Documentation Verification Report

Basic

πŸ“ Source: Mathlib/Algebra/Order/Monoid/Unbundled/Basic.lean

Statistics

MetricCount
DefinitionsAddLECancellable, toAddLeftCancelSemigroup, toAddRightCancelSemigroup, toLeftCancelSemigroup, toRightCancelSemigroup, MulLECancellable
6
Theoremsadd, add_le_add_iff_left, add_le_add_iff_right, add_le_iff_nonpos_left, add_le_iff_nonpos_right, inj, inj_left, injective_left, isAddLeftRegular, le_add_iff_nonneg_left, le_add_iff_nonneg_right, of_add_left, of_add_right, toIsLeftCancelAdd, toIsRightCancelAdd, add, add_const, add_strictAnti, const_add, const_mul', mul', mul_const', mul_strictAnti', add, add_const, add_strictAnti, const_add, const_mul', mul', mul_const', mul_strictAnti', AddLECancellable, MulLECancellable, instAddLeftMono, add_lt_add, add_neg, add_neg', add_neg_of_neg_of_nonpos, add_neg_of_nonpos_of_neg, add_nonneg, add_nonpos, add_pos, add_pos', add_pos_of_nonneg_of_pos, add_pos_of_pos_of_nonneg, min_le_max_of_add_le_add, min_le_max_of_mul_le_mul, mul_le_one, mul_lt_mul, mul_lt_one, mul_lt_one', mul_lt_one_of_le_of_lt, mul_lt_one_of_lt_of_le, one_le_mul, one_lt_mul, one_lt_mul', one_lt_mul_of_le_of_lt, one_lt_mul_of_lt_of_le, add, add_const, add_strictMono, const_add, const_mul', mul', mul_const', mul_strictMono', add, add_const, add_strictMono, const_add, const_mul', mul', mul_const', mul_strictMono', inj, inj_left, injective_left, isLeftRegular, le_mul_iff_one_le_left, le_mul_iff_one_le_right, mul, mul_le_iff_le_one_left, mul_le_iff_le_one_right, mul_le_mul_iff_left, mul_le_mul_iff_right, of_mul_left, of_mul_right, toIsLeftCancelMul, toIsRightCancelMul, instMulLeftMono, add_lt_add, add_neg, add_neg', add_neg_of_neg_of_nonpos, add_neg_of_nonpos_of_neg, add_nonneg, add_nonpos, add_pos, add_pos', add_pos_of_nonneg_of_pos, add_pos_of_pos_of_nonneg, min_le_max_of_add_le_add, min_le_max_of_mul_le_mul, mul_le_one, mul_lt_mul, mul_lt_one, mul_lt_one', mul_lt_one_of_le_of_lt, mul_lt_one_of_lt_of_le, one_le_mul, one_lt_mul, one_lt_mul', one_lt_mul_of_le_of_lt, one_lt_mul_of_lt_of_le, add, add_antitone, add_const, const_add, const_mul', mul', mul_antitone', mul_const', add, add_antitone, add_const, const_add, const_mul', mul', mul_antitone', mul_const', add, add_const, add_monotone, const_add, const_mul', mul', mul_const', mul_monotone', add, add_const, add_monotone, const_add, const_mul', mul', mul_const', mul_monotone', addLECancellable_add, addLECancellable_zero, add_eq_add_iff_eq_and_eq, add_eq_zero_iff_of_nonneg, add_le_add, add_le_add_iff_left, add_le_add_iff_of_ge, add_le_add_iff_right, add_le_add_left, add_le_add_right, add_le_add_three, add_le_iff_nonpos_left, add_le_iff_nonpos_right, add_le_of_add_le_left, add_le_of_add_le_right, add_le_of_le_of_nonpos, add_le_of_nonpos_left, add_le_of_nonpos_of_le, add_le_of_nonpos_right, add_left_cancel'', add_left_inj_of_comparable, add_left_mono, add_left_strictMono, add_lt_add, add_lt_add_iff_left, add_lt_add_iff_right, add_lt_add_left, add_lt_add_of_le_of_lt, add_lt_add_of_lt_of_le, add_lt_add_of_lt_of_lt, add_lt_add_right, add_lt_iff_neg_left, add_lt_iff_neg_right, add_lt_of_add_lt_left, add_lt_of_add_lt_right, add_lt_of_le_of_neg, add_lt_of_lt_of_neg, add_lt_of_lt_of_neg', add_lt_of_lt_of_nonpos, add_lt_of_neg_left, add_lt_of_neg_of_le, add_lt_of_neg_of_lt, add_lt_of_neg_of_lt', add_lt_of_neg_right, add_lt_of_nonpos_of_lt, add_max, add_min, add_neg, add_neg', add_neg_of_neg_of_nonpos, add_neg_of_nonpos_of_neg, add_nonneg, add_nonpos, add_pos, add_pos', add_pos_of_nonneg_of_pos, add_pos_of_pos_of_nonneg, add_right_cancel'', add_right_inj_of_comparable, add_right_mono, add_right_strictMono, cmp_add_left, cmp_add_right, cmp_mul_left', cmp_mul_right', eq_one_of_mul_le_one_left, eq_one_of_mul_le_one_right, eq_one_of_one_le_mul_left, eq_one_of_one_le_mul_right, eq_zero_of_add_nonneg_left, eq_zero_of_add_nonneg_right, eq_zero_of_add_nonpos_left, eq_zero_of_add_nonpos_right, exists_square_le, instIsLeftCancelAddOfAddLeftReflectLE, instIsLeftCancelMulOfMulLeftReflectLE, instIsRightCancelAddOfAddRightReflectLE, instIsRightCancelMulOfMulRightReflectLE, le_add_iff_nonneg_left, le_add_iff_nonneg_right, le_add_of_le_add_left, le_add_of_le_add_right, le_add_of_le_of_nonneg, le_add_of_nonneg_left, le_add_of_nonneg_of_le, le_add_of_nonneg_right, le_mul_iff_one_le_left', le_mul_iff_one_le_right', le_mul_of_le_mul_left, le_mul_of_le_mul_right, le_mul_of_le_of_one_le, le_mul_of_one_le_left', le_mul_of_one_le_of_le, le_mul_of_one_le_right', le_of_add_le_add_left, le_of_add_le_add_right, le_of_add_le_of_nonneg_left, le_of_add_le_of_nonneg_right, le_of_le_add_of_nonpos_left, le_of_le_add_of_nonpos_right, le_of_le_mul_of_le_one_left, le_of_le_mul_of_le_one_right, le_of_mul_le_mul_left', le_of_mul_le_mul_right', le_of_mul_le_of_one_le_left, le_of_mul_le_of_one_le_right, le_one_of_mul_le_left, le_one_of_mul_le_right, lt_add_iff_pos_left, lt_add_iff_pos_right, lt_add_of_le_of_pos, lt_add_of_lt_add_left, lt_add_of_lt_add_right, lt_add_of_lt_of_nonneg, lt_add_of_lt_of_pos, lt_add_of_lt_of_pos', lt_add_of_nonneg_of_lt, lt_add_of_pos_left, lt_add_of_pos_of_le, lt_add_of_pos_of_lt, lt_add_of_pos_of_lt', lt_add_of_pos_right, lt_mul_iff_one_lt_left', lt_mul_iff_one_lt_right', lt_mul_of_le_of_one_lt, lt_mul_of_lt_mul_left, lt_mul_of_lt_mul_right, lt_mul_of_lt_of_one_le, lt_mul_of_lt_of_one_lt, lt_mul_of_lt_of_one_lt', lt_mul_of_one_le_of_lt, lt_mul_of_one_lt_left', lt_mul_of_one_lt_of_le, lt_mul_of_one_lt_of_lt, lt_mul_of_one_lt_of_lt', lt_mul_of_one_lt_right', lt_of_add_lt_add_left, lt_of_add_lt_add_right, lt_of_add_lt_of_nonneg_left, lt_of_add_lt_of_nonneg_right, lt_of_lt_add_of_nonpos_left, lt_of_lt_add_of_nonpos_right, lt_of_lt_mul_of_le_one_left, lt_of_lt_mul_of_le_one_right, lt_of_mul_lt_mul_left', lt_of_mul_lt_mul_right', lt_of_mul_lt_of_one_le_left, lt_of_mul_lt_of_one_le_right, lt_one_of_mul_lt_left, lt_one_of_mul_lt_right, max_add, max_add_add_le_max_add_max, max_mul, max_mul_mul_le_max_mul_max', min_add, min_add_min_le_min_add_add, min_le_max_of_add_le_add, min_le_max_of_mul_le_mul, min_lt_max_of_add_lt_add, min_lt_max_of_mul_lt_mul, min_mul, min_mul_min_le_min_mul_mul', mulLECancellable_mul, mulLECancellable_one, mul_eq_mul_iff_eq_and_eq, mul_eq_one_iff_of_one_le, mul_le_iff_le_one_left', mul_le_iff_le_one_right', mul_le_mul', mul_le_mul_iff_left, mul_le_mul_iff_of_ge, mul_le_mul_iff_right, mul_le_mul_left, mul_le_mul_left', mul_le_mul_right, mul_le_mul_right', mul_le_mul_three, mul_le_of_le_of_le_one, mul_le_of_le_one_left', mul_le_of_le_one_of_le, mul_le_of_le_one_right', mul_le_of_mul_le_left, mul_le_of_mul_le_right, mul_le_one', mul_left_cancel'', mul_left_inj_of_comparable, mul_left_mono, mul_left_strictMono, mul_lt_iff_lt_one_left', mul_lt_iff_lt_one_right', mul_lt_mul_iff_left, mul_lt_mul_iff_right, mul_lt_mul_left, mul_lt_mul_of_le_of_lt, mul_lt_mul_of_lt_of_le, mul_lt_mul_of_lt_of_lt, mul_lt_mul_right, mul_lt_of_le_of_lt_one, mul_lt_of_le_one_of_lt, mul_lt_of_lt_of_le_one, mul_lt_of_lt_of_lt_one, mul_lt_of_lt_of_lt_one', mul_lt_of_lt_one_left', mul_lt_of_lt_one_of_le, mul_lt_of_lt_one_of_lt, mul_lt_of_lt_one_of_lt', mul_lt_of_lt_one_right', mul_lt_of_mul_lt_left, mul_lt_of_mul_lt_right, mul_lt_one, mul_lt_one', mul_lt_one_of_le_of_lt, mul_lt_one_of_lt_of_le, mul_max, mul_min, mul_right_cancel'', mul_right_inj_of_comparable, mul_right_mono, mul_right_strictMono, neg_of_add_lt_left, neg_of_add_lt_right, nonneg_of_le_add_left, nonneg_of_le_add_right, nonpos_of_add_le_left, nonpos_of_add_le_right, one_le_mul, one_le_of_le_mul_left, one_le_of_le_mul_right, one_lt_mul', one_lt_mul'', one_lt_mul_of_le_of_lt', one_lt_mul_of_lt_of_le', one_lt_of_lt_mul_left, one_lt_of_lt_mul_right, pos_of_lt_add_left, pos_of_lt_add_right, trichotomy_of_add_eq_add, trichotomy_of_mul_eq_mul
384
Total390

