Documentation Verification Report

Defs

📁 Source: Mathlib/Algebra/Order/Monoid/Canonical/Defs.lean

Statistics

MetricCount
DefinitionsCanonicallyOrderedAdd, toUniqueAddUnits, toUniqueUnits, CanonicallyOrderedMul
4
Theoremsle_add_self, le_self_add, toAddLeftMono, toExistsAddOfLE, toIsOrderedAddMonoid, le_mul_self, le_self_mul, toExistsMulOfLE, toIsOrderedMonoid, toMulLeftMono, one_lt, pos, one_lt, pos, of_ge, of_gt, of_gt', pos, add_pos_iff, bot_eq_one, bot_eq_one', bot_eq_zero, bot_eq_zero', eq_one_or_one_lt, eq_zero_or_pos, exists_one_lt_mul_of_lt, exists_pos_add_of_lt, isBot_one, isBot_zero, le_add_left, le_add_of_le_left, le_add_of_le_right, le_add_right, le_add_self, le_iff_exists_add, le_iff_exists_add', le_iff_exists_mul, le_iff_exists_mul', le_mul_left, le_mul_of_le_left, le_mul_of_le_right, le_mul_right, le_mul_self, le_of_add_le_left, le_of_add_le_right, le_of_mul_le_left, le_of_mul_le_right, le_one_iff_eq_one, le_self_add, le_self_mul, lt_iff_exists_add, lt_iff_exists_mul, min_add_distrib, min_add_distrib', min_mul_distrib, min_mul_distrib', min_one, min_zero, nonpos_iff_eq_zero, not_lt_one, not_lt_zero, not_neg, one_le, one_lt_iff_ne_one, one_lt_mul_iff, one_lt_of_gt, one_lt_of_ne_one, one_min, one_notMem_iff, pos_iff_ne_zero, pos_of_gt, pos_of_ne_zero, self_le_add_left, self_le_add_right, self_le_mul_left, self_le_mul_right, zero_le, zero_min, zero_notMem_iff
79
Total83

CanonicallyOrderedAdd

Theorems

NameKindAssumesProvesValidatesDepends On
le_add_self 📖
le_self_add 📖
toAddLeftMono 📖mathematicalAddLeftMono
AddSemigroup.toAdd
ExistsAddOfLE.exists_add_of_le
toExistsAddOfLE
le_iff_exists_add
add_assoc
toExistsAddOfLE 📖mathematicalExistsAddOfLE
toIsOrderedAddMonoid 📖mathematicalIsOrderedAddMonoidadd_le_add_left
covariant_swap_add_of_covariant_add
toAddLeftMono

CanonicallyOrderedCommMonoid

Definitions

NameCategoryTheorems
toUniqueAddUnits 📖CompOp
toUniqueUnits 📖CompOp

CanonicallyOrderedMul

Theorems

NameKindAssumesProvesValidatesDepends On
le_mul_self 📖
le_self_mul 📖
toExistsMulOfLE 📖mathematicalExistsMulOfLE
toIsOrderedMonoid 📖mathematicalIsOrderedMonoidmul_le_mul_left
covariant_swap_mul_of_covariant_mul
toMulLeftMono
toMulLeftMono 📖mathematicalMulLeftMono
Semigroup.toMul
ExistsMulOfLE.exists_mul_of_le
toExistsMulOfLE
le_iff_exists_mul
mul_assoc

LT.lt

Theorems

NameKindAssumesProvesValidatesDepends On
one_lt 📖mathematicalPreorder.toLTMulOne.toOne
MulOneClass.toMulOne
one_lt_of_gt
pos 📖mathematicalPreorder.toLTAddZero.toZero
AddZeroClass.toAddZero
pos_of_gt

NE.ne

Theorems

NameKindAssumesProvesValidatesDepends On
one_lt 📖mathematicalPreorder.toLT
PartialOrder.toPreorder
MulOne.toOne
MulOneClass.toMulOne
one_lt_of_ne_one
pos 📖mathematicalPreorder.toLT
PartialOrder.toPreorder
AddZero.toZero
AddZeroClass.toAddZero
pos_of_ne_zero

NeZero

Theorems

NameKindAssumesProvesValidatesDepends On
of_ge 📖mathematicalPreorder.toLE
PartialOrder.toPreorder
AddZero.toZero
AddZeroClass.toAddZero
of_pos
lt_of_lt_of_le
pos
of_gt 📖mathematicalPreorder.toLTAddZero.toZero
AddZeroClass.toAddZero
of_pos
pos_of_gt
of_gt' 📖mathematicalAddZero.toZero
AddZeroClass.toAddZero
of_gt
Fact.out
pos 📖mathematicalPreorder.toLT
PartialOrder.toPreorder
AddZero.toZero
AddZeroClass.toAddZero
LE.le.lt_of_ne
zero_le

(root)

