Documentation Verification Report

MinMax

📁 Source: Mathlib/Order/MinMax.lean

Statistics

MetricCount
Definitions0
Theoremsmap_max, map_min, map_max, map_min, left_comm, right_comm, map_max, map_min, map_max, map_min, instAssociativeMax, instAssociativeMin, instCommutativeMax, instCommutativeMin, instLawfulOrderInf_mathlib, instLawfulOrderSup_mathlib, le_max_iff, le_max_of_le_left, le_max_of_le_right, le_min_iff, le_of_max_le_left, le_of_max_le_right, lt_max_iff, lt_max_of_lt_left, lt_max_of_lt_right, lt_min_iff, max_cases, max_choice, max_eq_iff, max_eq_left_iff, max_eq_right_iff, max_idem, max_le_iff, max_le_max, max_le_max_left, max_le_max_right, max_left_commutative, max_lt_iff, max_lt_max, max_lt_max_left_iff, max_lt_max_right_iff, max_min_distrib_left, max_min_distrib_right, min_cases, min_choice, min_eq_iff, min_eq_left_iff, min_eq_right_iff, min_idem, min_le_iff, min_le_max, min_le_min, min_le_min_left, min_le_min_right, min_le_of_left_le, min_le_of_right_le, min_left_commutative, min_lt_iff, min_lt_max, min_lt_min, min_lt_min_left_iff, min_lt_min_right_iff, min_lt_of_left_lt, min_lt_of_right_lt, min_max_distrib_left, min_max_distrib_right, min_right_comm
67
Total67

Antitone

Theorems

NameKindAssumesProvesValidatesDepends On
map_max 📖mathematicalAntitone
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
SemilatticeSup.toMax
Lattice.toSemilatticeSup
SemilatticeInf.toMin
le_total
sup_of_le_right
inf_of_le_right
sup_of_le_left
inf_of_le_left
map_min 📖mathematicalAntitone
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
SemilatticeInf.toMin
SemilatticeSup.toMax
Lattice.toSemilatticeSup
map_max
dual

AntitoneOn

Theorems

NameKindAssumesProvesValidatesDepends On
map_max 📖mathematicalAntitoneOn
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Set
Set.instMembership
SemilatticeSup.toMax
Lattice.toSemilatticeSup
SemilatticeInf.toMin
MonotoneOn.map_max
dual_right
map_min 📖mathematicalAntitoneOn
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Set
Set.instMembership
SemilatticeInf.toMin
SemilatticeSup.toMax
Lattice.toSemilatticeSup
map_max
dual

Max

Theorems

NameKindAssumesProvesValidatesDepends On
left_comm 📖mathematicalSemilatticeSup.toMax
Lattice.toSemilatticeSup
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
right_comm 📖mathematicalSemilatticeSup.toMax
Lattice.toSemilatticeSup
DistribLattice.toLattice
instDistribLatticeOfLinearOrder

Monotone

Theorems

NameKindAssumesProvesValidatesDepends On
map_max 📖mathematicalMonotone
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
SemilatticeSup.toMax
Lattice.toSemilatticeSup
le_total
sup_of_le_right
sup_of_le_left
map_min 📖mathematicalMonotone
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
SemilatticeInf.toMinmap_max
dual

MonotoneOn

Theorems

NameKindAssumesProvesValidatesDepends On
map_max 📖mathematicalMonotoneOn
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Set
Set.instMembership
SemilatticeSup.toMax
Lattice.toSemilatticeSup
le_total
max_eq_right
max_eq_left
map_min 📖mathematicalMonotoneOn
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Set
Set.instMembership
SemilatticeInf.toMinmap_max
dual

(root)