AddLECancellable

Theorems

NameKindAssumesProvesValidatesDepends On
add πŸ“–mathematicalAddLECancellable
AddSemigroup.toAdd
AddLECancellable
AddSemigroup.toAdd
β€”add_assoc
add_le_add_iff_left πŸ“–β€”AddLECancellableβ€”β€”add_le_add_right
add_le_add_iff_right πŸ“–β€”AddLECancellableβ€”β€”add_le_add_iff_left
add_le_iff_nonpos_left πŸ“–mathematicalAddLECancellable
AddZero.toAdd
AddZeroClass.toAddZero
AddZero.toAdd
AddZeroClass.toAddZero
AddZero.toZero
β€”add_le_iff_nonpos_right
add_le_iff_nonpos_right πŸ“–mathematicalAddLECancellable
AddZero.toAdd
AddZeroClass.toAddZero
AddZero.toAdd
AddZeroClass.toAddZero
AddZero.toZero
β€”add_zero
add_le_add_iff_left
inj πŸ“–β€”AddLECancellable
Preorder.toLE
PartialOrder.toPreorder
β€”β€”Injective
inj_left πŸ“–β€”AddLECancellable
Preorder.toLE
PartialOrder.toPreorder
β€”β€”injective_left
injective_left πŸ“–β€”AddLECancellable
Preorder.toLE
PartialOrder.toPreorder
β€”β€”Injective
isAddLeftRegular πŸ“–mathematicalAddLECancellable
Preorder.toLE
PartialOrder.toPreorder
IsAddLeftRegularβ€”Injective
le_add_iff_nonneg_left πŸ“–mathematicalAddLECancellable
AddZero.toAdd
AddZeroClass.toAddZero
AddZero.toAdd
AddZeroClass.toAddZero
AddZero.toZero
β€”le_add_iff_nonneg_right
le_add_iff_nonneg_right πŸ“–mathematicalAddLECancellable
AddZero.toAdd
AddZeroClass.toAddZero
AddZero.toAdd
AddZeroClass.toAddZero
AddZero.toZero
β€”add_zero
add_le_add_iff_left
of_add_left πŸ“–mathematicalAddLECancellable
AddCommMagma.toAdd
AddCommSemigroup.toAddCommMagma
AddLECancellable
AddCommMagma.toAdd
AddCommSemigroup.toAddCommMagma
β€”of_add_right
add_comm
of_add_right πŸ“–mathematicalAddLECancellable
AddSemigroup.toAdd
AddLECancellable
AddSemigroup.toAdd
β€”add_assoc
add_le_add_right

AddLeftStrictMono

Theorems

NameKindAssumesProvesValidatesDepends On
toIsLeftCancelAdd πŸ“–mathematicalβ€”IsLeftCancelAddβ€”StrictMono.injective
add_right_strictMono

AddRightStrictMono

Theorems

NameKindAssumesProvesValidatesDepends On
toIsRightCancelAdd πŸ“–mathematicalβ€”IsRightCancelAddβ€”StrictMono.injective
add_left_strictMono

Antitone

Theorems

NameKindAssumesProvesValidatesDepends On
add πŸ“–mathematicalAntitoneAntitoneβ€”add_le_add
add_const πŸ“–mathematicalAntitoneAntitoneβ€”Monotone.comp_antitone
add_left_mono
add_strictAnti πŸ“–mathematicalAntitone
StrictAnti
StrictAntiβ€”add_lt_add_of_le_of_lt
LT.lt.le
const_add πŸ“–mathematicalAntitoneAntitoneβ€”Monotone.comp_antitone
add_right_mono
const_mul' πŸ“–mathematicalAntitoneAntitoneβ€”Monotone.comp_antitone
mul_right_mono
mul' πŸ“–mathematicalAntitoneAntitoneβ€”mul_le_mul'
mul_const' πŸ“–mathematicalAntitoneAntitoneβ€”Monotone.comp_antitone
mul_left_mono
mul_strictAnti' πŸ“–mathematicalAntitone
StrictAnti
StrictAntiβ€”mul_lt_mul_of_le_of_lt
LT.lt.le

AntitoneOn

Theorems

NameKindAssumesProvesValidatesDepends On
add πŸ“–mathematicalAntitoneOnAntitoneOnβ€”add_le_add
add_const πŸ“–mathematicalAntitoneOnAntitoneOnβ€”Monotone.comp_antitoneOn
add_left_mono
add_strictAnti πŸ“–mathematicalAntitoneOn
StrictAntiOn
StrictAntiOnβ€”add_lt_add_of_le_of_lt
LT.lt.le
const_add πŸ“–mathematicalAntitoneOnAntitoneOnβ€”Monotone.comp_antitoneOn
add_right_mono
const_mul' πŸ“–mathematicalAntitoneOnAntitoneOnβ€”Monotone.comp_antitoneOn
mul_right_mono
mul' πŸ“–mathematicalAntitoneOnAntitoneOnβ€”mul_le_mul'
mul_const' πŸ“–mathematicalAntitoneOnAntitoneOnβ€”Monotone.comp_antitoneOn
mul_left_mono
mul_strictAnti' πŸ“–mathematicalAntitoneOn
StrictAntiOn
StrictAntiOnβ€”mul_lt_mul_of_le_of_lt
LT.lt.le

Contravariant

Definitions

NameCategoryTheorems
toAddLeftCancelSemigroup πŸ“–CompOpβ€”
toAddRightCancelSemigroup πŸ“–CompOpβ€”
toLeftCancelSemigroup πŸ“–CompOpβ€”
toRightCancelSemigroup πŸ“–CompOpβ€”

Theorems

NameKindAssumesProvesValidatesDepends On
AddLECancellable πŸ“–mathematicalβ€”AddLECancellableβ€”le_of_add_le_add_left
MulLECancellable πŸ“–mathematicalβ€”MulLECancellableβ€”le_of_mul_le_mul_left'

Int

Theorems

NameKindAssumesProvesValidatesDepends On
instAddLeftMono πŸ“–mathematicalβ€”AddLeftMonoβ€”β€”

Left

Theorems

NameKindAssumesProvesValidatesDepends On
add_lt_add πŸ“–mathematicalPreorder.toLTPreorder.toLTβ€”add_lt_add_of_le_of_lt
LT.lt.le
add_neg πŸ“–mathematicalPreorder.toLT
AddZero.toZero
AddZeroClass.toAddZero
Preorder.toLT
AddZero.toAdd
AddZeroClass.toAddZero
AddZero.toZero
β€”add_lt_of_lt_of_neg
add_neg' πŸ“–mathematicalPreorder.toLT
AddZero.toZero
AddZeroClass.toAddZero
Preorder.toLT
AddZero.toAdd
AddZeroClass.toAddZero
AddZero.toZero
β€”add_lt_of_lt_of_neg'
add_neg_of_neg_of_nonpos πŸ“–mathematicalPreorder.toLT
AddZero.toZero
AddZeroClass.toAddZero
Preorder.toLE
Preorder.toLT
AddZero.toAdd
AddZeroClass.toAddZero
AddZero.toZero
β€”add_lt_of_lt_of_nonpos
add_neg_of_nonpos_of_neg πŸ“–mathematicalPreorder.toLE
AddZero.toZero
AddZeroClass.toAddZero
Preorder.toLT
Preorder.toLT
AddZero.toAdd
AddZeroClass.toAddZero
AddZero.toZero
β€”add_lt_of_le_of_neg
add_nonneg πŸ“–mathematicalPreorder.toLE
AddZero.toZero
AddZeroClass.toAddZero
Preorder.toLE
AddZero.toZero
AddZeroClass.toAddZero
AddZero.toAdd
β€”le_add_of_le_of_nonneg
add_nonpos πŸ“–mathematicalPreorder.toLE
AddZero.toZero
AddZeroClass.toAddZero
Preorder.toLE
AddZero.toAdd
AddZeroClass.toAddZero
AddZero.toZero
β€”add_le_of_le_of_nonpos
add_pos πŸ“–mathematicalPreorder.toLT
AddZero.toZero
AddZeroClass.toAddZero
Preorder.toLT
AddZero.toZero
AddZeroClass.toAddZero
AddZero.toAdd
β€”lt_add_of_lt_of_pos
add_pos' πŸ“–mathematicalPreorder.toLT
AddZero.toZero
AddZeroClass.toAddZero
Preorder.toLT
AddZero.toZero
AddZeroClass.toAddZero
AddZero.toAdd
β€”lt_add_of_lt_of_pos'
add_pos_of_nonneg_of_pos πŸ“–mathematicalPreorder.toLE
AddZero.toZero
AddZeroClass.toAddZero
Preorder.toLT
Preorder.toLT
AddZero.toZero
AddZeroClass.toAddZero
AddZero.toAdd
β€”lt_add_of_le_of_pos
add_pos_of_pos_of_nonneg πŸ“–mathematicalPreorder.toLT
AddZero.toZero
AddZeroClass.toAddZero
Preorder.toLE
Preorder.toLT
AddZero.toZero
AddZeroClass.toAddZero
AddZero.toAdd
β€”lt_add_of_lt_of_nonneg
min_le_max_of_add_le_add πŸ“–mathematicalPreorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
SemilatticeInf.toMin
SemilatticeSup.toMax
Lattice.toSemilatticeSup
β€”min_le_iff
le_max_iff
Mathlib.Tactic.Contrapose.contrapose₁
not_le
add_lt_add_of_le_of_lt
LT.lt.le
min_le_max_of_mul_le_mul πŸ“–mathematicalPreorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
SemilatticeInf.toMin
SemilatticeSup.toMax
Lattice.toSemilatticeSup
β€”Mathlib.Tactic.Contrapose.contrapose₁
mul_lt_mul_of_le_of_lt
LT.lt.le
mul_le_one πŸ“–mathematicalPreorder.toLE
MulOne.toOne
MulOneClass.toMulOne
Preorder.toLE
MulOne.toMul
MulOneClass.toMulOne
MulOne.toOne
β€”mul_le_of_le_of_le_one
mul_lt_mul πŸ“–mathematicalPreorder.toLTPreorder.toLTβ€”mul_lt_mul_of_le_of_lt
LT.lt.le
mul_lt_one πŸ“–mathematicalPreorder.toLT
MulOne.toOne
MulOneClass.toMulOne
Preorder.toLT
MulOne.toMul
MulOneClass.toMulOne
MulOne.toOne
β€”mul_lt_of_lt_of_lt_one
mul_lt_one' πŸ“–mathematicalPreorder.toLT
MulOne.toOne
MulOneClass.toMulOne
Preorder.toLT
MulOne.toMul
MulOneClass.toMulOne
MulOne.toOne
β€”mul_lt_of_lt_of_lt_one'
mul_lt_one_of_le_of_lt πŸ“–mathematicalPreorder.toLE
MulOne.toOne
MulOneClass.toMulOne
Preorder.toLT
Preorder.toLT
MulOne.toMul
MulOneClass.toMulOne
MulOne.toOne
β€”mul_lt_of_le_of_lt_one
mul_lt_one_of_lt_of_le πŸ“–mathematicalPreorder.toLT
MulOne.toOne
MulOneClass.toMulOne
Preorder.toLE
Preorder.toLT
MulOne.toMul
MulOneClass.toMulOne
MulOne.toOne
β€”mul_lt_of_lt_of_le_one
one_le_mul πŸ“–mathematicalPreorder.toLE
MulOne.toOne
MulOneClass.toMulOne
Preorder.toLE
MulOne.toOne
MulOneClass.toMulOne
MulOne.toMul
β€”le_mul_of_le_of_one_le
one_lt_mul πŸ“–mathematicalPreorder.toLT
MulOne.toOne
MulOneClass.toMulOne
Preorder.toLT
MulOne.toOne
MulOneClass.toMulOne
MulOne.toMul
β€”lt_mul_of_lt_of_one_lt
one_lt_mul' πŸ“–mathematicalPreorder.toLT
MulOne.toOne
MulOneClass.toMulOne
Preorder.toLT
MulOne.toOne
MulOneClass.toMulOne
MulOne.toMul
β€”lt_mul_of_lt_of_one_lt'
one_lt_mul_of_le_of_lt πŸ“–mathematicalPreorder.toLE
MulOne.toOne
MulOneClass.toMulOne
Preorder.toLT
Preorder.toLT
MulOne.toOne
MulOneClass.toMulOne
MulOne.toMul
β€”lt_mul_of_le_of_one_lt
one_lt_mul_of_lt_of_le πŸ“–mathematicalPreorder.toLT
MulOne.toOne
MulOneClass.toMulOne
Preorder.toLE
Preorder.toLT
MulOne.toOne
MulOneClass.toMulOne
MulOne.toMul
β€”lt_mul_of_lt_of_one_le

