Theorems · Theorem · logic and foundations

Set.injective_piecewise_iff

∀ {α : Type u_1} {β : Type u_2} (s : Set α) [inst : (j : α) → Decidable (j ∈ s)] {f g : α → β},
  Function.Injective (s.piecewise f g) ↔ Set.InjOn f s ∧ Set.InjOn g sᶜ ∧ ∀ x ∈ s, ∀ y ∉ s, f x ≠ g y

Defined in

Mathlib.Data.Set.Piecewise

Cited by

1 results in Mathlib

Foundations

Depth 58 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

Decidable