Theorems · Theorem · logic and foundations

Set.piecewise_preimage

∀ {α : Type u_1} {β : Type u_2} (s : Set α) [inst : (j : α) → Decidable (j ∈ s)] (f g : α → β) (t : Set β),
  s.piecewise f g ⁻¹' t = s.ite (f ⁻¹' t) (g ⁻¹' t)

Defined in

Mathlib.Data.Set.Piecewise

Cited by

6 results in Mathlib

Foundations

Depth 9 from the axioms · uses propext, Quot.sound

Assumes

Decidable