Monotone

Theorems

NameKindAssumesProvesValidatesDepends On
add πŸ“–mathematicalMonotoneMonotoneβ€”add_le_add
add_const πŸ“–mathematicalMonotoneMonotoneβ€”comp
add_left_mono
add_strictMono πŸ“–mathematicalMonotone
StrictMono
StrictMonoβ€”add_lt_add_of_le_of_lt
LT.lt.le
const_add πŸ“–mathematicalMonotoneMonotoneβ€”comp
add_right_mono
const_mul' πŸ“–mathematicalMonotoneMonotoneβ€”comp
mul_right_mono
mul' πŸ“–mathematicalMonotoneMonotoneβ€”mul_le_mul'
mul_const' πŸ“–mathematicalMonotoneMonotoneβ€”comp
mul_left_mono
mul_strictMono' πŸ“–mathematicalMonotone
StrictMono
StrictMonoβ€”mul_lt_mul_of_le_of_lt
LT.lt.le

MonotoneOn

Theorems

NameKindAssumesProvesValidatesDepends On
add πŸ“–mathematicalMonotoneOnMonotoneOnβ€”add_le_add
add_const πŸ“–mathematicalMonotoneOnMonotoneOnβ€”Monotone.comp_monotoneOn
add_left_mono
add_strictMono πŸ“–mathematicalMonotoneOn
StrictMonoOn
StrictMonoOnβ€”add_lt_add_of_le_of_lt
LT.lt.le
const_add πŸ“–mathematicalMonotoneOnMonotoneOnβ€”Monotone.comp_monotoneOn
add_right_mono
const_mul' πŸ“–mathematicalMonotoneOnMonotoneOnβ€”Monotone.comp_monotoneOn
mul_right_mono
mul' πŸ“–mathematicalMonotoneOnMonotoneOnβ€”mul_le_mul'
mul_const' πŸ“–mathematicalMonotoneOnMonotoneOnβ€”Monotone.comp_monotoneOn
mul_left_mono
mul_strictMono' πŸ“–mathematicalMonotoneOn
StrictMonoOn
StrictMonoOnβ€”mul_lt_mul_of_le_of_lt
LT.lt.le

MulLECancellable

Theorems

NameKindAssumesProvesValidatesDepends On
inj πŸ“–β€”MulLECancellable
Preorder.toLE
PartialOrder.toPreorder
β€”β€”Injective
inj_left πŸ“–β€”MulLECancellable
Preorder.toLE
PartialOrder.toPreorder
β€”β€”injective_left
injective_left πŸ“–β€”MulLECancellable
Preorder.toLE
PartialOrder.toPreorder
β€”β€”Injective
isLeftRegular πŸ“–mathematicalMulLECancellable
Preorder.toLE
PartialOrder.toPreorder
IsLeftRegularβ€”Injective
le_mul_iff_one_le_left πŸ“–mathematicalMulLECancellable
MulOne.toMul
MulOneClass.toMulOne
MulOne.toMul
MulOneClass.toMulOne
MulOne.toOne
β€”le_mul_iff_one_le_right
le_mul_iff_one_le_right πŸ“–mathematicalMulLECancellable
MulOne.toMul
MulOneClass.toMulOne
MulOne.toMul
MulOneClass.toMulOne
MulOne.toOne
β€”mul_one
mul_le_mul_iff_left
mul πŸ“–mathematicalMulLECancellable
Semigroup.toMul
MulLECancellable
Semigroup.toMul
β€”mul_assoc
mul_le_iff_le_one_left πŸ“–mathematicalMulLECancellable
MulOne.toMul
MulOneClass.toMulOne
MulOne.toMul
MulOneClass.toMulOne
MulOne.toOne
β€”mul_le_iff_le_one_right
mul_le_iff_le_one_right πŸ“–mathematicalMulLECancellable
MulOne.toMul
MulOneClass.toMulOne
MulOne.toMul
MulOneClass.toMulOne
MulOne.toOne
β€”mul_one
mul_le_mul_iff_left
mul_le_mul_iff_left πŸ“–β€”MulLECancellableβ€”β€”mul_le_mul_right
mul_le_mul_iff_right πŸ“–β€”MulLECancellableβ€”β€”mul_le_mul_iff_left
of_mul_left πŸ“–mathematicalMulLECancellable
CommMagma.toMul
CommSemigroup.toCommMagma
MulLECancellable
CommMagma.toMul
CommSemigroup.toCommMagma
β€”of_mul_right
mul_comm
of_mul_right πŸ“–mathematicalMulLECancellable
Semigroup.toMul
MulLECancellable
Semigroup.toMul
β€”mul_assoc
mul_le_mul_right

MulLeftStrictMono

Theorems

NameKindAssumesProvesValidatesDepends On
toIsLeftCancelMul πŸ“–mathematicalβ€”IsLeftCancelMulβ€”StrictMono.injective
mul_right_strictMono

MulRightStrictMono

Theorems

NameKindAssumesProvesValidatesDepends On
toIsRightCancelMul πŸ“–mathematicalβ€”IsRightCancelMulβ€”StrictMono.injective
mul_left_strictMono

Nat

Theorems

NameKindAssumesProvesValidatesDepends On
instMulLeftMono πŸ“–mathematicalβ€”MulLeftMonoβ€”β€”

Right

Theorems

NameKindAssumesProvesValidatesDepends On
add_lt_add πŸ“–mathematicalPreorder.toLTPreorder.toLTβ€”add_lt_add_of_lt_of_le
LT.lt.le
add_neg πŸ“–mathematicalPreorder.toLT
AddZero.toZero
AddZeroClass.toAddZero
Preorder.toLT
AddZero.toAdd
AddZeroClass.toAddZero
AddZero.toZero
β€”add_lt_of_neg_of_lt
add_neg' πŸ“–mathematicalPreorder.toLT
AddZero.toZero
AddZeroClass.toAddZero
Preorder.toLT
AddZero.toAdd
AddZeroClass.toAddZero
AddZero.toZero
β€”add_lt_of_neg_of_lt'
add_neg_of_neg_of_nonpos πŸ“–mathematicalPreorder.toLT
AddZero.toZero
AddZeroClass.toAddZero
Preorder.toLE
Preorder.toLT
AddZero.toAdd
AddZeroClass.toAddZero
AddZero.toZero
β€”add_lt_of_neg_of_le
add_neg_of_nonpos_of_neg πŸ“–mathematicalPreorder.toLE
AddZero.toZero
AddZeroClass.toAddZero
Preorder.toLT
Preorder.toLT
AddZero.toAdd
AddZeroClass.toAddZero
AddZero.toZero
β€”add_lt_of_nonpos_of_lt
add_nonneg πŸ“–mathematicalPreorder.toLE
AddZero.toZero
AddZeroClass.toAddZero
Preorder.toLE
AddZero.toZero
AddZeroClass.toAddZero
AddZero.toAdd
β€”le_add_of_nonneg_of_le
add_nonpos πŸ“–mathematicalPreorder.toLE
AddZero.toZero
AddZeroClass.toAddZero
Preorder.toLE
AddZero.toAdd
AddZeroClass.toAddZero
AddZero.toZero
β€”add_le_of_nonpos_of_le
add_pos πŸ“–mathematicalPreorder.toLT
AddZero.toZero
AddZeroClass.toAddZero
Preorder.toLT
AddZero.toZero
AddZeroClass.toAddZero
AddZero.toAdd
β€”lt_add_of_pos_of_lt
add_pos' πŸ“–mathematicalPreorder.toLT
AddZero.toZero
AddZeroClass.toAddZero
Preorder.toLT
AddZero.toZero
AddZeroClass.toAddZero
AddZero.toAdd
β€”lt_add_of_pos_of_lt'
add_pos_of_nonneg_of_pos πŸ“–mathematicalPreorder.toLE
AddZero.toZero
AddZeroClass.toAddZero
Preorder.toLT
Preorder.toLT
AddZero.toZero
AddZeroClass.toAddZero
AddZero.toAdd
β€”lt_add_of_nonneg_of_lt
add_pos_of_pos_of_nonneg πŸ“–mathematicalPreorder.toLT
AddZero.toZero
AddZeroClass.toAddZero
Preorder.toLE
Preorder.toLT
AddZero.toZero
AddZeroClass.toAddZero
AddZero.toAdd
β€”lt_add_of_pos_of_le
min_le_max_of_add_le_add πŸ“–mathematicalPreorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
SemilatticeInf.toMin
SemilatticeSup.toMax
Lattice.toSemilatticeSup
β€”min_le_iff
le_max_iff
Mathlib.Tactic.Contrapose.contrapose₁
not_le
add_lt_add_of_lt_of_le
LT.lt.le
min_le_max_of_mul_le_mul πŸ“–mathematicalPreorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
SemilatticeInf.toMin
SemilatticeSup.toMax
Lattice.toSemilatticeSup
β€”Mathlib.Tactic.Contrapose.contrapose₁
mul_lt_mul_of_lt_of_le
LT.lt.le
mul_le_one πŸ“–mathematicalPreorder.toLE
MulOne.toOne
MulOneClass.toMulOne
Preorder.toLE
MulOne.toMul
MulOneClass.toMulOne
MulOne.toOne
β€”mul_le_of_le_one_of_le
mul_lt_mul πŸ“–mathematicalPreorder.toLTPreorder.toLTβ€”mul_lt_mul_of_lt_of_le
LT.lt.le
mul_lt_one πŸ“–mathematicalPreorder.toLT
MulOne.toOne
MulOneClass.toMulOne
Preorder.toLT
MulOne.toMul
MulOneClass.toMulOne
MulOne.toOne
β€”mul_lt_of_lt_one_of_lt
mul_lt_one' πŸ“–mathematicalPreorder.toLT
MulOne.toOne
MulOneClass.toMulOne
Preorder.toLT
MulOne.toMul
MulOneClass.toMulOne
MulOne.toOne
β€”mul_lt_of_lt_one_of_lt'
mul_lt_one_of_le_of_lt πŸ“–mathematicalPreorder.toLE
MulOne.toOne
MulOneClass.toMulOne
Preorder.toLT
Preorder.toLT
MulOne.toMul
MulOneClass.toMulOne
MulOne.toOne
β€”mul_lt_of_le_one_of_lt
mul_lt_one_of_lt_of_le πŸ“–mathematicalPreorder.toLT
MulOne.toOne
MulOneClass.toMulOne
Preorder.toLE
Preorder.toLT
MulOne.toMul
MulOneClass.toMulOne
MulOne.toOne
β€”mul_lt_of_lt_one_of_le
one_le_mul πŸ“–mathematicalPreorder.toLE
MulOne.toOne
MulOneClass.toMulOne
Preorder.toLE
MulOne.toOne
MulOneClass.toMulOne
MulOne.toMul
β€”le_mul_of_one_le_of_le
one_lt_mul πŸ“–mathematicalPreorder.toLT
MulOne.toOne
MulOneClass.toMulOne
Preorder.toLT
MulOne.toOne
MulOneClass.toMulOne
MulOne.toMul
β€”lt_mul_of_one_lt_of_lt
one_lt_mul' πŸ“–mathematicalPreorder.toLT
MulOne.toOne
MulOneClass.toMulOne
Preorder.toLT
MulOne.toOne
MulOneClass.toMulOne
MulOne.toMul
β€”lt_mul_of_one_lt_of_lt'
one_lt_mul_of_le_of_lt πŸ“–mathematicalPreorder.toLE
MulOne.toOne
MulOneClass.toMulOne
Preorder.toLT
Preorder.toLT
MulOne.toOne
MulOneClass.toMulOne
MulOne.toMul
β€”lt_mul_of_one_le_of_lt
one_lt_mul_of_lt_of_le πŸ“–mathematicalPreorder.toLT
MulOne.toOne
MulOneClass.toMulOne
Preorder.toLE
Preorder.toLT
MulOne.toOne
MulOneClass.toMulOne
MulOne.toMul
β€”lt_mul_of_one_lt_of_le

