LeanMachineLearning exposition

measurable_argmin🔗

This page has the declaration's own card below, then its dependency graph, then a card for each dependency (type dependencies first, then the rest of the transitive closure). For a theorem, the graph and the dependency cards only follow its statement's dependencies (its proof is replaced by sorry, so what it proves doesn't depend on how); for everything else, both the type and the body/value are followed, since their content is part of what later declarations build on.

Minimal Lean file

measurable_argmin🔗

Theoremmeasurable_argmin
Details

No docstring.

🔗theorem
measurable_argmin.{u_1, u_2} {ι : Type u_1} {α : Type u_2}
  [LinearOrder α] [Fintype ι] [Nonempty ι] [MeasurableSpace α]
  [MeasurableSpace ι] [MeasurableEq α] [MeasurableInf₂ α] :
  Measurable fun f => argmin f
measurable_argmin.{u_1, u_2}
  {ι : Type u_1} {α : Type u_2}
  [LinearOrder α] [Fintype ι] [Nonempty ι]
  [MeasurableSpace α] [MeasurableSpace ι]
  [MeasurableEq α] [MeasurableInf₂ α] :
  Measurable fun f => argmin f

Code

theorem measurable_argmin : ∀ {ι : Type u_1} {α : Type u_2} [inst : LinearOrder α] [inst_1 : Fintype ι] [inst_2 : Nonempty ι]
  [inst_3 : MeasurableSpace α] [inst_4 : MeasurableSpace ι] [MeasurableEq α] [MeasurableInf₂ α],
  Measurable fun f => argmin f
Type uses (1)
Body uses (3)

Actions: Source · Open Issue

Proof
fun_prop) measurable_argmin]

Dependency graph

Type dependencies (1)

argmin🔗

Definitionargmin
Details

The index of the minimum value of a tuple.

🔗def
argmin.{u_1, u_2} {ι : Type u_1} {α : Type u_2} [LinearOrder α]
  [Fintype ι] [Nonempty ι] (f : ι → α) : ι
argmin.{u_1, u_2} {ι : Type u_1}
  {α : Type u_2} [LinearOrder α]
  [Fintype ι] [Nonempty ι] (f : ι → α) : ι

Code

def argmin : {ι : Type u_1} → {α : Type u_2} → [LinearOrder α] → [Fintype ι] → [Nonempty ι] → (ι → α) → ι
Body uses (2)
Used by (3)

Actions: Source · Open Issue

All dependencies, transitively (2)

min🔗

DefinitionFunction.min
Details

The minimum value of a tuple.

🔗def
Function.min.{u_1, u_2} {ι : Type u_1} {α : Type u_2} [LinearOrder α]
  [Fintype ι] [Nonempty ι] (f : ι → α) : α
Function.min.{u_1, u_2} {ι : Type u_1}
  {α : Type u_2} [LinearOrder α]
  [Fintype ι] [Nonempty ι] (f : ι → α) : α

Code

def min : {ι : Type u_1} → {α : Type u_2} → [LinearOrder α] → [Fintype ι] → [Nonempty ι] → (ι → α) → α
Used by (8)

Actions: Source · Open Issue

exists_argmin🔗

Theoremexists_argmin
Details

No docstring.

🔗theorem
exists_argmin.{u_1, u_2} {ι : Type u_1} {α : Type u_2} [LinearOrder α]
  [Fintype ι] [Nonempty ι] (f : ι → α) : ∃ i, f i = Function.min f
exists_argmin.{u_1, u_2} {ι : Type u_1}
  {α : Type u_2} [LinearOrder α]
  [Fintype ι] [Nonempty ι] (f : ι → α) :
  ∃ i, f i = Function.min f

Code

theorem exists_argmin : ∀ {ι : Type u_1} {α : Type u_2} [inst : LinearOrder α] [inst_1 : Fintype ι] [inst_2 : Nonempty ι] (f : ι → α),
  ∃ i, f i = Function.min f
Type uses (1)
Used by (3)

Actions: Source · Open Issue

Proof
@[to_dual exists_argmin]