Theorems · Theorem · order theory

Function.argminOn_le

∀ {α : Type u_1} {β : Type u_2} (f : α → β) [inst : LinearOrder β] [inst_1 : WellFoundedLT β] (s : Set α) {a : α}
  (ha : a ∈ s), f (Function.argminOn f s ⋯) ≤ f a

Defined in

Mathlib.Order.WellFounded

Cited by

5 results in Mathlib

Foundations

Depth 17 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

LinearOrderWellFoundedLT