Theorems · Theorem · order theory

Set.image_update_Ioc

∀ {ι : Type u_1} {α : ι → Type u_2} [inst : DecidableEq ι] [inst_1 : (i : ι) → PartialOrder (α i)] (f : (i : ι) → α i)
  (i : ι) (a b : α i), Function.update f i '' Set.Ioc a b = Set.Ioc (Function.update f i a) (Function.update f i b)

Defined in

Mathlib.Order.Interval.Set.Pi

Cited by

4 results in Mathlib

Foundations

Depth 61 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

DecidableEqPartialOrder