUnits πŸ“–CompOp
4 mathmath: unit_of_mem_ofUnits_spec_val_eq_of_mem, unit_eq_unit_of_mem_ofUnits, unit_of_mem_ofUnits_spec_eq_of_val_mem, unit_of_mem_ofUnits_spec_mem
unitsEquivSelf πŸ“–CompOpβ€”

Theorems

NameKindAssumesProvesValidatesDepends On
exists_mem_ofUnits_val_eq πŸ“–mathematicalSubmonoid
Monoid.toMulOneClass
SetLike.instMembership
Submonoid.instSetLike
ofUnits
Units
Subgroup
Units.instGroup
instSetLike
Units.val
β€”β€”
isUnit_of_mem_ofUnits πŸ“–mathematicalSubmonoid
Monoid.toMulOneClass
SetLike.instMembership
Submonoid.instSetLike
ofUnits
IsUnitβ€”β€”
mem_iff_toUnits_mem_units πŸ“–mathematicalβ€”Units
DivInvMonoid.toMonoid
Group.toDivInvMonoid
Subgroup
Units.instGroup
SetLike.instMembership
instSetLike
Submonoid.units
toSubmonoid
DFunLike.coe
MulEquiv
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
Units.instMul
EquivLike.toFunLike
MulEquiv.instEquivLike
toUnits
β€”β€”
mem_ofUnits πŸ“–mathematicalUnits
Subgroup
Units.instGroup
SetLike.instMembership
instSetLike
Units.val
Submonoid
Monoid.toMulOneClass
Submonoid.instSetLike
ofUnits
β€”β€”
mem_ofUnits_iff πŸ“–mathematicalβ€”Submonoid
Monoid.toMulOneClass
SetLike.instMembership
Submonoid.instSetLike
ofUnits
Units
Subgroup
Units.instGroup
instSetLike
Units.val
β€”β€”
mem_ofUnits_iff_exists_isUnit πŸ“–mathematicalβ€”Submonoid
Monoid.toMulOneClass
SetLike.instMembership
Submonoid.instSetLike
ofUnits
Units
Subgroup
Units.instGroup
instSetLike
IsUnit.unit
β€”isUnit_of_mem_ofUnits
unit_mem_of_mem_ofUnits
mem_ofUnits_of_isUnit_of_unit_mem
mem_ofUnits_iff_toUnits_mem πŸ“–mathematicalβ€”Submonoid
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
SetLike.instMembership
Submonoid.instSetLike
ofUnits
Units
Subgroup
Units.instGroup
instSetLike
DFunLike.coe
MulEquiv
MulOne.toMul
MulOneClass.toMulOne
Units.instMul
EquivLike.toFunLike
MulEquiv.instEquivLike
toUnits
β€”Function.Surjective.exists
MulEquiv.surjective
mem_ofUnits_of_isUnit_of_unit_mem πŸ“–mathematicalIsUnit
Units
Subgroup
Units.instGroup
SetLike.instMembership
instSetLike
IsUnit.unit
Submonoid
Monoid.toMulOneClass
Submonoid.instSetLike
ofUnits
β€”mem_ofUnits
IsUnit.unit_spec
mem_of_mem_val_ofUnits πŸ“–mathematicalSubmonoid
Monoid.toMulOneClass
SetLike.instMembership
Submonoid.instSetLike
ofUnits
Units.val
Units
Subgroup
Units.instGroup
instSetLike
β€”Units.ext
mem_units_iff_val_mem πŸ“–mathematicalβ€”Units
DivInvMonoid.toMonoid
Group.toDivInvMonoid
Subgroup
Units.instGroup
SetLike.instMembership
instSetLike
Submonoid.units
toSubmonoid
Units.val
β€”Units.val_inv_eq_inv_val
SubgroupClass.toInvMemClass
instSubgroupClass
ofUnits_bot πŸ“–mathematicalβ€”ofUnits
Bot.bot
Subgroup
Units
Units.instGroup
instBot
Submonoid
Monoid.toMulOneClass
Submonoid.instBot
β€”GaloisConnection.l_bot
ofUnits_units_gc
ofUnits_iSup πŸ“–mathematicalβ€”ofUnits
iSup
Subgroup
Units
Units.instGroup
ConditionallyCompletePartialOrderSup.toSupSet
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
CompleteLattice.toConditionallyCompleteLattice
instCompleteLattice
Submonoid
Monoid.toMulOneClass
Submonoid.instCompleteLattice
β€”GaloisConnection.l_iSup
ofUnits_units_gc
ofUnits_iSupβ‚‚ πŸ“–mathematicalβ€”ofUnits
iSup
Subgroup
Units
Units.instGroup
ConditionallyCompletePartialOrderSup.toSupSet
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
CompleteLattice.toConditionallyCompleteLattice
instCompleteLattice
Submonoid
Monoid.toMulOneClass
Submonoid.instCompleteLattice
β€”GaloisConnection.l_iSupβ‚‚
ofUnits_units_gc