Definitions

NameCategoryTheorems
CanonicallyOrderedAdd 📖CompData
21 mathmath: ENNReal.instCanonicallyOrderedAdd, Finsupp.instCanonicallyOrderedAddOfAddLeftMono, Nat.instCanonicallyOrderedAdd, PartENat.instCanonicallyOrderedAdd, Nonneg.canonicallyOrderedAdd, Multiset.instCanonicallyOrderedAdd, Filter.Germ.instCanonicallyOrderedAdd, NNReal.instCanonicallyOrderedAdd, SetSemiring.instCanonicallyOrderedAdd, Cardinal.canonicallyOrderedAdd, NNRat.instCanonicallyOrderedAdd, LieSubalgebra.instCanonicallyOrderedAdd, Additive.canonicallyOrderedAdd, Submodule.instCanonicallyOrderedAdd, IdemSemiring.toCanonicallyOrderedAdd, Prod.instCanonicallyOrderedAdd, WithTop.canonicallyOrderedAdd, PUnit.canonicallyOrderedAdd, Ordinal.canonicallyOrderedAdd, FractionalIdeal.instCanonicallyOrderedAdd, WithZero.instCanonicallyOrderedAdd
CanonicallyOrderedMul 📖CompData
4 mathmath: Prod.instCanonicallyOrderedMul, Filter.Germ.instCanonicallyOrderedMul, Multiplicative.canonicallyOrderedMul, Associates.instCanonicallyOrderedMul

