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_addUnitsEquivAddUnitsType_apply_coe, val_addUnitsEquivAddUnitsType_symm_apply_coe, val_mem_of_mem_addUnits, val_neg_addUnitsEquivAddUnitsType_apply_coe, val_neg_addUnitsEquivAddUnitsType_symm_apply_coe, 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_inv_unitsEquivUnitsType_apply_coe, val_inv_unitsEquivUnitsType_symm_apply_coe, val_mem_of_mem_units, val_unitsEquivUnitsType_apply_coe, val_unitsEquivUnitsType_symm_apply_coe, ofAddUnits_addUnits_gc, ofAddUnits_le_iff_le_addUnits, ofUnits_le_iff_le_units, ofUnits_units_gc
112
Total130

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
SetLike.instMembership
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_ofAddUnits
AddUnits.val
β€”AddUnits.ext
addUnit_of_mem_ofAddUnits_spec_mem πŸ“–mathematicalAddSubmonoid
AddMonoid.toAddZeroClass
SetLike.instMembership
AddSubmonoid.instSetLike
ofAddUnits
AddUnits
AddSubgroup
AddUnits.instAddGroup
SetLike.instMembership
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
SetLike.instMembership
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
SetLike.instMembership
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
IsAddUnit
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
SetLike.instMembership
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
SetLike.instMembership
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.leftInverse_u_l
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
28 mathmath: AddSubgroup.ofAddUnits_right_inverse, val_addUnitsEquivAddUnitsType_symm_apply_coe, 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, val_neg_addUnitsEquivAddUnitsType_symm_apply_coe, AddSubgroup.ofAddUnits_inf_addUnits, isOpen_addUnits, neg_mem_addUnits, addUnits_left_inverse, AddSubgroup.ofAddUnits_sup_addUnits, AddSubgroup.mem_addUnits_iff_val_mem, mem_addUnits_iff, add_mem_addUnits, ofAddUnits_addUnits_le, val_neg_addUnitsEquivAddUnitsType_apply_coe, addUnits_surjective, addUnits_top, val_addUnitsEquivAddUnitsType_apply_coe, AddSubgroup.addUnits_ofAddUnits_eq
addUnitsEquivAddUnitsType πŸ“–CompOp
4 mathmath: val_addUnitsEquivAddUnitsType_symm_apply_coe, val_neg_addUnitsEquivAddUnitsType_symm_apply_coe, val_neg_addUnitsEquivAddUnitsType_apply_coe, val_addUnitsEquivAddUnitsType_apply_coe
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.leftInverse_u_l
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
AddSubgroup
AddUnits.instAddGroup
SetLike.instMembership
AddSubgroup.instSetLike
addUnits
AddUnits.instAdd
β€”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
AddUnits
AddSubgroup
AddUnits.instAddGroup
SetLike.instMembership
AddSubgroup.instSetLike
addUnits
β€”β€”
mk_add_mk_neg_eq_zero πŸ“–mathematicalAddUnits
AddSubgroup
AddUnits.instAddGroup
SetLike.instMembership
AddSubgroup.instSetLike
addUnits
AddSubmonoid
AddMonoid.toAddZeroClass
SetLike.instMembership
instSetLike
add
DFunLike.coe
AddMonoidHom
AddUnits
AddZeroClass.toAddZero
AddUnits.instAddZeroClass
AddMonoidHom.instFunLike
AddUnits.coeHom
Set
Set.instMembership
SetLike.coe
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddUnits.instAddGroup
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
SetLike.instMembership
instSetLike
add
DFunLike.coe
AddMonoidHom
AddUnits
AddZeroClass.toAddZero
AddUnits.instAddZeroClass
AddMonoidHom.instFunLike
AddUnits.coeHom
NegZeroClass.toNeg
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
AddGroup.toSubtractionMonoid
AddUnits.instAddGroup
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
AddSubgroup
AddUnits.instAddGroup
SetLike.instMembership
AddSubgroup.instSetLike
addUnits
AddUnits.instNeg
β€”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
SetLike.instMembership
instSetLike
AddUnits.val
AddUnits