ofUnits_inf πŸ“–mathematicalβ€”ofUnits
Subgroup
Units
Units.instGroup
SemilatticeSup.toMax
Lattice.toSemilatticeSup
ConditionallyCompleteLattice.toLattice
CompleteLattice.toConditionallyCompleteLattice
instCompleteLattice
Submonoid
Monoid.toMulOneClass
Submonoid.instCompleteLattice
β€”GaloisConnection.l_sup
ofUnits_units_gc
ofUnits_inf_units πŸ“–mathematicalβ€”Submonoid.units
Submonoid
Monoid.toMulOneClass
Submonoid.instMin
ofUnits
Subgroup
Units
Units.instGroup
instMin
β€”GaloisCoinsertion.u_inf_l
ofUnits_injective πŸ“–mathematicalβ€”Subgroup
Units
Units.instGroup
Submonoid
Monoid.toMulOneClass
ofUnits
β€”GaloisCoinsertion.l_injective
ofUnits_le_ofUnits_iff πŸ“–mathematicalβ€”Submonoid
Monoid.toMulOneClass
Preorder.toLE
PartialOrder.toPreorder
Submonoid.instPartialOrder
ofUnits
Subgroup
Units
Units.instGroup
instPartialOrder
β€”GaloisCoinsertion.l_le_l_iff
ofUnits_mono πŸ“–mathematicalβ€”Monotone
Subgroup
Units
Units.instGroup
Submonoid
Monoid.toMulOneClass
PartialOrder.toPreorder
instPartialOrder
Submonoid.instPartialOrder
ofUnits
β€”β€”
ofUnits_right_inverse πŸ“–mathematicalβ€”Submonoid
Monoid.toMulOneClass
Subgroup
Units
Units.instGroup
ofUnits
Submonoid.units
β€”GaloisCoinsertion.u_l_leftInverse
ofUnits_sSup πŸ“–mathematicalβ€”ofUnits
SupSet.sSup
Subgroup
Units
Units.instGroup
ConditionallyCompletePartialOrderSup.toSupSet
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
CompleteLattice.toConditionallyCompleteLattice
instCompleteLattice
iSup
Submonoid
Monoid.toMulOneClass
Submonoid.instCompleteLattice
Set
Set.instMembership
β€”GaloisConnection.l_sSup
ofUnits_units_gc
ofUnits_strictMono πŸ“–mathematicalβ€”StrictMono
Subgroup
Units
Units.instGroup
Submonoid
Monoid.toMulOneClass
PartialOrder.toPreorder
instPartialOrder
Submonoid.instPartialOrder
ofUnits
β€”GaloisCoinsertion.strictMono_l
ofUnits_sup_units πŸ“–mathematicalβ€”Submonoid.units
Submonoid
Monoid.toMulOneClass
SemilatticeSup.toMax
Lattice.toSemilatticeSup
ConditionallyCompleteLattice.toLattice
CompleteLattice.toConditionallyCompleteLattice
Submonoid.instCompleteLattice
ofUnits
Subgroup
Units
Units.instGroup
instCompleteLattice
β€”GaloisCoinsertion.u_sup_l
unit_eq_unit_of_mem_ofUnits πŸ“–mathematicalIsUnit
Submonoid
Monoid.toMulOneClass
SetLike.instMembership
Submonoid.instSetLike
ofUnits
IsUnit.unit
unit_of_mem_ofUnits
β€”Units.ext
unit_mem_of_mem_ofUnits πŸ“–mathematicalIsUnit
Submonoid
Monoid.toMulOneClass
SetLike.instMembership
Submonoid.instSetLike
ofUnits
Units
Subgroup
Units.instGroup
instSetLike
IsUnit.unit
β€”unit_of_mem_ofUnits_spec_mem
unit_eq_unit_of_mem_ofUnits
unit_of_mem_ofUnits_spec_eq_of_val_mem πŸ“–mathematicalSubmonoid
Monoid.toMulOneClass
SetLike.instMembership
Submonoid.instSetLike
ofUnits
Units.val
unit_of_mem_ofUnitsβ€”Units.ext
unit_of_mem_ofUnits_spec_mem πŸ“–mathematicalSubmonoid
Monoid.toMulOneClass
SetLike.instMembership
Submonoid.instSetLike
ofUnits
Units
Subgroup
Units.instGroup
instSetLike
unit_of_mem_ofUnits
β€”mem_of_mem_val_ofUnits
unit_of_mem_ofUnits_spec_val_eq_of_mem πŸ“–mathematicalSubmonoid
Monoid.toMulOneClass
SetLike.instMembership
Submonoid.instSetLike
ofUnits
Units.val
unit_of_mem_ofUnits
β€”β€”
units_ofUnits_eq πŸ“–mathematicalβ€”Submonoid.units
ofUnits
β€”ext
Units.ext
inv_mem
val_mem_ofUnits_iff_mem πŸ“–mathematicalβ€”Submonoid
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
SetLike.instMembership
Submonoid.instSetLike
ofUnits
Units.val
Units
Subgroup
Units.instGroup
instSetLike
β€”toUnits_val_apply

