Documentation Verification Report

Units

📁 Source: Mathlib/Algebra/Group/Commute/Units.lean

Statistics

MetricCount
DefinitionsleftOfAdd, ofNSMul, ofNSMulEqZero, rightOfAdd, leftOfMul, ofPow, ofPowEqOne, rightOfMul
8
TheoremsaddUnits_neg_left, addUnits_neg_left_iff, addUnits_neg_right, addUnits_neg_right_iff, addUnits_of_val, addUnits_val, addUnits_val_iff, addUnits_zsmul_left, addUnits_zsmul_right, add_neg_eq_add_neg_iff_of_isAddUnit, isAddUnit_add_iff, neg_add_eq_neg_add_iff_of_isAddUnit, sub_eq_sub_iff_of_isAddUnit, addCommute_iff_add_neg_cancel, addCommute_iff_add_neg_cancel_assoc, addCommute_iff_neg_add_cancel, addCommute_iff_neg_add_cancel_assoc, nsmul_ofNSMulEqZero, val_neg_ofNSMulEqZero, val_ofNSMulEqZero, div_eq_div_iff_of_isUnit, inv_mul_eq_inv_mul_iff_of_isUnit, isUnit_mul_iff, mul_inv_eq_mul_inv_iff_of_isUnit, units_inv_left, units_inv_left_iff, units_inv_right, units_inv_right_iff, units_of_val, units_val, units_val_iff, units_zpow_left, units_zpow_right, of_nsmul_eq_zero, of_pow_eq_one, commute_iff_inv_mul_cancel, commute_iff_inv_mul_cancel_assoc, commute_iff_mul_inv_cancel, commute_iff_mul_inv_cancel_assoc, pow_ofPowEqOne, val_inv_ofPowEqOne, val_ofPowEqOne, isAddUnit_add_self_iff, isAddUnit_nsmul_iff, isAddUnit_nsmul_succ_iff, isUnit_mul_self_iff, isUnit_pow_iff, isUnit_pow_iff_of_not_isUnit, isUnit_pow_succ_iff
49
Total57

AddCommute

Theorems

NameKindAssumesProvesValidatesDepends On
addUnits_neg_left 📖mathematicalAddCommute
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddUnits.val
AddUnits
AddUnits.instNeg
AddSemiconjBy.addUnits_neg_symm_left
addUnits_neg_left_iff 📖mathematicalAddCommute
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddUnits.val
AddUnits
AddUnits.instNeg
AddSemiconjBy.addUnits_neg_symm_left_iff
addUnits_neg_right 📖mathematicalAddCommute
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddUnits.val
AddUnits
AddUnits.instNeg
AddSemiconjBy.addUnits_neg_right
addUnits_neg_right_iff 📖mathematicalAddCommute
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddUnits.val
AddUnits
AddUnits.instNeg
AddSemiconjBy.addUnits_neg_right_iff
addUnits_of_val 📖mathematicalAddCommute
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddUnits.val
AddUnits
AddUnits.instAdd
AddSemiconjBy.addUnits_of_val
addUnits_val 📖mathematicalAddCommute
AddUnits
AddUnits.instAdd
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddUnits.val
AddSemiconjBy.addUnits_val
addUnits_val_iff 📖mathematicalAddCommute
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddUnits.val
AddUnits
AddUnits.instAdd
AddSemiconjBy.addUnits_val_iff
addUnits_zsmul_left 📖mathematicalAddCommute
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddUnits.val
AddUnits
SubNegMonoid.toZSMul
AddUnits.instSubNegAddMonoid
symm
addUnits_zsmul_right
addUnits_zsmul_right 📖mathematicalAddCommute
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddUnits.val
AddUnits
SubNegMonoid.toZSMul
AddUnits.instSubNegAddMonoid
AddSemiconjBy.addUnits_zsmul_right
add_neg_eq_add_neg_iff_of_isAddUnit 📖mathematicalAddCommute
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
SubtractionMonoid.toSubNegMonoid
IsAddUnit
NegZeroClass.toNeg
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
sub_eq_add_neg
sub_eq_sub_iff_of_isAddUnit
isAddUnit_add_iff 📖mathematicalAddCommute
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
IsAddUnitAddUnits.isAddUnit
IsAddUnit.add
neg_add_eq_neg_add_iff_of_isAddUnit 📖mathematicalAddCommute
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
SubtractionMonoid.toSubNegMonoid
IsAddUnit
NegZeroClass.toNeg
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
IsAddUnit.add
add_assoc
IsAddUnit.add_neg_cancel
add_zero
left_comm
symm
sub_eq_sub_iff_of_isAddUnit 📖mathematicalAddCommute
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
SubtractionMonoid.toSubNegMonoid
IsAddUnit
SubNegMonoid.toSubIsAddUnit.add
add_assoc
IsAddUnit.sub_add_cancel
right_comm

