Function.min_le🔗

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

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

theorem min_le : ∀ {ι : Type u_1} {α : Type u_2} [inst : LinearOrder α] [inst_1 : Fintype ι] [inst_2 : Nonempty ι] (f : ι → α) (x : ι),
  Function.min f ≤ f x

@[to_dual min_le]

Dependency graph

Type dependencies (1)

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

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