StrictAnti

Theorems

NameKindAssumesProvesValidatesDepends On
add πŸ“–mathematicalStrictAntiStrictAntiβ€”add_lt_add_of_lt_of_lt
add_antitone πŸ“–mathematicalStrictAnti
Antitone
StrictAntiβ€”add_lt_add_of_lt_of_le
LT.lt.le
add_const πŸ“–mathematicalStrictAntiStrictAntiβ€”add_lt_add_left
const_add πŸ“–mathematicalStrictAntiStrictAntiβ€”add_lt_add_right
const_mul' πŸ“–mathematicalStrictAntiStrictAntiβ€”mul_lt_mul_right
mul' πŸ“–mathematicalStrictAntiStrictAntiβ€”mul_lt_mul_of_lt_of_lt
mul_antitone' πŸ“–mathematicalStrictAnti
Antitone
StrictAntiβ€”mul_lt_mul_of_lt_of_le
LT.lt.le
mul_const' πŸ“–mathematicalStrictAntiStrictAntiβ€”mul_lt_mul_left

StrictAntiOn

Theorems

NameKindAssumesProvesValidatesDepends On
add πŸ“–mathematicalStrictAntiOnStrictAntiOnβ€”add_lt_add_of_lt_of_lt
add_antitone πŸ“–mathematicalStrictAntiOn
AntitoneOn
StrictAntiOnβ€”add_lt_add_of_lt_of_le
LT.lt.le
add_const πŸ“–mathematicalStrictAntiOnStrictAntiOnβ€”add_lt_add_left
const_add πŸ“–mathematicalStrictAntiOnStrictAntiOnβ€”add_lt_add_right
const_mul' πŸ“–mathematicalStrictAntiOnStrictAntiOnβ€”mul_lt_mul_right
mul' πŸ“–mathematicalStrictAntiOnStrictAntiOnβ€”mul_lt_mul_of_lt_of_lt
mul_antitone' πŸ“–mathematicalStrictAntiOn
AntitoneOn
StrictAntiOnβ€”mul_lt_mul_of_lt_of_le
LT.lt.le
mul_const' πŸ“–mathematicalStrictAntiOnStrictAntiOnβ€”mul_lt_mul_left

StrictMono

Theorems

NameKindAssumesProvesValidatesDepends On
add πŸ“–mathematicalStrictMonoStrictMonoβ€”add_lt_add_of_lt_of_lt
add_const πŸ“–mathematicalStrictMonoStrictMonoβ€”add_lt_add_left
add_monotone πŸ“–mathematicalStrictMono
Monotone
StrictMonoβ€”add_lt_add_of_lt_of_le
LT.lt.le
const_add πŸ“–mathematicalStrictMonoStrictMonoβ€”add_lt_add_right
const_mul' πŸ“–mathematicalStrictMonoStrictMonoβ€”mul_lt_mul_right
mul' πŸ“–mathematicalStrictMonoStrictMonoβ€”mul_lt_mul_of_lt_of_lt
mul_const' πŸ“–mathematicalStrictMonoStrictMonoβ€”mul_lt_mul_left
mul_monotone' πŸ“–mathematicalStrictMono
Monotone
StrictMonoβ€”mul_lt_mul_of_lt_of_le
LT.lt.le

StrictMonoOn

Theorems

NameKindAssumesProvesValidatesDepends On
add πŸ“–mathematicalStrictMonoOnStrictMonoOnβ€”add_lt_add_of_lt_of_lt
add_const πŸ“–mathematicalStrictMonoOnStrictMonoOnβ€”add_lt_add_left
add_monotone πŸ“–mathematicalStrictMonoOn
MonotoneOn
StrictMonoOnβ€”add_lt_add_of_lt_of_le
LT.lt.le
const_add πŸ“–mathematicalStrictMonoOnStrictMonoOnβ€”add_lt_add_right
const_mul' πŸ“–mathematicalStrictMonoOnStrictMonoOnβ€”mul_lt_mul_right
mul' πŸ“–mathematicalStrictMonoOnStrictMonoOnβ€”mul_lt_mul_of_lt_of_lt
mul_const' πŸ“–mathematicalStrictMonoOnStrictMonoOnβ€”mul_lt_mul_left
mul_monotone' πŸ“–mathematicalStrictMonoOn
MonotoneOn
StrictMonoOnβ€”mul_lt_mul_of_lt_of_le
LT.lt.le

(root)

Definitions

NameCategoryTheorems
AddLECancellable πŸ“–MathDef
26 mathmath: EReal.addLECancellable_coe, WithTop.addLECancellable_coe, WithBot.addLECancellable_of_ne_bot, AddLECancellable.withTop, ENNReal.cancel_of_ne, WithBot.addLECancellable_coe, addLECancellable_zero, AddLECancellable.of_add_left, addLECancellable_add, ENat.addLECancellable_coe, WithBot.addLECancellable_of_lt_bot, WithBot.addLECancellable_iff_ne_bot, ENat.addLECancellable_of_ne_top, ENNReal.addLECancellable_iff_ne, Finset.addLECancellable_sum, ENNReal.cancel_coe, AddLECancellable.add, ENat.addLECancellable_of_lt_top, ENNReal.cancel_of_lt, Contravariant.AddLECancellable, WithTop.addLECancellable_of_lt_top, ENNReal.cancel_of_lt', WithTop.addLECancellable_of_ne_top, WithTop.addLECancellable_iff_ne_top, AddLECancellable.withBot, AddLECancellable.of_add_right
MulLECancellable πŸ“–MathDef
9 mathmath: mulLECancellable_mul, mulLECancellable_one, MulLECancellable.mul, MulLECancellable.of_mul_right, Contravariant.MulLECancellable, IsUnit.mulLECancellable, MulLECancellable.of_mul_left, Finset.mulLECancellable_prod, Units.mulLECancellable_val