AddUnits.instNeg
β€”β€”
ofAddUnits_addUnits_le πŸ“–mathematicalβ€”AddSubmonoid
AddMonoid.toAddZeroClass
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
AddSubgroup.ofAddUnits
addUnits
β€”β€”
val_addUnitsEquivAddUnitsType_apply_coe πŸ“–mathematicalβ€”AddSubmonoid
AddMonoid.toAddZeroClass
SetLike.instMembership
instSetLike
AddUnits.val
toAddMonoid
DFunLike.coe
AddEquiv
AddUnits
AddSubgroup
AddUnits.instAddGroup
AddSubgroup.instSetLike
addUnits
AddSubgroup.add
AddUnits.instAdd
EquivLike.toFunLike
AddEquiv.instEquivLike
addUnitsEquivAddUnitsType
AddMonoidHom
AddZeroClass.toAddZero
AddUnits.instAddZeroClass
AddMonoidHom.instFunLike
AddUnits.coeHom
β€”β€”
val_addUnitsEquivAddUnitsType_symm_apply_coe πŸ“–mathematicalβ€”AddUnits.val
AddUnits
AddSubgroup
AddUnits.instAddGroup
SetLike.instMembership
AddSubgroup.instSetLike
addUnits
DFunLike.coe
AddEquiv
AddSubmonoid
AddMonoid.toAddZeroClass
instSetLike
toAddMonoid
AddUnits.instAdd
AddSubgroup.add
EquivLike.toFunLike
AddEquiv.instEquivLike
AddEquiv.symm
addUnitsEquivAddUnitsType
β€”β€”
val_mem_of_mem_addUnits πŸ“–mathematicalAddUnits
AddSubgroup
AddUnits.instAddGroup
SetLike.instMembership
AddSubgroup.instSetLike
addUnits
AddSubmonoid
AddMonoid.toAddZeroClass
SetLike.instMembership
instSetLike
AddUnits.val
β€”β€”
val_neg_addUnitsEquivAddUnitsType_apply_coe πŸ“–mathematicalβ€”AddSubmonoid
AddMonoid.toAddZeroClass
SetLike.instMembership
instSetLike
AddUnits.val
toAddMonoid
AddUnits
AddUnits.instNeg
DFunLike.coe
AddEquiv
AddSubgroup
AddUnits.instAddGroup
AddSubgroup.instSetLike
addUnits
AddSubgroup.add
AddUnits.instAdd
EquivLike.toFunLike
AddEquiv.instEquivLike
addUnitsEquivAddUnitsType
AddMonoidHom
AddZeroClass.toAddZero
AddUnits.instAddZeroClass
AddMonoidHom.instFunLike
AddUnits.coeHom
NegZeroClass.toNeg
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
AddGroup.toSubtractionMonoid
β€”β€”
val_neg_addUnitsEquivAddUnitsType_symm_apply_coe πŸ“–mathematicalβ€”AddUnits.val
AddUnits
AddUnits.instNeg
AddSubgroup
AddUnits.instAddGroup
SetLike.instMembership
AddSubgroup.instSetLike
addUnits
DFunLike.coe
AddEquiv
AddSubmonoid
AddMonoid.toAddZeroClass
instSetLike
toAddMonoid
AddUnits.instAdd
AddSubgroup.add
EquivLike.toFunLike
AddEquiv.instEquivLike
AddEquiv.symm
addUnitsEquivAddUnitsType
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
SetLike.instMembership
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
SetLike.instMembership
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
IsUnit
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
SetLike.instMembership
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
SetLike.instMembership
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.leftInverse_u_l
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
SetLike.instMembership
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_ofUnits
Units.val
β€”Units.ext
unit_of_mem_ofUnits_spec_mem πŸ“–mathematicalSubmonoid
Monoid.toMulOneClass
SetLike.instMembership
Submonoid.instSetLike
ofUnits
Units
Subgroup
Units.instGroup
SetLike.instMembership
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
33 mathmath: units_iInf, ofUnits_le_iff_le_units, inv_mem_units_iff, units_bot, val_inv_unitsEquivUnitsType_symm_apply_coe, ofUnits_units_le, RestrictedProduct.coe_unitsEquiv_apply, inv_mem_units, MulChar.restrict_ofUnitHom, units_isCompact, units_top, isOpen_units, units_sInf, units_surjective, val_unitsEquivUnitsType_apply_coe, units_left_inverse, val_inv_unitsEquivUnitsType_apply_coe, ofUnits_units_gc, units_inf, Subgroup.ofUnits_inf_units, RestrictedProduct.unitsEquiv_apply, mem_units_iff, units_iInfβ‚‚, Subgroup.mem_iff_toUnits_mem_units, Subgroup.ofUnits_right_inverse, IsDedekindDomain.HeightOneSpectrum.adicCompletionIntegers.mem_units_iff_valued_eq_one, val_unitsEquivUnitsType_symm_apply_coe, Subgroup.mem_units_iff_val_mem, Subgroup.units_ofUnits_eq, units_mono, Subgroup.ofUnits_sup_units, mem_units_of_val_mem_inv_val_mem, mul_mem_units