Theorems

NameKindAssumesProvesValidatesDepends On
add_pos_iff 📖mathematicalPreorder.toLT
PartialOrder.toPreorder
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
AddZero.toAdd
pos_iff_ne_zero
add_eq_zero
Unique.instSubsingleton
not_and_or
bot_eq_one 📖mathematicalBot.bot
OrderBot.toBot
Preorder.toLE
PartialOrder.toPreorder
MulOne.toOne
MulOneClass.toMulOne
IsBot.eq_bot
isBot_one
bot_eq_one' 📖mathematicalBot.bot
OrderBot.toBot
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
MulOne.toOne
MulOneClass.toMulOne
Monoid.toMulOneClass
bot_eq_one
bot_eq_zero 📖mathematicalBot.bot
OrderBot.toBot
Preorder.toLE
PartialOrder.toPreorder
AddZero.toZero
AddZeroClass.toAddZero
IsBot.eq_bot
isBot_zero
bot_eq_zero' 📖mathematicalBot.bot
OrderBot.toBot
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
bot_eq_zero
eq_one_or_one_lt 📖mathematicalMulOne.toOne
MulOneClass.toMulOne
Preorder.toLT
PartialOrder.toPreorder
LE.le.eq_or_lt
one_le
eq_zero_or_pos 📖mathematicalAddZero.toZero
AddZeroClass.toAddZero
Preorder.toLT
PartialOrder.toPreorder
LE.le.eq_or_lt
zero_le
exists_one_lt_mul_of_lt 📖mathematicalPreorder.toLT
PartialOrder.toPreorder
MulOne.toMul
MulOneClass.toMulOne
le_iff_exists_mul
LT.lt.le
one_lt_iff_ne_one
mul_one
exists_pos_add_of_lt 📖mathematicalPreorder.toLT
PartialOrder.toPreorder
AddZero.toAdd
AddZeroClass.toAddZero
le_iff_exists_add
LT.lt.le
pos_iff_ne_zero
add_zero
lt_self_iff_false
isBot_one 📖mathematicalIsBot
MulOne.toOne
MulOneClass.toMulOne
one_le
isBot_zero 📖mathematicalIsBot
AddZero.toZero
AddZeroClass.toAddZero
zero_le
le_add_left 📖Preorder.toLEle_add_of_le_right
le_add_of_le_left 📖Preorder.toLELE.le.trans'
le_self_add
le_add_of_le_right 📖Preorder.toLELE.le.trans'
le_add_self
le_add_right 📖Preorder.toLEle_add_of_le_left
le_add_self 📖CanonicallyOrderedAdd.le_add_self
le_iff_exists_add 📖ExistsAddOfLE.exists_add_of_le
CanonicallyOrderedAdd.toExistsAddOfLE
le_self_add
le_iff_exists_add' 📖mathematicalPreorder.toLE
AddCommMagma.toAdd
le_iff_exists_add
add_comm
le_iff_exists_mul 📖ExistsMulOfLE.exists_mul_of_le
CanonicallyOrderedMul.toExistsMulOfLE
le_self_mul
le_iff_exists_mul' 📖mathematicalPreorder.toLE
CommMagma.toMul
mul_comm
le_mul_left 📖Preorder.toLEle_mul_of_le_right
le_mul_of_le_left 📖Preorder.toLELE.le.trans'
le_self_mul
le_mul_of_le_right 📖Preorder.toLELE.le.trans'
le_mul_self
le_mul_right 📖Preorder.toLEle_mul_of_le_left
le_mul_self 📖CanonicallyOrderedMul.le_mul_self
le_of_add_le_left 📖Preorder.toLELE.le.trans
le_self_add
le_of_add_le_right 📖Preorder.toLELE.le.trans
le_add_self
le_of_mul_le_left 📖Preorder.toLELE.le.trans
le_self_mul
le_of_mul_le_right 📖Preorder.toLELE.le.trans
le_mul_self
le_one_iff_eq_one 📖mathematicalPreorder.toLE
PartialOrder.toPreorder
MulOne.toOne
MulOneClass.toMulOne
LE.le.ge_iff_eq'
one_le
le_self_add 📖CanonicallyOrderedAdd.le_self_add
le_self_mul 📖CanonicallyOrderedMul.le_self_mul
lt_iff_exists_add 📖mathematicalPreorder.toLT
PartialOrder.toPreorder
AddZero.toZero
AddZeroClass.toAddZero
AddZero.toAdd
lt_iff_le_and_ne
le_iff_exists_add
pos_iff_ne_zero
add_zero
LE.le.lt_iff_ne
self_le_add_right
lt_add_of_pos_right
lt_iff_exists_mul 📖mathematicalPreorder.toLT
PartialOrder.toPreorder
MulOne.toOne
MulOneClass.toMulOne
MulOne.toMul
lt_iff_le_and_ne
le_iff_exists_mul
one_lt_iff_ne_one
mul_one
LE.le.lt_iff_ne
self_le_mul_right
lt_mul_of_one_lt_right'
min_add_distrib 📖mathematicalSemilatticeInf.toMin
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
le_total
inf_of_le_left
le_add_right
self_le_add_right
le_add_left
self_le_add_left
inf_of_le_right
min_add_distrib' 📖mathematicalSemilatticeInf.toMin
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
min_comm
min_add_distrib
min_mul_distrib 📖mathematicalSemilatticeInf.toMin
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
le_total
inf_of_le_left
inf_of_le_right
min_mul_distrib' 📖mathematicalSemilatticeInf.toMin
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
min_comm
min_mul_distrib
min_one 📖mathematicalSemilatticeInf.toMin
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
MulOne.toOne
MulOneClass.toMulOne
Monoid.toMulOneClass
min_eq_right
one_le
min_zero 📖mathematicalSemilatticeInf.toMin
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
min_eq_right
zero_le
nonpos_iff_eq_zero 📖mathematicalPreorder.toLE
PartialOrder.toPreorder
AddZero.toZero
AddZeroClass.toAddZero
LE.le.ge_iff_eq'
zero_le
not_lt_one 📖mathematicalPreorder.toLT
MulOne.toOne
MulOneClass.toMulOne
LE.le.not_gt
one_le
not_lt_zero 📖mathematicalPreorder.toLT
AddZero.toZero
AddZeroClass.toAddZero
LE.le.not_gt
zero_le
not_neg 📖mathematicalPreorder.toLT
MulOne.toOne
MulOneClass.toMulOne
not_lt_one
one_le 📖mathematicalMulOne.toOne
MulOneClass.toMulOne
LE.le.trans_eq
le_self_mul
one_mul
one_lt_iff_ne_one 📖mathematicalPreorder.toLT
PartialOrder.toPreorder
MulOne.toOne
MulOneClass.toMulOne
LE.le.lt_iff_ne
one_le
one_lt_mul_iff 📖mathematicalPreorder.toLT
PartialOrder.toPreorder
MulOne.toOne
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
MulOne.toMul
Unique.instSubsingleton
one_lt_of_gt 📖mathematicalPreorder.toLTMulOne.toOne
MulOneClass.toMulOne
LE.le.trans_lt
one_le
one_lt_of_ne_one 📖mathematicalPreorder.toLT
PartialOrder.toPreorder
MulOne.toOne
MulOneClass.toMulOne
one_lt_iff_ne_one
one_min 📖mathematicalSemilatticeInf.toMin
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
MulOne.toOne
MulOneClass.toMulOne
Monoid.toMulOneClass
min_eq_left
one_le
one_notMem_iff 📖mathematicalSet
Set.instMembership
MulOne.toOne
MulOneClass.toMulOne
Preorder.toLT
PartialOrder.toPreorder
bot_notMem_iff
bot_eq_one
pos_iff_ne_zero 📖mathematicalPreorder.toLT
PartialOrder.toPreorder
AddZero.toZero
AddZeroClass.toAddZero
LE.le.lt_iff_ne
zero_le
pos_of_gt 📖mathematicalPreorder.toLTAddZero.toZero
AddZeroClass.toAddZero
LE.le.trans_lt
zero_le
pos_of_ne_zero 📖mathematicalPreorder.toLT
PartialOrder.toPreorder
AddZero.toZero
AddZeroClass.toAddZero
pos_iff_ne_zero
self_le_add_left 📖le_add_self
self_le_add_right 📖le_self_add
self_le_mul_left 📖le_mul_self
self_le_mul_right 📖le_self_mul
zero_le 📖mathematicalAddZero.toZero
AddZeroClass.toAddZero
LE.le.trans_eq
le_self_add
zero_add
zero_min 📖mathematicalSemilatticeInf.toMin
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
min_eq_left
zero_le
zero_notMem_iff 📖mathematicalSet
Set.instMembership
AddZero.toZero
AddZeroClass.toAddZero
Preorder.toLT
PartialOrder.toPreorder
bot_notMem_iff
bot_eq_zero

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