AddUnits

Definitions

NameCategoryTheorems
leftOfAdd 📖CompOp
ofNSMul 📖CompOp
ofNSMulEqZero 📖CompOp
3 mathmath: val_ofNSMulEqZero, nsmul_ofNSMulEqZero, val_neg_ofNSMulEqZero
rightOfAdd 📖CompOp

Theorems

NameKindAssumesProvesValidatesDepends On
addCommute_iff_add_neg_cancel 📖mathematicalAddCommute
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
val
AddUnits
instNeg
add_neg_eq_iff_eq_add
AddCommute.eq_1
AddSemiconjBy.eq_1
addCommute_iff_add_neg_cancel_assoc 📖mathematicalAddCommute
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
val
AddUnits
instNeg
addCommute_iff_add_neg_cancel
add_assoc
addCommute_iff_neg_add_cancel 📖mathematicalAddCommute
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
val
AddUnits
instNeg
add_assoc
neg_add_eq_iff_eq_add
AddCommute.eq_1
AddSemiconjBy.eq_1
addCommute_iff_neg_add_cancel_assoc 📖mathematicalAddCommute
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
val
AddUnits
instNeg
addCommute_iff_neg_add_cancel
add_assoc
nsmul_ofNSMulEqZero 📖mathematicalAddMonoid.toNatSMul
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddUnits
instAddMonoid
ofNSMulEqZero
instZero
ext
val_neg_ofNSMulEqZero 📖mathematicalAddMonoid.toNatSMul
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
val
AddUnits
instNeg
ofNSMulEqZero
neg_zero
add_zero
val_ofNSMulEqZero 📖mathematicalAddMonoid.toNatSMul
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
val
ofNSMulEqZero

Commute

Theorems

NameKindAssumesProvesValidatesDepends On
div_eq_div_iff_of_isUnit 📖mathematicalCommute
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
DivisionMonoid.toDivInvMonoid
IsUnit
DivInvMonoid.toDivIsUnit.mul
mul_assoc
IsUnit.div_mul_cancel
right_comm
inv_mul_eq_inv_mul_iff_of_isUnit 📖mathematicalCommute
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
DivisionMonoid.toDivInvMonoid
IsUnit
InvOneClass.toInv
DivInvOneMonoid.toInvOneClass
DivisionMonoid.toDivInvOneMonoid
IsUnit.mul
mul_assoc
IsUnit.mul_inv_cancel
mul_one
left_comm
symm
isUnit_mul_iff 📖mathematicalCommute
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
IsUnitUnits.isUnit
IsUnit.mul
mul_inv_eq_mul_inv_iff_of_isUnit 📖mathematicalCommute
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
DivisionMonoid.toDivInvMonoid
IsUnit
InvOneClass.toInv
DivInvOneMonoid.toInvOneClass
DivisionMonoid.toDivInvOneMonoid
div_eq_mul_inv
div_eq_div_iff_of_isUnit
units_inv_left 📖mathematicalCommute
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
Units.val
Units
Units.instInv
SemiconjBy.units_inv_symm_left
units_inv_left_iff 📖mathematicalCommute
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
Units.val
Units
Units.instInv
SemiconjBy.units_inv_symm_left_iff
units_inv_right 📖mathematicalCommute
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
Units.val
Units
Units.instInv
SemiconjBy.units_inv_right
units_inv_right_iff 📖mathematicalCommute
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
Units.val
Units
Units.instInv
SemiconjBy.units_inv_right_iff
units_of_val 📖mathematicalCommute
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
Units.val
Units
Units.instMul
SemiconjBy.units_of_val
units_val 📖mathematicalCommute
Units
Units.instMul
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
Units.val
SemiconjBy.units_val
units_val_iff 📖mathematicalCommute
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
Units.val
Units
Units.instMul
SemiconjBy.units_val_iff
units_zpow_left 📖mathematicalCommute
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
Units.val
Units
DivInvMonoid.toZPow
Units.instDivInvMonoid
symm
units_zpow_right
units_zpow_right 📖mathematicalCommute
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
Units.val
Units
DivInvMonoid.toZPow
Units.instDivInvMonoid
SemiconjBy.units_zpow_right