Submonoid

Definitions

NameCategoryTheorems
units πŸ“–CompOp
24 mathmath: units_iInf, ofUnits_le_iff_le_units, inv_mem_units_iff, units_bot, ofUnits_units_le, units_isCompact, units_top, isOpen_units, units_sInf, units_surjective, units_left_inverse, ofUnits_units_gc, units_inf, Subgroup.ofUnits_inf_units, mem_units_iff, units_iInfβ‚‚, Subgroup.mem_iff_toUnits_mem_units, Subgroup.ofUnits_right_inverse, IsDedekindDomain.HeightOneSpectrum.adicCompletionIntegers.mem_units_iff_valued_eq_one, Subgroup.mem_units_iff_val_mem, Subgroup.units_ofUnits_eq, units_mono, Subgroup.ofUnits_sup_units, mem_units_of_val_mem_inv_val_mem
unitsEquivIsUnitSubmonoid πŸ“–CompOpβ€”
unitsEquivUnitsType πŸ“–CompOpβ€”

Theorems

NameKindAssumesProvesValidatesDepends On
coe_inv_val_mul_coe_val πŸ“–mathematicalβ€”MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
Submonoid
SetLike.instMembership
instSetLike
Units.val
toMonoid
Units
Units.instInv
MulOne.toOne
β€”DFunLike.congr_arg
Units.inv_mul
coe_val_mul_coe_inv_val πŸ“–mathematicalβ€”MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
Submonoid
SetLike.instMembership
instSetLike
Units.val
toMonoid
Units
Units.instInv
MulOne.toOne
β€”DFunLike.congr_arg
Units.mul_inv
instSubsingletonUnits πŸ“–mathematicalβ€”Units
Submonoid
Monoid.toMulOneClass
SetLike.instMembership
instSetLike
toMonoid
β€”Subsingleton.units_of_isUnit
IsUnit.eq_one
IsUnit.map
MonoidHom.instMonoidHomClass
inv_mem_units πŸ“–mathematicalUnits
Subgroup
Units.instGroup
SetLike.instMembership
Subgroup.instSetLike
units
Units.instInvβ€”InvMemClass.inv_mem
SubgroupClass.toInvMemClass
Subgroup.instSubgroupClass
inv_mem_units_iff πŸ“–mathematicalβ€”Units
Subgroup
Units.instGroup
SetLike.instMembership
Subgroup.instSetLike
units
Units.instInv
β€”inv_mem_iff
SubgroupClass.toInvMemClass
Subgroup.instSubgroupClass
inv_val_mem_of_mem_units πŸ“–mathematicalUnits
Subgroup
Units.instGroup
SetLike.instMembership
Subgroup.instSetLike
units
Submonoid
Monoid.toMulOneClass
instSetLike
Units.val
Units.instInv
β€”β€”
mem_units_iff πŸ“–mathematicalβ€”Units
Subgroup
Units.instGroup
SetLike.instMembership
Subgroup.instSetLike
units
Submonoid
Monoid.toMulOneClass
instSetLike
Units.val
Units.instInv
β€”β€”
mem_units_of_val_mem_inv_val_mem πŸ“–mathematicalSubmonoid
Monoid.toMulOneClass
SetLike.instMembership
instSetLike
Units.val
Units
Units.instInv
Subgroup
Units.instGroup
Subgroup.instSetLike
units
β€”β€”
mk_inv_mul_mk_eq_one πŸ“–mathematicalUnits
Subgroup
Units.instGroup
SetLike.instMembership
Subgroup.instSetLike
units
Submonoid
Monoid.toMulOneClass
instSetLike
mul
DFunLike.coe
MonoidHom
MulOneClass.toMulOne
Units.instMulOneClass
MonoidHom.instFunLike
Units.coeHom
InvOneClass.toInv
DivInvOneMonoid.toInvOneClass