Theorems

NameKindAssumesProvesValidatesDepends On
instAssociativeMax 📖mathematicalSemilatticeSup.toMax
Lattice.toSemilatticeSup
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
max_assoc
instAssociativeMin 📖mathematicalSemilatticeInf.toMin
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
min_assoc
instCommutativeMax 📖mathematicalSemilatticeSup.toMax
Lattice.toSemilatticeSup
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
max_comm
instCommutativeMin 📖mathematicalSemilatticeInf.toMin
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
min_comm
instLawfulOrderInf_mathlib 📖mathematicalSemilatticeInf.toMin
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
le_min_iff
instLawfulOrderSup_mathlib 📖mathematicalSemilatticeSup.toMax
Lattice.toSemilatticeSup
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
max_le_iff
le_max_iff 📖mathematicalPreorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
SemilatticeSup.toMax
Lattice.toSemilatticeSup
le_sup_iff
le_max_of_le_left 📖mathematicalPreorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
SemilatticeSup.toMax
Lattice.toSemilatticeSup
le_sup_of_le_left
le_max_of_le_right 📖mathematicalPreorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
SemilatticeSup.toMax
Lattice.toSemilatticeSup
le_sup_of_le_right
le_min_iff 📖mathematicalPreorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
SemilatticeInf.toMin
le_inf_iff
le_of_max_le_left 📖Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
SemilatticeSup.toMax
Lattice.toSemilatticeSup
le_trans
le_max_left
le_of_max_le_right 📖Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
SemilatticeSup.toMax
Lattice.toSemilatticeSup
le_trans
le_max_right
lt_max_iff 📖mathematicalPreorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
SemilatticeSup.toMax
Lattice.toSemilatticeSup
lt_sup_iff
lt_max_of_lt_left 📖mathematicalPreorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
SemilatticeSup.toMax
Lattice.toSemilatticeSup
LT.lt.trans_le
le_max_left
lt_max_of_lt_right 📖mathematicalPreorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
SemilatticeSup.toMax
Lattice.toSemilatticeSup
LT.lt.trans_le
le_max_right
lt_min_iff 📖mathematicalPreorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
SemilatticeInf.toMin
lt_inf_iff
max_cases 📖mathematicalSemilatticeSup.toMax
Lattice.toSemilatticeSup
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
Preorder.toLT
min_cases
max_choice 📖mathematicalSemilatticeSup.toMax
Lattice.toSemilatticeSup
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
min_choice
max_eq_iff 📖mathematicalSemilatticeSup.toMax
Lattice.toSemilatticeSup
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
min_eq_iff
max_eq_left_iff 📖mathematicalSemilatticeSup.toMax
Lattice.toSemilatticeSup
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
sup_eq_left
max_eq_right_iff 📖mathematicalSemilatticeSup.toMax
Lattice.toSemilatticeSup
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
sup_eq_right
max_idem 📖mathematicalSemilatticeSup.toMax
Lattice.toSemilatticeSup
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
max_self
max_le_iff 📖mathematicalPreorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
SemilatticeSup.toMax
Lattice.toSemilatticeSup
sup_le_iff
max_le_max 📖mathematicalPreorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
SemilatticeSup.toMax
Lattice.toSemilatticeSup
sup_le_sup
max_le_max_left 📖mathematicalPreorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
SemilatticeSup.toMax
Lattice.toSemilatticeSup
sup_le_sup_left
max_le_max_right 📖mathematicalPreorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
SemilatticeSup.toMax
Lattice.toSemilatticeSup
sup_le_sup_right
max_left_commutative 📖mathematicalLeftCommutative
SemilatticeSup.toMax
Lattice.toSemilatticeSup
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
max_left_comm
max_lt_iff 📖mathematicalPreorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
SemilatticeSup.toMax
Lattice.toSemilatticeSup
sup_lt_iff
max_lt_max 📖mathematicalPreorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
SemilatticeSup.toMax
Lattice.toSemilatticeSup
max_lt
lt_max_of_lt_left
lt_max_of_lt_right
max_lt_max_left_iff 📖mathematicalPreorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
SemilatticeSup.toMax
Lattice.toSemilatticeSup
min_lt_min_left_iff
max_lt_max_right_iff 📖mathematicalPreorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
SemilatticeSup.toMax
Lattice.toSemilatticeSup
min_lt_min_right_iff
max_min_distrib_left 📖mathematicalSemilatticeSup.toMax
Lattice.toSemilatticeSup
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
SemilatticeInf.toMin
Lattice.toSemilatticeInf
sup_inf_left
max_min_distrib_right 📖mathematicalSemilatticeSup.toMax
Lattice.toSemilatticeSup
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
SemilatticeInf.toMin
Lattice.toSemilatticeInf
sup_inf_right
min_cases 📖mathematicalSemilatticeInf.toMin
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Preorder.toLT
min_choice 📖mathematicalSemilatticeInf.toMin
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
le_total
inf_of_le_left
inf_of_le_right
min_eq_iff 📖mathematicalSemilatticeInf.toMin
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
min_eq_left_iff 📖mathematicalSemilatticeInf.toMin
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
inf_eq_left
min_eq_right_iff 📖mathematicalSemilatticeInf.toMin
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
inf_eq_right
min_idem 📖mathematicalSemilatticeInf.toMin
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
min_self
min_le_iff 📖mathematicalPreorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
SemilatticeInf.toMin
inf_le_iff
min_le_max 📖mathematicalPreorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
SemilatticeInf.toMin
SemilatticeSup.toMax
Lattice.toSemilatticeSup
le_trans
min_le_left
le_max_left
min_le_min 📖mathematicalPreorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
SemilatticeInf.toMininf_le_inf
min_le_min_left 📖mathematicalPreorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
SemilatticeInf.toMininf_le_inf_left
min_le_min_right 📖mathematicalPreorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
SemilatticeInf.toMininf_le_inf_right
min_le_of_left_le 📖mathematicalPreorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
SemilatticeInf.toMininf_le_of_left_le
min_le_of_right_le 📖mathematicalPreorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
SemilatticeInf.toMininf_le_of_right_le
min_left_commutative 📖mathematicalLeftCommutative
SemilatticeInf.toMin
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
min_left_comm
min_lt_iff 📖mathematicalPreorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
SemilatticeInf.toMin
inf_lt_iff
min_lt_max 📖mathematicalPreorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
SemilatticeInf.toMin
SemilatticeSup.toMax
Lattice.toSemilatticeSup
inf_lt_sup
min_lt_min 📖mathematicalPreorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
SemilatticeInf.toMinmax_lt_max
min_lt_min_left_iff 📖mathematicalPreorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
SemilatticeInf.toMin
min_lt_min_right_iff 📖mathematicalPreorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
SemilatticeInf.toMin
min_lt_of_left_lt 📖mathematicalPreorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
SemilatticeInf.toMinLE.le.trans_lt
min_le_left
min_lt_of_right_lt 📖mathematicalPreorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
SemilatticeInf.toMinLE.le.trans_lt
min_le_right
min_max_distrib_left 📖mathematicalSemilatticeInf.toMin
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
SemilatticeSup.toMax
Lattice.toSemilatticeSup
inf_sup_left
min_max_distrib_right 📖mathematicalSemilatticeInf.toMin
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
SemilatticeSup.toMax
Lattice.toSemilatticeSup
inf_sup_right
min_right_comm 📖mathematicalSemilatticeInf.toMin
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder

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