Theorems

NameKindAssumesProvesValidatesDepends On
addLECancellable_add πŸ“–mathematicalβ€”AddLECancellable
AddCommMagma.toAdd
AddCommSemigroup.toAddCommMagma
β€”AddLECancellable.of_add_left
AddLECancellable.of_add_right
AddLECancellable.add
addLECancellable_zero πŸ“–mathematicalβ€”AddLECancellable
AddZero.toAdd
AddZeroClass.toAddZero
AddZero.toZero
β€”zero_add
add_eq_add_iff_eq_and_eq πŸ“–β€”Preorder.toLE
PartialOrder.toPreorder
β€”β€”le_antisymm_iff
add_le_add
addLeftMono_of_addLeftStrictMono
addRightMono_of_addRightStrictMono
add_le_add_iff_of_ge
add_eq_zero_iff_of_nonneg πŸ“–mathematicalPreorder.toLE
PartialOrder.toPreorder
AddZero.toZero
AddZeroClass.toAddZero
AddZero.toAdd
AddZeroClass.toAddZero
AddZero.toZero
β€”le_add_of_le_of_nonneg
le_rfl
le_antisymm
le_add_of_nonneg_of_le
add_zero
add_le_add πŸ“–mathematicalPreorder.toLEPreorder.toLEβ€”le_imp_le_of_le_of_le
add_le_add_left
le_refl
add_le_add_right
add_le_add_iff_left πŸ“–β€”β€”β€”β€”rel_iff_cov
add_le_add_iff_of_ge πŸ“–mathematicalPreorder.toLE
PartialOrder.toPreorder
Preorder.toLE
PartialOrder.toPreorder
β€”eq_iff_le_not_lt
LE.le.not_gt
add_lt_add_of_lt_of_le
addLeftMono_of_addLeftStrictMono
add_lt_add_of_le_of_lt
addRightMono_of_addRightStrictMono
le_refl
add_le_add_iff_right πŸ“–β€”β€”β€”β€”rel_iff_cov
add_le_add_left πŸ“–β€”β€”β€”β€”CovariantClass.elim
add_le_add_right πŸ“–β€”β€”β€”β€”CovariantClass.elim
add_le_add_three πŸ“–mathematicalPreorder.toLEPreorder.toLEβ€”add_le_add
add_le_iff_nonpos_left πŸ“–mathematicalβ€”AddZero.toAdd
AddZeroClass.toAddZero
AddZero.toZero
β€”zero_add
add_le_add_iff_right
add_le_iff_nonpos_right πŸ“–mathematicalβ€”AddZero.toAdd
AddZeroClass.toAddZero
AddZero.toZero
β€”add_zero
add_le_add_iff_left
add_le_of_add_le_left πŸ“–mathematicalPreorder.toLEPreorder.toLEβ€”act_rel_of_rel_of_act_rel
instIsTransLe
add_le_of_add_le_right πŸ“–mathematicalPreorder.toLEPreorder.toLEβ€”LE.le.trans
add_le_add_left
add_le_of_le_of_nonpos πŸ“–mathematicalPreorder.toLE
AddZero.toZero
AddZeroClass.toAddZero
Preorder.toLE
AddZero.toAdd
AddZeroClass.toAddZero
β€”add_le_add_right
add_zero
add_le_of_nonpos_left πŸ“–mathematicalAddZero.toZero
AddZeroClass.toAddZero
AddZero.toAdd
AddZeroClass.toAddZero
β€”add_le_add_left
zero_add
add_le_of_nonpos_of_le πŸ“–mathematicalPreorder.toLE
AddZero.toZero
AddZeroClass.toAddZero
Preorder.toLE
AddZero.toAdd
AddZeroClass.toAddZero
β€”add_le_add_left
zero_add
add_le_of_nonpos_right πŸ“–mathematicalAddZero.toZero
AddZeroClass.toAddZero
AddZero.toAdd
AddZeroClass.toAddZero
β€”add_le_add_right
add_zero
add_left_cancel'' πŸ“–β€”β€”β€”β€”add_left_cancel
add_left_inj_of_comparable πŸ“–β€”Preorder.toLE
PartialOrder.toPreorder
β€”β€”Mathlib.Tactic.Contrapose.contrapose₁
LT.lt.ne'
add_lt_add_left
LE.le.lt_of_ne'
LT.lt.ne
LE.le.lt_of_ne
add_left_mono πŸ“–mathematicalβ€”Monotoneβ€”add_le_add_left
add_left_strictMono πŸ“–mathematicalβ€”StrictMonoβ€”add_lt_add_left
add_lt_add πŸ“–mathematicalPreorder.toLTPreorder.toLTβ€”add_lt_add_of_lt_of_lt
add_lt_add_iff_left πŸ“–β€”β€”β€”β€”rel_iff_cov
add_lt_add_iff_right πŸ“–β€”β€”β€”β€”rel_iff_cov
add_lt_add_left πŸ“–β€”β€”β€”β€”CovariantClass.elim
add_lt_add_of_le_of_lt πŸ“–mathematicalPreorder.toLE
Preorder.toLT
Preorder.toLTβ€”LE.le.trans_lt
add_le_add_left
add_lt_add_right
add_lt_add_of_lt_of_le πŸ“–mathematicalPreorder.toLT
Preorder.toLE
Preorder.toLTβ€”LE.le.trans_lt
add_le_add_right
add_lt_add_left
add_lt_add_of_lt_of_lt πŸ“–mathematicalPreorder.toLTPreorder.toLTβ€”add_lt_add_right
add_lt_add_left
add_lt_add_right πŸ“–β€”β€”β€”β€”CovariantClass.elim
add_lt_iff_neg_left πŸ“–mathematicalβ€”AddZero.toAdd
AddZeroClass.toAddZero
AddZero.toZero
β€”add_zero
add_lt_add_iff_left
add_lt_iff_neg_right πŸ“–mathematicalβ€”AddZero.toAdd
AddZeroClass.toAddZero
AddZero.toZero
β€”zero_add
add_lt_add_iff_right
add_lt_of_add_lt_left πŸ“–mathematicalPreorder.toLT
Preorder.toLE
Preorder.toLTβ€”LE.le.trans_lt
add_le_add_right
add_lt_of_add_lt_right πŸ“–mathematicalPreorder.toLT
Preorder.toLE
Preorder.toLTβ€”LE.le.trans_lt
add_le_add_left
add_lt_of_le_of_neg πŸ“–mathematicalPreorder.toLE
Preorder.toLT
AddZero.toZero
AddZeroClass.toAddZero
Preorder.toLT
AddZero.toAdd
AddZeroClass.toAddZero
β€”add_lt_add_right
add_zero
add_lt_of_lt_of_neg πŸ“–mathematicalPreorder.toLT
AddZero.toZero
AddZeroClass.toAddZero
Preorder.toLT
AddZero.toAdd
AddZeroClass.toAddZero
β€”add_lt_add_right
add_zero
add_lt_of_lt_of_neg' πŸ“–mathematicalPreorder.toLT
AddZero.toZero
AddZeroClass.toAddZero
Preorder.toLT
AddZero.toAdd
AddZeroClass.toAddZero
β€”add_lt_of_lt_of_nonpos
LT.lt.le
add_lt_of_lt_of_nonpos πŸ“–mathematicalPreorder.toLT
Preorder.toLE
AddZero.toZero
AddZeroClass.toAddZero
Preorder.toLT
AddZero.toAdd
AddZeroClass.toAddZero
β€”add_le_add_right
add_zero
add_lt_of_neg_left πŸ“–mathematicalAddZero.toZero
AddZeroClass.toAddZero
AddZero.toAdd
AddZeroClass.toAddZero
β€”add_lt_add_left
zero_add
add_lt_of_neg_of_le πŸ“–mathematicalPreorder.toLT
AddZero.toZero
AddZeroClass.toAddZero
Preorder.toLE
Preorder.toLT
AddZero.toAdd
AddZeroClass.toAddZero
β€”add_lt_add_left
zero_add
add_lt_of_neg_of_lt πŸ“–mathematicalPreorder.toLT
AddZero.toZero
AddZeroClass.toAddZero
Preorder.toLT
AddZero.toAdd
AddZeroClass.toAddZero
β€”add_lt_add_left
zero_add
add_lt_of_neg_of_lt' πŸ“–mathematicalPreorder.toLT
AddZero.toZero
AddZeroClass.toAddZero
Preorder.toLT
AddZero.toAdd
AddZeroClass.toAddZero
β€”add_lt_of_nonpos_of_lt
LT.lt.le
add_lt_of_neg_right πŸ“–mathematicalAddZero.toZero
AddZeroClass.toAddZero
AddZero.toAdd
AddZeroClass.toAddZero
β€”add_lt_add_right
add_zero
add_lt_of_nonpos_of_lt πŸ“–mathematicalPreorder.toLE
AddZero.toZero
AddZeroClass.toAddZero
Preorder.toLT
Preorder.toLT
AddZero.toAdd
AddZeroClass.toAddZero
β€”add_le_add_left
zero_add
add_max πŸ“–mathematicalβ€”SemilatticeSup.toMax
Lattice.toSemilatticeSup
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
β€”Monotone.map_max
add_right_mono
add_min πŸ“–mathematicalβ€”SemilatticeInf.toMin
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
β€”Monotone.map_min
add_right_mono
add_neg πŸ“–mathematicalPreorder.toLT
AddZero.toZero
AddZeroClass.toAddZero
Preorder.toLT
AddZero.toAdd
AddZeroClass.toAddZero
AddZero.toZero
β€”Left.add_neg
add_neg' πŸ“–mathematicalPreorder.toLT
AddZero.toZero
AddZeroClass.toAddZero
Preorder.toLT
AddZero.toAdd
AddZeroClass.toAddZero
AddZero.toZero
β€”Left.add_neg'
add_neg_of_neg_of_nonpos πŸ“–mathematicalPreorder.toLT
AddZero.toZero
AddZeroClass.toAddZero
Preorder.toLE
Preorder.toLT
AddZero.toAdd
AddZeroClass.toAddZero
AddZero.toZero
β€”Left.add_neg_of_neg_of_nonpos
add_neg_of_nonpos_of_neg πŸ“–mathematicalPreorder.toLE
AddZero.toZero
AddZeroClass.toAddZero
Preorder.toLT
Preorder.toLT
AddZero.toAdd
AddZeroClass.toAddZero
AddZero.toZero
β€”Left.add_neg_of_nonpos_of_neg
add_nonneg πŸ“–mathematicalPreorder.toLE
AddZero.toZero
AddZeroClass.toAddZero
Preorder.toLE
AddZero.toZero
AddZeroClass.toAddZero
AddZero.toAdd
β€”Left.add_nonneg
add_nonpos πŸ“–mathematicalPreorder.toLE
AddZero.toZero
AddZeroClass.toAddZero
Preorder.toLE
AddZero.toAdd
AddZeroClass.toAddZero
AddZero.toZero
β€”Left.add_nonpos
add_pos πŸ“–mathematicalPreorder.toLT
AddZero.toZero
AddZeroClass.toAddZero
Preorder.toLT
AddZero.toZero
AddZeroClass.toAddZero
AddZero.toAdd
β€”Left.add_pos
add_pos' πŸ“–mathematicalPreorder.toLT
AddZero.toZero
AddZeroClass.toAddZero
Preorder.toLT
AddZero.toZero
AddZeroClass.toAddZero
AddZero.toAdd
β€”Left.add_pos'
add_pos_of_nonneg_of_pos πŸ“–mathematicalPreorder.toLE
AddZero.toZero
AddZeroClass.toAddZero
Preorder.toLT
Preorder.toLT
AddZero.toZero
AddZeroClass.toAddZero
AddZero.toAdd
β€”Left.add_pos_of_nonneg_of_pos
add_pos_of_pos_of_nonneg πŸ“–mathematicalPreorder.toLT
AddZero.toZero
AddZeroClass.toAddZero
Preorder.toLE
Preorder.toLT
AddZero.toZero
AddZeroClass.toAddZero
AddZero.toAdd
β€”Left.add_pos_of_pos_of_nonneg
add_right_cancel'' πŸ“–β€”β€”β€”β€”add_right_cancel
add_right_inj_of_comparable πŸ“–β€”Preorder.toLE
PartialOrder.toPreorder
β€”β€”Mathlib.Tactic.Contrapose.contrapose₁
LT.lt.ne'
add_lt_add_right
LE.le.lt_of_ne'
LT.lt.ne
LE.le.lt_of_ne
add_right_mono πŸ“–mathematicalβ€”Monotoneβ€”add_le_add_right
add_right_strictMono πŸ“–mathematicalβ€”StrictMonoβ€”add_lt_add_right
cmp_add_left πŸ“–mathematicalβ€”cmp
Preorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
LinearOrder.toDecidableLT
β€”StrictMono.cmp_map_eq
StrictMono.const_add
strictMono_id
cmp_add_right πŸ“–mathematicalβ€”cmp
Preorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
LinearOrder.toDecidableLT
β€”StrictMono.cmp_map_eq
StrictMono.add_const