DivisionMonoid.toDivInvOneMonoid
Group.toDivisionMonoid
Set
Set.instMembership
SetLike.coe
DivInvMonoid.toMonoid
Group.toDivInvMonoid
comap
inv
one
β€”Units.inv_mul
mk_mul_mk_inv_eq_one πŸ“–mathematicalUnits
Subgroup
Units.instGroup
SetLike.instMembership
Subgroup.instSetLike
units
Submonoid
Monoid.toMulOneClass
instSetLike
mul
DFunLike.coe
MonoidHom
MulOneClass.toMulOne
Units.instMulOneClass
MonoidHom.instFunLike
Units.coeHom
Set
Set.instMembership
SetLike.coe
DivInvMonoid.toMonoid
Group.toDivInvMonoid
comap
inv
InvOneClass.toInv
DivInvOneMonoid.toInvOneClass
DivisionMonoid.toDivInvOneMonoid
Group.toDivisionMonoid
one
β€”Units.mul_inv
mul_mem_units πŸ“–mathematicalUnits
Subgroup
Units.instGroup
SetLike.instMembership
Subgroup.instSetLike
units
Units.instMulβ€”MulMemClass.mul_mem
SubmonoidClass.toMulMemClass
SubgroupClass.toSubmonoidClass
Subgroup.instSubgroupClass
ofUnits_units_le πŸ“–mathematicalβ€”Submonoid
Monoid.toMulOneClass
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
Subgroup.ofUnits
units
β€”β€”
units_bot πŸ“–mathematicalβ€”units
Bot.bot
Submonoid
Monoid.toMulOneClass
instBot
Subgroup
Units
Units.instGroup
Subgroup.instBot
β€”GaloisCoinsertion.u_bot
units_iInf πŸ“–mathematicalβ€”units
iInf
Submonoid
Monoid.toMulOneClass
instInfSet
Subgroup
Units
Units.instGroup
Subgroup.instInfSet
β€”GaloisConnection.u_iInf
ofUnits_units_gc
units_iInfβ‚‚ πŸ“–mathematicalβ€”units
iInf
Submonoid
Monoid.toMulOneClass
instInfSet
Subgroup
Units
Units.instGroup
Subgroup.instInfSet
β€”GaloisConnection.u_iInfβ‚‚
ofUnits_units_gc
units_inf πŸ“–mathematicalβ€”units
Submonoid
Monoid.toMulOneClass
instMin
Subgroup
Units
Units.instGroup
Subgroup.instMin
β€”GaloisConnection.u_inf
ofUnits_units_gc
units_left_inverse πŸ“–mathematicalβ€”Subgroup
Units
Units.instGroup
Submonoid
Monoid.toMulOneClass
units
Subgroup.ofUnits
β€”GaloisCoinsertion.u_l_leftInverse
units_mono πŸ“–mathematicalβ€”Monotone
Submonoid
Monoid.toMulOneClass
Subgroup
Units
Units.instGroup
PartialOrder.toPreorder
instPartialOrder
Subgroup.instPartialOrder
units
β€”β€”
units_sInf πŸ“–mathematicalβ€”units
InfSet.sInf
Submonoid
Monoid.toMulOneClass
instInfSet
iInf
Subgroup
Units
Units.instGroup
Subgroup.instInfSet
Set
Set.instMembership
β€”GaloisConnection.u_sInf
ofUnits_units_gc
units_surjective πŸ“–mathematicalβ€”Submonoid
Monoid.toMulOneClass
Subgroup
Units
Units.instGroup
units
β€”GaloisCoinsertion.u_surjective
units_top πŸ“–mathematicalβ€”units
Top.top
Submonoid
Monoid.toMulOneClass
instTop
Subgroup
Units
Units.instGroup
Subgroup.instTop
β€”GaloisConnection.u_top
ofUnits_units_gc
val_mem_of_mem_units πŸ“–mathematicalUnits
Subgroup
Units.instGroup
SetLike.instMembership
Subgroup.instSetLike
units
Submonoid
Monoid.toMulOneClass
instSetLike
Units.val
β€”β€”