IsAddUnit

Theorems

NameKindAssumesProvesValidatesDepends On
of_nsmul_eq_zero 📖mathematicalAddMonoid.toNatSMul
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
IsAddUnitAddUnits.isAddUnit

IsUnit

Theorems

NameKindAssumesProvesValidatesDepends On
of_pow_eq_one 📖mathematicalMonoid.toNatPow
MulOne.toOne
MulOneClass.toMulOne
Monoid.toMulOneClass
IsUnitUnits.isUnit

Units

Definitions

NameCategoryTheorems
leftOfMul 📖CompOp
ofPow 📖CompOp
ofPowEqOne 📖CompOp
3 mathmath: pow_ofPowEqOne, val_inv_ofPowEqOne, val_ofPowEqOne
rightOfMul 📖CompOp

Theorems

NameKindAssumesProvesValidatesDepends On
commute_iff_inv_mul_cancel 📖mathematicalCommute
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
val
Units
instInv
mul_assoc
inv_mul_eq_iff_eq_mul
Commute.eq_1
SemiconjBy.eq_1
commute_iff_inv_mul_cancel_assoc 📖mathematicalCommute
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
val
Units
instInv
commute_iff_inv_mul_cancel
mul_assoc
commute_iff_mul_inv_cancel 📖mathematicalCommute
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
val
Units
instInv
mul_inv_eq_iff_eq_mul
Commute.eq_1
SemiconjBy.eq_1
commute_iff_mul_inv_cancel_assoc 📖mathematicalCommute
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
val
Units
instInv
commute_iff_mul_inv_cancel
mul_assoc
pow_ofPowEqOne 📖mathematicalMonoid.toNatPow
MulOne.toOne
MulOneClass.toMulOne
Monoid.toMulOneClass
Units
instMonoid
ofPowEqOne
instOne
ext
val_inv_ofPowEqOne 📖mathematicalMonoid.toNatPow
MulOne.toOne
MulOneClass.toMulOne
Monoid.toMulOneClass
val
Units
instInv
ofPowEqOne
inv_one
mul_one
val_ofPowEqOne 📖mathematicalMonoid.toNatPow
MulOne.toOne
MulOneClass.toMulOne
Monoid.toMulOneClass
val
ofPowEqOne

(root)

Theorems

NameKindAssumesProvesValidatesDepends On
isAddUnit_add_self_iff 📖mathematicalIsAddUnit
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommute.isAddUnit_add_iff
AddCommute.refl
isAddUnit_nsmul_iff 📖mathematicalIsAddUnit
AddMonoid.toNatSMul
AddUnits.isAddUnit
IsAddUnit.nsmul
isAddUnit_nsmul_succ_iff 📖mathematicalIsAddUnit
AddMonoid.toNatSMul
isAddUnit_nsmul_iff
isUnit_mul_self_iff 📖mathematicalIsUnit
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
Commute.isUnit_mul_iff
Commute.refl
isUnit_pow_iff 📖mathematicalIsUnit
Monoid.toNatPow
Units.isUnit
IsUnit.pow
isUnit_pow_iff_of_not_isUnit 📖mathematicalIsUnitMonoid.toNatPowpow_zero
isUnit_pow_succ_iff 📖mathematicalIsUnit
Monoid.toNatPow
isUnit_pow_iff

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