strictMono_id
cmp_mul_left' πŸ“–mathematicalβ€”cmp
Preorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
LinearOrder.toDecidableLT
β€”StrictMono.cmp_map_eq
StrictMono.const_mul'
strictMono_id
cmp_mul_right' πŸ“–mathematicalβ€”cmp
Preorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
LinearOrder.toDecidableLT
β€”StrictMono.cmp_map_eq
StrictMono.mul_const'
strictMono_id
eq_one_of_mul_le_one_left πŸ“–mathematicalPreorder.toLE
PartialOrder.toPreorder
MulOne.toOne
MulOneClass.toMulOne
MulOne.toMul
MulOne.toOne
MulOneClass.toMulOne
β€”LE.le.eq_of_not_lt'
LE.le.not_gt
one_lt_mul_of_lt_of_le'
eq_one_of_mul_le_one_right πŸ“–mathematicalPreorder.toLE
PartialOrder.toPreorder
MulOne.toOne
MulOneClass.toMulOne
MulOne.toMul
MulOne.toOne
MulOneClass.toMulOne
β€”LE.le.eq_of_not_lt'
LE.le.not_gt
Right.one_lt_mul_of_le_of_lt
eq_one_of_one_le_mul_left πŸ“–mathematicalPreorder.toLE
PartialOrder.toPreorder
MulOne.toOne
MulOneClass.toMulOne
MulOne.toMul
MulOne.toOne
MulOneClass.toMulOne
β€”LE.le.eq_of_not_lt
LE.le.not_gt
mul_lt_one_of_lt_of_le
eq_one_of_one_le_mul_right πŸ“–mathematicalPreorder.toLE
PartialOrder.toPreorder
MulOne.toOne
MulOneClass.toMulOne
MulOne.toMul
MulOne.toOne
MulOneClass.toMulOne
β€”LE.le.eq_of_not_lt
LE.le.not_gt
Right.mul_lt_one_of_le_of_lt
eq_zero_of_add_nonneg_left πŸ“–mathematicalPreorder.toLE
PartialOrder.toPreorder
AddZero.toZero
AddZeroClass.toAddZero
AddZero.toAdd
AddZero.toZero
AddZeroClass.toAddZero
β€”LE.le.eq_of_not_lt
LE.le.not_gt
add_neg_of_neg_of_nonpos
eq_zero_of_add_nonneg_right πŸ“–mathematicalPreorder.toLE
PartialOrder.toPreorder
AddZero.toZero
AddZeroClass.toAddZero
AddZero.toAdd
AddZero.toZero
AddZeroClass.toAddZero
β€”LE.le.eq_of_not_lt
LE.le.not_gt
Right.add_neg_of_nonpos_of_neg
eq_zero_of_add_nonpos_left πŸ“–mathematicalPreorder.toLE
PartialOrder.toPreorder
AddZero.toZero
AddZeroClass.toAddZero
AddZero.toAdd
AddZero.toZero
AddZeroClass.toAddZero
β€”LE.le.eq_of_not_lt'
LE.le.not_gt
add_pos_of_pos_of_nonneg
eq_zero_of_add_nonpos_right πŸ“–mathematicalPreorder.toLE
PartialOrder.toPreorder
AddZero.toZero
AddZeroClass.toAddZero
AddZero.toAdd
AddZero.toZero
AddZeroClass.toAddZero
β€”LE.le.eq_of_not_lt'
LE.le.not_gt
Right.add_pos_of_nonneg_of_pos
exists_square_le πŸ“–mathematicalβ€”Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
MulOne.toMul
MulOneClass.toMulOne
β€”mul_lt_mul_right
le_of_lt
mul_one
instIsLeftCancelAddOfAddLeftReflectLE πŸ“–mathematicalβ€”IsLeftCancelAddβ€”LE.le.antisymm
le_of_add_le_add_left
Eq.le
Eq.ge
instIsLeftCancelMulOfMulLeftReflectLE πŸ“–mathematicalβ€”IsLeftCancelMulβ€”LE.le.antisymm
le_of_mul_le_mul_left'
Eq.le
Eq.ge
instIsRightCancelAddOfAddRightReflectLE πŸ“–mathematicalβ€”IsRightCancelAddβ€”LE.le.antisymm
le_of_add_le_add_right
Eq.le
Eq.ge
instIsRightCancelMulOfMulRightReflectLE πŸ“–mathematicalβ€”IsRightCancelMulβ€”LE.le.antisymm
le_of_mul_le_mul_right'
Eq.le
Eq.ge
le_add_iff_nonneg_left πŸ“–mathematicalβ€”AddZero.toAdd
AddZeroClass.toAddZero
AddZero.toZero
β€”zero_add
add_le_add_iff_right
le_add_iff_nonneg_right πŸ“–mathematicalβ€”AddZero.toAdd
AddZeroClass.toAddZero
AddZero.toZero
β€”add_zero
add_le_add_iff_left
le_add_of_le_add_left πŸ“–mathematicalPreorder.toLEPreorder.toLEβ€”rel_act_of_rel_of_rel_act
instIsTransLe
le_add_of_le_add_right πŸ“–mathematicalPreorder.toLEPreorder.toLEβ€”LE.le.trans
add_le_add_left
le_add_of_le_of_nonneg πŸ“–mathematicalPreorder.toLE
AddZero.toZero
AddZeroClass.toAddZero
Preorder.toLE
AddZero.toAdd
AddZeroClass.toAddZero
β€”add_zero
add_le_add_right
le_add_of_nonneg_left πŸ“–mathematicalAddZero.toZero
AddZeroClass.toAddZero
AddZero.toAdd
AddZeroClass.toAddZero
β€”zero_add
add_le_add_left
le_add_of_nonneg_of_le πŸ“–mathematicalPreorder.toLE
AddZero.toZero
AddZeroClass.toAddZero
Preorder.toLE
AddZero.toAdd
AddZeroClass.toAddZero
β€”zero_add
add_le_add_left
le_add_of_nonneg_right πŸ“–mathematicalAddZero.toZero
AddZeroClass.toAddZero
AddZero.toAdd
AddZeroClass.toAddZero
β€”add_zero
add_le_add_right
le_mul_iff_one_le_left' πŸ“–mathematicalβ€”MulOne.toMul
MulOneClass.toMulOne
MulOne.toOne
β€”one_mul
mul_le_mul_iff_right
le_mul_iff_one_le_right' πŸ“–mathematicalβ€”MulOne.toMul
MulOneClass.toMulOne
MulOne.toOne
β€”mul_one
mul_le_mul_iff_left
le_mul_of_le_mul_left πŸ“–mathematicalPreorder.toLEPreorder.toLEβ€”rel_act_of_rel_of_rel_act
instIsTransLe
le_mul_of_le_mul_right πŸ“–mathematicalPreorder.toLEPreorder.toLEβ€”LE.le.trans
mul_le_mul_left
le_mul_of_le_of_one_le πŸ“–mathematicalPreorder.toLE
MulOne.toOne
MulOneClass.toMulOne
Preorder.toLE
MulOne.toMul
MulOneClass.toMulOne
β€”mul_one
mul_le_mul_right
le_mul_of_one_le_left' πŸ“–mathematicalMulOne.toOne
MulOneClass.toMulOne
MulOne.toMul
MulOneClass.toMulOne
β€”one_mul
mul_le_mul_left
le_mul_of_one_le_of_le πŸ“–mathematicalPreorder.toLE
MulOne.toOne
MulOneClass.toMulOne
Preorder.toLE
MulOne.toMul
MulOneClass.toMulOne
β€”one_mul
mul_le_mul_left
le_mul_of_one_le_right' πŸ“–mathematicalMulOne.toOne
MulOneClass.toMulOne
MulOne.toMul
MulOneClass.toMulOne
β€”mul_one
mul_le_mul_right
le_of_add_le_add_left πŸ“–β€”β€”β€”β€”ContravariantClass.elim
le_of_add_le_add_right πŸ“–β€”β€”β€”β€”ContravariantClass.elim
le_of_add_le_of_nonneg_left πŸ“–mathematicalPreorder.toLE
AddZero.toAdd
AddZeroClass.toAddZero
AddZero.toZero
Preorder.toLEβ€”LE.le.trans
le_add_of_nonneg_right
le_of_add_le_of_nonneg_right πŸ“–mathematicalPreorder.toLE
AddZero.toAdd
AddZeroClass.toAddZero
AddZero.toZero
Preorder.toLEβ€”LE.le.trans
le_add_of_nonneg_left
le_of_le_add_of_nonpos_left πŸ“–mathematicalPreorder.toLE
AddZero.toAdd
AddZeroClass.toAddZero
AddZero.toZero
Preorder.toLEβ€”LE.le.trans
add_le_of_nonpos_right
le_of_le_add_of_nonpos_right πŸ“–mathematicalPreorder.toLE
AddZero.toAdd
AddZeroClass.toAddZero
AddZero.toZero
Preorder.toLEβ€”LE.le.trans
add_le_of_nonpos_left
le_of_le_mul_of_le_one_left πŸ“–mathematicalPreorder.toLE
MulOne.toMul
MulOneClass.toMulOne
MulOne.toOne
Preorder.toLEβ€”LE.le.trans
mul_le_of_le_one_right'
le_of_le_mul_of_le_one_right πŸ“–mathematicalPreorder.toLE
MulOne.toMul
MulOneClass.toMulOne
MulOne.toOne
Preorder.toLEβ€”LE.le.trans
mul_le_of_le_one_left'
le_of_mul_le_mul_left' πŸ“–β€”β€”β€”β€”ContravariantClass.elim
le_of_mul_le_mul_right' πŸ“–β€”β€”β€”β€”ContravariantClass.elim
le_of_mul_le_of_one_le_left πŸ“–mathematicalPreorder.toLE
MulOne.toMul
MulOneClass.toMulOne
MulOne.toOne
Preorder.toLEβ€”LE.le.trans
le_mul_of_one_le_right'
le_of_mul_le_of_one_le_right πŸ“–mathematicalPreorder.toLE
MulOne.toMul
MulOneClass.toMulOne
MulOne.toOne
Preorder.toLEβ€”LE.le.trans
le_mul_of_one_le_left'
le_one_of_mul_le_left πŸ“–mathematicalMulOne.toMul
MulOneClass.toMulOne
MulOne.toOne
MulOneClass.toMulOne
β€”le_of_mul_le_mul_right'
one_mul
le_one_of_mul_le_right πŸ“–mathematicalMulOne.toMul
MulOneClass.toMulOne
MulOne.toOne
MulOneClass.toMulOne
β€”le_of_mul_le_mul_left'
mul_one
lt_add_iff_pos_left πŸ“–mathematicalβ€”AddZero.toAdd
AddZeroClass.toAddZero
AddZero.toZero
β€”zero_add
add_lt_add_iff_right
lt_add_iff_pos_right πŸ“–mathematicalβ€”AddZero.toAdd
AddZeroClass.toAddZero
AddZero.toZero
β€”add_zero
add_lt_add_iff_left
lt_add_of_le_of_pos πŸ“–mathematicalPreorder.toLE
Preorder.toLT
AddZero.toZero
AddZeroClass.toAddZero
Preorder.toLT
AddZero.toAdd
AddZeroClass.toAddZero
β€”add_zero
add_lt_add_right
lt_add_of_lt_add_left πŸ“–mathematicalPreorder.toLT
Preorder.toLE
Preorder.toLTβ€”LT.lt.trans_le
add_le_add_right
lt_add_of_lt_add_right πŸ“–mathematicalPreorder.toLT
Preorder.toLE
Preorder.toLTβ€”LT.lt.trans_le
add_le_add_left
lt_add_of_lt_of_nonneg πŸ“–mathematicalPreorder.toLT
Preorder.toLE
AddZero.toZero
AddZeroClass.toAddZero
Preorder.toLT
AddZero.toAdd
AddZeroClass.toAddZero
β€”add_zero
add_le_add_right
lt_add_of_lt_of_pos πŸ“–mathematicalPreorder.toLT
AddZero.toZero
AddZeroClass.toAddZero
Preorder.toLT
AddZero.toAdd
AddZeroClass.toAddZero
β€”add_zero
add_lt_add_right
lt_add_of_lt_of_pos' πŸ“–mathematicalPreorder.toLT
AddZero.toZero
AddZeroClass.toAddZero
Preorder.toLT
AddZero.toAdd
AddZeroClass.toAddZero
β€”lt_add_of_lt_of_nonneg
LT.lt.le
lt_add_of_nonneg_of_lt πŸ“–mathematicalPreorder.toLE
AddZero.toZero
AddZeroClass.toAddZero
Preorder.toLT
Preorder.toLT
AddZero.toAdd
AddZeroClass.toAddZero
β€”zero_add
add_le_add_left
lt_add_of_pos_left πŸ“–mathematicalAddZero.toZero
AddZeroClass.toAddZero
AddZero.toAdd
AddZeroClass.toAddZero
β€”zero_add
add_lt_add_left
lt_add_of_pos_of_le πŸ“–mathematicalPreorder.toLT
AddZero.toZero
AddZeroClass.toAddZero
Preorder.toLE
Preorder.toLT
AddZero.toAdd
AddZeroClass.toAddZero
β€”zero_add
add_lt_add_left