(root)

Definitions

NameCategoryTheorems
ofAddUnits_addUnits_gci πŸ“–CompOpβ€”
ofUnits_units_gci πŸ“–CompOpβ€”

Theorems

NameKindAssumesProvesValidatesDepends On
ofAddUnits_addUnits_gc πŸ“–mathematicalβ€”GaloisConnection
AddSubgroup
AddUnits
AddUnits.instAddGroup
AddSubmonoid
AddMonoid.toAddZeroClass
PartialOrder.toPreorder
AddSubgroup.instPartialOrder
AddSubmonoid.instPartialOrder
AddSubgroup.ofAddUnits
AddSubmonoid.addUnits
β€”GaloisCoinsertion.gc
ofAddUnits_le_iff_le_addUnits πŸ“–mathematicalβ€”AddSubmonoid
AddMonoid.toAddZeroClass
Preorder.toLE
PartialOrder.toPreorder
AddSubmonoid.instPartialOrder
AddSubgroup.ofAddUnits
AddSubgroup
AddUnits
AddUnits.instAddGroup
AddSubgroup.instPartialOrder
AddSubmonoid.addUnits
β€”ofAddUnits_addUnits_gc
ofUnits_le_iff_le_units πŸ“–mathematicalβ€”Submonoid
Monoid.toMulOneClass
Preorder.toLE
PartialOrder.toPreorder
Submonoid.instPartialOrder
Subgroup.ofUnits
Subgroup
Units
Units.instGroup
Subgroup.instPartialOrder
Submonoid.units
β€”ofUnits_units_gc
ofUnits_units_gc πŸ“–mathematicalβ€”GaloisConnection
Subgroup
Units
Units.instGroup
Submonoid
Monoid.toMulOneClass
PartialOrder.toPreorder
Subgroup.instPartialOrder
Submonoid.instPartialOrder
Subgroup.ofUnits
Submonoid.units
β€”GaloisCoinsertion.gc

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