unitsEquivIsUnitSubmonoid πŸ“–CompOpβ€”
unitsEquivUnitsType πŸ“–CompOp
5 mathmath: val_inv_unitsEquivUnitsType_symm_apply_coe, MulChar.restrict_ofUnitHom, val_unitsEquivUnitsType_apply_coe, val_inv_unitsEquivUnitsType_apply_coe, val_unitsEquivUnitsType_symm_apply_coe

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
Subgroup
Units.instGroup
SetLike.instMembership
Subgroup.instSetLike
units
Units.instInv
β€”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
SetLike.instMembership
instSetLike
Units.val
Units
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
Units
Subgroup
Units.instGroup
SetLike.instMembership
Subgroup.instSetLike
units
β€”β€”
mk_inv_mul_mk_eq_one πŸ“–mathematicalUnits
Subgroup
Units.instGroup
SetLike.instMembership
Subgroup.instSetLike
units
Submonoid
Monoid.toMulOneClass
SetLike.instMembership
instSetLike
mul
DFunLike.coe
MonoidHom
Units
MulOneClass.toMulOne
Units.instMulOneClass
MonoidHom.instFunLike
Units.coeHom
InvOneClass.toInv
DivInvOneMonoid.toInvOneClass
DivisionMonoid.toDivInvOneMonoid
Group.toDivisionMonoid
Units.instGroup
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
SetLike.instMembership
instSetLike
mul
DFunLike.coe
MonoidHom
Units
MulOneClass.toMulOne
Units.instMulOneClass
MonoidHom.instFunLike
Units.coeHom
Set
Set.instMembership
SetLike.coe
DivInvMonoid.toMonoid
Group.toDivInvMonoid
Units.instGroup
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
Subgroup
Units.instGroup
SetLike.instMembership
Subgroup.instSetLike
units
Units.instMul
β€”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.leftInverse_u_l
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_inv_unitsEquivUnitsType_apply_coe πŸ“–mathematicalβ€”Submonoid
Monoid.toMulOneClass
SetLike.instMembership
instSetLike
Units.val
toMonoid
Units
Units.instInv
DFunLike.coe
MulEquiv
Subgroup
Units.instGroup
Subgroup.instSetLike
units
Subgroup.mul
Units.instMul
EquivLike.toFunLike
MulEquiv.instEquivLike
unitsEquivUnitsType
MonoidHom
MulOneClass.toMulOne
Units.instMulOneClass
MonoidHom.instFunLike
Units.coeHom
InvOneClass.toInv
DivInvOneMonoid.toInvOneClass
DivisionMonoid.toDivInvOneMonoid
Group.toDivisionMonoid
β€”β€”
val_inv_unitsEquivUnitsType_symm_apply_coe πŸ“–mathematicalβ€”Units.val
Units
Units.instInv
Subgroup
Units.instGroup
SetLike.instMembership
Subgroup.instSetLike
units
DFunLike.coe
MulEquiv
Submonoid
Monoid.toMulOneClass
instSetLike
toMonoid
Units.instMul
Subgroup.mul
EquivLike.toFunLike
MulEquiv.instEquivLike
MulEquiv.symm
unitsEquivUnitsType
β€”β€”
val_mem_of_mem_units πŸ“–mathematicalUnits
Subgroup
Units.instGroup
SetLike.instMembership
Subgroup.instSetLike
units
Submonoid
Monoid.toMulOneClass
SetLike.instMembership
instSetLike
Units.val
β€”β€”
val_unitsEquivUnitsType_apply_coe πŸ“–mathematicalβ€”Submonoid
Monoid.toMulOneClass
SetLike.instMembership
instSetLike
Units.val
toMonoid
DFunLike.coe
MulEquiv
Units
Subgroup
Units.instGroup
Subgroup.instSetLike
units
Subgroup.mul
Units.instMul
EquivLike.toFunLike
MulEquiv.instEquivLike
unitsEquivUnitsType
MonoidHom
MulOneClass.toMulOne
Units.instMulOneClass
MonoidHom.instFunLike
Units.coeHom
β€”β€”
val_unitsEquivUnitsType_symm_apply_coe πŸ“–mathematicalβ€”Units.val
Units
Subgroup
Units.instGroup
SetLike.instMembership
Subgroup.instSetLike
units
DFunLike.coe
MulEquiv
Submonoid
Monoid.toMulOneClass
instSetLike
toMonoid
Units.instMul
Subgroup.mul
EquivLike.toFunLike
MulEquiv.instEquivLike
MulEquiv.symm
unitsEquivUnitsType
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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