lt_add_of_pos_of_lt πŸ“–mathematicalPreorder.toLT
AddZero.toZero
AddZeroClass.toAddZero
Preorder.toLT
AddZero.toAdd
AddZeroClass.toAddZero
β€”zero_add
add_lt_add_left
lt_add_of_pos_of_lt' πŸ“–mathematicalPreorder.toLT
AddZero.toZero
AddZeroClass.toAddZero
Preorder.toLT
AddZero.toAdd
AddZeroClass.toAddZero
β€”lt_add_of_nonneg_of_lt
LT.lt.le
lt_add_of_pos_right πŸ“–mathematicalAddZero.toZero
AddZeroClass.toAddZero
AddZero.toAdd
AddZeroClass.toAddZero
β€”add_zero
add_lt_add_right
lt_mul_iff_one_lt_left' πŸ“–mathematicalβ€”MulOne.toMul
MulOneClass.toMulOne
MulOne.toOne
β€”one_mul
mul_lt_mul_iff_right
lt_mul_iff_one_lt_right' πŸ“–mathematicalβ€”MulOne.toMul
MulOneClass.toMulOne
MulOne.toOne
β€”mul_one
mul_lt_mul_iff_left
lt_mul_of_le_of_one_lt πŸ“–mathematicalPreorder.toLE
Preorder.toLT
MulOne.toOne
MulOneClass.toMulOne
Preorder.toLT
MulOne.toMul
MulOneClass.toMulOne
β€”mul_one
mul_lt_mul_right
lt_mul_of_lt_mul_left πŸ“–mathematicalPreorder.toLT
Preorder.toLE
Preorder.toLTβ€”LT.lt.trans_le
mul_le_mul_right
lt_mul_of_lt_mul_right πŸ“–mathematicalPreorder.toLT
Preorder.toLE
Preorder.toLTβ€”LT.lt.trans_le
mul_le_mul_left
lt_mul_of_lt_of_one_le πŸ“–mathematicalPreorder.toLT
Preorder.toLE
MulOne.toOne
MulOneClass.toMulOne
Preorder.toLT
MulOne.toMul
MulOneClass.toMulOne
β€”mul_one
mul_le_mul_right
lt_mul_of_lt_of_one_lt πŸ“–mathematicalPreorder.toLT
MulOne.toOne
MulOneClass.toMulOne
Preorder.toLT
MulOne.toMul
MulOneClass.toMulOne
β€”mul_one
mul_lt_mul_right
lt_mul_of_lt_of_one_lt' πŸ“–mathematicalPreorder.toLT
MulOne.toOne
MulOneClass.toMulOne
Preorder.toLT
MulOne.toMul
MulOneClass.toMulOne
β€”lt_mul_of_lt_of_one_le
LT.lt.le
lt_mul_of_one_le_of_lt πŸ“–mathematicalPreorder.toLE
MulOne.toOne
MulOneClass.toMulOne
Preorder.toLT
Preorder.toLT
MulOne.toMul
MulOneClass.toMulOne
β€”one_mul
mul_le_mul_left
lt_mul_of_one_lt_left' πŸ“–mathematicalMulOne.toOne
MulOneClass.toMulOne
MulOne.toMul
MulOneClass.toMulOne
β€”one_mul
mul_lt_mul_left
lt_mul_of_one_lt_of_le πŸ“–mathematicalPreorder.toLT
MulOne.toOne
MulOneClass.toMulOne
Preorder.toLE
Preorder.toLT
MulOne.toMul
MulOneClass.toMulOne
β€”one_mul
mul_lt_mul_left
lt_mul_of_one_lt_of_lt πŸ“–mathematicalPreorder.toLT
MulOne.toOne
MulOneClass.toMulOne
Preorder.toLT
MulOne.toMul
MulOneClass.toMulOne
β€”one_mul
mul_lt_mul_left
lt_mul_of_one_lt_of_lt' πŸ“–mathematicalPreorder.toLT
MulOne.toOne
MulOneClass.toMulOne
Preorder.toLT
MulOne.toMul
MulOneClass.toMulOne
β€”lt_mul_of_one_le_of_lt
LT.lt.le
lt_mul_of_one_lt_right' πŸ“–mathematicalMulOne.toOne
MulOneClass.toMulOne
MulOne.toMul
MulOneClass.toMulOne
β€”mul_one
mul_lt_mul_right
lt_of_add_lt_add_left πŸ“–β€”β€”β€”β€”ContravariantClass.elim
lt_of_add_lt_add_right πŸ“–β€”β€”β€”β€”ContravariantClass.elim
lt_of_add_lt_of_nonneg_left πŸ“–mathematicalPreorder.toLT
AddZero.toAdd
AddZeroClass.toAddZero
Preorder.toLE
AddZero.toZero
Preorder.toLTβ€”LE.le.trans_lt
le_add_of_nonneg_right
lt_of_add_lt_of_nonneg_right πŸ“–mathematicalPreorder.toLT
AddZero.toAdd
AddZeroClass.toAddZero
Preorder.toLE
AddZero.toZero
Preorder.toLTβ€”LE.le.trans_lt
le_add_of_nonneg_left
lt_of_lt_add_of_nonpos_left πŸ“–mathematicalPreorder.toLT
AddZero.toAdd
AddZeroClass.toAddZero
Preorder.toLE
AddZero.toZero
Preorder.toLTβ€”LT.lt.trans_le
add_le_of_nonpos_right
lt_of_lt_add_of_nonpos_right πŸ“–mathematicalPreorder.toLT
AddZero.toAdd
AddZeroClass.toAddZero
Preorder.toLE
AddZero.toZero
Preorder.toLTβ€”LT.lt.trans_le
add_le_of_nonpos_left
lt_of_lt_mul_of_le_one_left πŸ“–mathematicalPreorder.toLT
MulOne.toMul
MulOneClass.toMulOne
Preorder.toLE
MulOne.toOne
Preorder.toLTβ€”LT.lt.trans_le
mul_le_of_le_one_right'
lt_of_lt_mul_of_le_one_right πŸ“–mathematicalPreorder.toLT
MulOne.toMul
MulOneClass.toMulOne
Preorder.toLE
MulOne.toOne
Preorder.toLTβ€”LT.lt.trans_le
mul_le_of_le_one_left'
lt_of_mul_lt_mul_left' πŸ“–β€”β€”β€”β€”ContravariantClass.elim
lt_of_mul_lt_mul_right' πŸ“–β€”β€”β€”β€”ContravariantClass.elim
lt_of_mul_lt_of_one_le_left πŸ“–mathematicalPreorder.toLT
MulOne.toMul
MulOneClass.toMulOne
Preorder.toLE
MulOne.toOne
Preorder.toLTβ€”LE.le.trans_lt
le_mul_of_one_le_right'
lt_of_mul_lt_of_one_le_right πŸ“–mathematicalPreorder.toLT
MulOne.toMul
MulOneClass.toMulOne
Preorder.toLE
MulOne.toOne
Preorder.toLTβ€”LE.le.trans_lt
le_mul_of_one_le_left'
lt_one_of_mul_lt_left πŸ“–mathematicalMulOne.toMul
MulOneClass.toMulOne
MulOne.toOne
MulOneClass.toMulOne
β€”lt_of_mul_lt_mul_right'
one_mul
lt_one_of_mul_lt_right πŸ“–mathematicalMulOne.toMul
MulOneClass.toMulOne
MulOne.toOne
MulOneClass.toMulOne
β€”lt_of_mul_lt_mul_left'
mul_one
max_add πŸ“–mathematicalβ€”SemilatticeSup.toMax
Lattice.toSemilatticeSup
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
β€”Monotone.map_max
add_left_mono
max_add_add_le_max_add_max πŸ“–mathematicalβ€”Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
SemilatticeSup.toMax
Lattice.toSemilatticeSup
β€”max_le
add_le_add
le_max_left
le_max_right
max_mul πŸ“–mathematicalβ€”SemilatticeSup.toMax
Lattice.toSemilatticeSup
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
β€”Monotone.map_max
mul_left_mono
max_mul_mul_le_max_mul_max' πŸ“–mathematicalβ€”Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
SemilatticeSup.toMax
Lattice.toSemilatticeSup
β€”max_le
mul_le_mul'
le_max_left
le_max_right
min_add πŸ“–mathematicalβ€”SemilatticeInf.toMin
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
β€”Monotone.map_min
add_left_mono
min_add_min_le_min_add_add πŸ“–mathematicalβ€”Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
SemilatticeInf.toMin
β€”le_min
add_le_add
min_le_left
min_le_right
min_le_max_of_add_le_add πŸ“–mathematicalPreorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
SemilatticeInf.toMin
SemilatticeSup.toMax
Lattice.toSemilatticeSup
β€”Left.min_le_max_of_add_le_add
addRightMono_of_addRightStrictMono
min_le_max_of_mul_le_mul πŸ“–mathematicalPreorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
SemilatticeInf.toMin
SemilatticeSup.toMax
Lattice.toSemilatticeSup
β€”Left.min_le_max_of_mul_le_mul
mulRightMono_of_mulRightStrictMono
min_lt_max_of_add_lt_add πŸ“–mathematicalPreorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Preorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
SemilatticeInf.toMin
SemilatticeSup.toMax
Lattice.toSemilatticeSup
β€”min_lt_iff
lt_max_iff
Mathlib.Tactic.Contrapose.contrapose₁
not_lt
add_le_add
min_lt_max_of_mul_lt_mul πŸ“–mathematicalPreorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Preorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
SemilatticeInf.toMin
SemilatticeSup.toMax
Lattice.toSemilatticeSup
β€”Mathlib.Tactic.Contrapose.contrapose₁
mul_le_mul'
min_mul πŸ“–mathematicalβ€”SemilatticeInf.toMin
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
β€”Monotone.map_min
mul_left_mono
min_mul_min_le_min_mul_mul' πŸ“–mathematicalβ€”Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
SemilatticeInf.toMin
β€”le_min
mul_le_mul'
min_le_left
min_le_right
mulLECancellable_mul πŸ“–mathematicalβ€”MulLECancellable
CommMagma.toMul
CommSemigroup.toCommMagma
β€”MulLECancellable.of_mul_left
MulLECancellable.of_mul_right
MulLECancellable.mul
mulLECancellable_one πŸ“–mathematicalβ€”MulLECancellable
MulOne.toMul
MulOneClass.toMulOne
MulOne.toOne
β€”one_mul
mul_eq_mul_iff_eq_and_eq πŸ“–β€”Preorder.toLE
PartialOrder.toPreorder
β€”β€”le_antisymm_iff
mul_le_mul'
mulLeftMono_of_mulLeftStrictMono
mulRightMono_of_mulRightStrictMono
mul_le_mul_iff_of_ge
mul_eq_one_iff_of_one_le πŸ“–mathematicalPreorder.toLE
PartialOrder.toPreorder
MulOne.toOne
MulOneClass.toMulOne
MulOne.toMul
MulOneClass.toMulOne
MulOne.toOne
β€”le_mul_of_le_of_one_le
le_rfl
le_antisymm
le_mul_of_one_le_of_le
mul_one
mul_le_iff_le_one_left' πŸ“–mathematicalβ€”MulOne.toMul
MulOneClass.toMulOne
MulOne.toOne
β€”one_mul
mul_le_mul_iff_right
mul_le_iff_le_one_right' πŸ“–mathematicalβ€”MulOne.toMul
MulOneClass.toMulOne
MulOne.toOne
β€”mul_one
mul_le_mul_iff_left
mul_le_mul' πŸ“–mathematicalPreorder.toLEPreorder.toLEβ€”le_imp_le_of_le_of_le
mul_le_mul_left
le_refl
mul_le_mul_right
mul_le_mul_iff_left πŸ“–β€”β€”β€”β€”rel_iff_cov
mul_le_mul_iff_of_ge πŸ“–mathematicalPreorder.toLE
PartialOrder.toPreorder
Preorder.toLE
PartialOrder.toPreorder
β€”LE.le.not_gt
mul_lt_mul_of_lt_of_le
mulLeftMono_of_mulLeftStrictMono
mul_lt_mul_of_le_of_lt
mulRightMono_of_mulRightStrictMono
le_refl
mul_le_mul_iff_right πŸ“–β€”β€”β€”β€”rel_iff_cov
mul_le_mul_left πŸ“–β€”β€”β€”β€”CovariantClass.elim
mul_le_mul_left' πŸ“–β€”β€”β€”β€”mul_le_mul_right
mul_le_mul_right πŸ“–β€”β€”β€”β€”CovariantClass.elim
mul_le_mul_right' πŸ“–β€”β€”β€”β€”mul_le_mul_left
mul_le_mul_three πŸ“–mathematicalPreorder.toLEPreorder.toLEβ€”mul_le_mul'
mul_le_of_le_of_le_one πŸ“–mathematicalPreorder.toLE
MulOne.toOne
MulOneClass.toMulOne
Preorder.toLE
MulOne.toMul
MulOneClass.toMulOne
β€”mul_le_mul_right
mul_one
mul_le_of_le_one_left' πŸ“–mathematicalMulOne.toOne
MulOneClass.toMulOne
MulOne.toMul
MulOneClass.toMulOne
β€”mul_le_mul_left
one_mul
mul_le_of_le_one_of_le πŸ“–mathematicalPreorder.toLE
MulOne.toOne
MulOneClass.toMulOne
Preorder.toLE
MulOne.toMul
MulOneClass.toMulOne
β€”mul_le_mul_left
one_mul
mul_le_of_le_one_right' πŸ“–mathematicalMulOne.toOne
MulOneClass.toMulOne
MulOne.toMul
MulOneClass.toMulOne
β€”mul_le_mul_right
mul_one
mul_le_of_mul_le_left πŸ“–mathematicalPreorder.toLEPreorder.toLEβ€”act_rel_of_rel_of_act_rel
instIsTransLe
mul_le_of_mul_le_right πŸ“–mathematicalPreorder.toLEPreorder.toLEβ€”LE.le.trans
mul_le_mul_left
mul_le_one' πŸ“–mathematicalPreorder.toLE
MulOne.toOne
MulOneClass.toMulOne
Preorder.toLE
MulOne.toMul
MulOneClass.toMulOne
MulOne.toOne
β€”Left.mul_le_one
mul_left_cancel'' πŸ“–β€”β€”β€”β€”mul_left_cancel
mul_left_inj_of_comparable πŸ“–β€”Preorder.toLE
PartialOrder.toPreorder
β€”β€”Mathlib.Tactic.Contrapose.contrapose₁
LT.lt.ne'
mul_lt_mul_left
LE.le.lt_of_ne'
LT.lt.ne
LE.le.lt_of_ne
mul_left_mono πŸ“–mathematicalβ€”Monotoneβ€”mul_le_mul_left
mul_left_strictMono πŸ“–mathematicalβ€”StrictMonoβ€”mul_lt_mul_left
mul_lt_iff_lt_one_left' πŸ“–mathematicalβ€”MulOne.toMul
MulOneClass.toMulOne
MulOne.toOne
β€”mul_one
mul_lt_mul_iff_left
mul_lt_iff_lt_one_right' πŸ“–mathematicalβ€”MulOne.toMul
MulOneClass.toMulOne
MulOne.toOne
β€”one_mul
mul_lt_mul_iff_right
mul_lt_mul_iff_left πŸ“–β€”β€”β€”β€”rel_iff_cov
mul_lt_mul_iff_right πŸ“–β€”β€”β€”β€”rel_iff_cov
mul_lt_mul_left πŸ“–β€”β€”β€”β€”CovariantClass.elim
mul_lt_mul_of_le_of_lt πŸ“–mathematicalPreorder.toLE
Preorder.toLT
Preorder.toLTβ€”LE.le.trans_lt
mul_le_mul_left
mul_lt_mul_right
mul_lt_mul_of_lt_of_le πŸ“–mathematicalPreorder.toLT
Preorder.toLE
Preorder.toLTβ€”LE.le.trans_lt
mul_le_mul_right
mul_lt_mul_left
mul_lt_mul_of_lt_of_lt πŸ“–mathematicalPreorder.toLTPreorder.toLTβ€”mul_lt_mul_right
mul_lt_mul_left
mul_lt_mul_right πŸ“–β€”β€”β€”β€”CovariantClass.elim
mul_lt_of_le_of_lt_one πŸ“–mathematicalPreorder.toLE
Preorder.toLT
MulOne.toOne
MulOneClass.toMulOne
Preorder.toLT
MulOne.toMul
MulOneClass.toMulOne
β€”mul_lt_mul_right
mul_one
mul_lt_of_le_one_of_lt πŸ“–mathematicalPreorder.toLE
MulOne.toOne
MulOneClass.toMulOne
Preorder.toLT
Preorder.toLT
MulOne.toMul
MulOneClass.toMulOne
β€”mul_le_mul_left
one_mul
mul_lt_of_lt_of_le_one πŸ“–mathematicalPreorder.toLT
Preorder.toLE
MulOne.toOne
MulOneClass.toMulOne
Preorder.toLT
MulOne.toMul
MulOneClass.toMulOne
β€”mul_le_mul_right
mul_one
mul_lt_of_lt_of_lt_one πŸ“–mathematicalPreorder.toLT
MulOne.toOne
MulOneClass.toMulOne
Preorder.toLT
MulOne.toMul
MulOneClass.toMulOne
β€”mul_lt_mul_right
mul_one
mul_lt_of_lt_of_lt_one' πŸ“–mathematicalPreorder.toLT
MulOne.toOne
MulOneClass.toMulOne
Preorder.toLT
MulOne.toMul
MulOneClass.toMulOne
β€”mul_lt_of_lt_of_le_one
LT.lt.le
mul_lt_of_lt_one_left' πŸ“–mathematicalMulOne.toOne
MulOneClass.toMulOne
MulOne.toMul
MulOneClass.toMulOne
β€”mul_lt_mul_left
one_mul
mul_lt_of_lt_one_of_le πŸ“–mathematicalPreorder.toLT
MulOne.toOne
MulOneClass.toMulOne
Preorder.toLE
Preorder.toLT
MulOne.toMul
MulOneClass.toMulOne
β€”mul_lt_mul_left
one_mul
mul_lt_of_lt_one_of_lt πŸ“–mathematicalPreorder.toLT
MulOne.toOne
MulOneClass.toMulOne
Preorder.toLT
MulOne.toMul
MulOneClass.toMulOne
β€”mul_lt_mul_left
one_mul
mul_lt_of_lt_one_of_lt' πŸ“–mathematicalPreorder.toLT
MulOne.toOne
MulOneClass.toMulOne
Preorder.toLT
MulOne.toMul
MulOneClass.toMulOne
β€”mul_lt_of_le_one_of_lt
LT.lt.le
mul_lt_of_lt_one_right' πŸ“–mathematicalMulOne.toOne
MulOneClass.toMulOne
MulOne.toMul
MulOneClass.toMulOne
β€”mul_lt_mul_right
mul_one
mul_lt_of_mul_lt_left πŸ“–mathematicalPreorder.toLT
Preorder.toLE
Preorder.toLTβ€”LE.le.trans_lt
mul_le_mul_right
mul_lt_of_mul_lt_right πŸ“–mathematicalPreorder.toLT
Preorder.toLE
Preorder.toLTβ€”LE.le.trans_lt
mul_le_mul_left
mul_lt_one πŸ“–mathematicalPreorder.toLT
MulOne.toOne
MulOneClass.toMulOne
Preorder.toLT
MulOne.toMul
MulOneClass.toMulOne
MulOne.toOne
β€”Left.mul_lt_one
mul_lt_one' πŸ“–mathematicalPreorder.toLT
MulOne.toOne
MulOneClass.toMulOne
Preorder.toLT
MulOne.toMul
MulOneClass.toMulOne
MulOne.toOne
β€”Left.mul_lt_one'
mul_lt_one_of_le_of_lt πŸ“–mathematicalPreorder.toLE
MulOne.toOne
MulOneClass.toMulOne
Preorder.toLT
Preorder.toLT
MulOne.toMul
MulOneClass.toMulOne
MulOne.toOne
β€”Left.mul_lt_one_of_le_of_lt
mul_lt_one_of_lt_of_le πŸ“–mathematicalPreorder.toLT
MulOne.toOne
MulOneClass.toMulOne
Preorder.toLE
Preorder.toLT
MulOne.toMul
MulOneClass.toMulOne
MulOne.toOne
β€”Left.mul_lt_one_of_lt_of_le
mul_max πŸ“–mathematicalβ€”SemilatticeSup.toMax
Lattice.toSemilatticeSup
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
β€”Monotone.map_max
mul_right_mono
mul_min πŸ“–mathematicalβ€”SemilatticeInf.toMin
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
β€”Monotone.map_min
mul_right_mono
mul_right_cancel'' πŸ“–β€”β€”β€”β€”mul_right_cancel
mul_right_inj_of_comparable πŸ“–β€”Preorder.toLE
PartialOrder.toPreorder
β€”β€”Mathlib.Tactic.Contrapose.contrapose₁
LT.lt.ne'
mul_lt_mul_right
LE.le.lt_of_ne'
LT.lt.ne
LE.le.lt_of_ne
mul_right_mono πŸ“–mathematicalβ€”Monotoneβ€”mul_le_mul_right
mul_right_strictMono πŸ“–mathematicalβ€”StrictMonoβ€”mul_lt_mul_right
neg_of_add_lt_left πŸ“–mathematicalAddZero.toAdd
AddZeroClass.toAddZero
AddZero.toZero
AddZeroClass.toAddZero
β€”lt_of_add_lt_add_right
zero_add
neg_of_add_lt_right πŸ“–mathematicalAddZero.toAdd
AddZeroClass.toAddZero
AddZero.toZero
AddZeroClass.toAddZero
β€”lt_of_add_lt_add_left
add_zero
nonneg_of_le_add_left πŸ“–mathematicalAddZero.toAdd
AddZeroClass.toAddZero
AddZero.toZero
AddZeroClass.toAddZero
β€”le_of_add_le_add_right
zero_add
nonneg_of_le_add_right πŸ“–mathematicalAddZero.toAdd
AddZeroClass.toAddZero
AddZero.toZero
AddZeroClass.toAddZero
β€”le_of_add_le_add_left
add_zero
nonpos_of_add_le_left πŸ“–mathematicalAddZero.toAdd
AddZeroClass.toAddZero
AddZero.toZero
AddZeroClass.toAddZero
β€”le_of_add_le_add_right
zero_add
nonpos_of_add_le_right πŸ“–mathematicalAddZero.toAdd
AddZeroClass.toAddZero
AddZero.toZero
AddZeroClass.toAddZero
β€”le_of_add_le_add_left
add_zero
one_le_mul πŸ“–mathematicalPreorder.toLE
MulOne.toOne
MulOneClass.toMulOne
Preorder.toLE
MulOne.toOne
MulOneClass.toMulOne
MulOne.toMul
β€”Left.one_le_mul
one_le_of_le_mul_left πŸ“–mathematicalMulOne.toMul
MulOneClass.toMulOne
MulOne.toOne
MulOneClass.toMulOne
β€”le_of_mul_le_mul_right'
one_mul
one_le_of_le_mul_right πŸ“–mathematicalMulOne.toMul
MulOneClass.toMulOne
MulOne.toOne
MulOneClass.toMulOne
β€”le_of_mul_le_mul_left'
mul_one
one_lt_mul' πŸ“–mathematicalPreorder.toLT
MulOne.toOne
MulOneClass.toMulOne
Preorder.toLT
MulOne.toOne
MulOneClass.toMulOne
MulOne.toMul
β€”Left.one_lt_mul
one_lt_mul'' πŸ“–mathematicalPreorder.toLT
MulOne.toOne
MulOneClass.toMulOne
Preorder.toLT
MulOne.toOne
MulOneClass.toMulOne
MulOne.toMul
β€”Left.one_lt_mul'
one_lt_mul_of_le_of_lt' πŸ“–mathematicalPreorder.toLE
MulOne.toOne
MulOneClass.toMulOne
Preorder.toLT
Preorder.toLT
MulOne.toOne
MulOneClass.toMulOne
MulOne.toMul
β€”Left.one_lt_mul_of_le_of_lt
one_lt_mul_of_lt_of_le' πŸ“–mathematicalPreorder.toLT
MulOne.toOne
MulOneClass.toMulOne
Preorder.toLE
Preorder.toLT
MulOne.toOne
MulOneClass.toMulOne
MulOne.toMul
β€”Left.one_lt_mul_of_lt_of_le
one_lt_of_lt_mul_left πŸ“–mathematicalMulOne.toMul
MulOneClass.toMulOne
MulOne.toOne
MulOneClass.toMulOne
β€”lt_of_mul_lt_mul_right'
one_mul
one_lt_of_lt_mul_right πŸ“–mathematicalMulOne.toMul
MulOneClass.toMulOne
MulOne.toOne
MulOneClass.toMulOne
β€”lt_of_mul_lt_mul_left'
mul_one
pos_of_lt_add_left πŸ“–mathematicalAddZero.toAdd
AddZeroClass.toAddZero
AddZero.toZero
AddZeroClass.toAddZero
β€”lt_of_add_lt_add_right
zero_add
pos_of_lt_add_right πŸ“–mathematicalAddZero.toAdd
AddZeroClass.toAddZero
AddZero.toZero
AddZeroClass.toAddZero
β€”lt_of_add_lt_add_left
add_zero
trichotomy_of_add_eq_add πŸ“–mathematicalβ€”Preorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
β€”lt_trichotomy
add_right_inj_of_comparable
le_total
ne_of_lt
add_lt_add_left
add_lt_add_of_lt_of_lt
trichotomy_of_mul_eq_mul πŸ“–mathematicalβ€”Preorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
β€”lt_trichotomy
mul_right_inj_of_comparable
le_total
ne_of_lt
mul_lt_mul_left
mul_lt_mul_of_lt_of_lt

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