Theorems · Theorem · logic and foundations

Set.DefinableFun.ofPred_eq

∀ {M : Type u_1} {L : FirstOrder.Language} [inst : L.Structure M] {α : Type u_2} {A : Set M} {f g : (α → M) → M},
  Set.DefinableFun L A f → Set.DefinableFun L A g → A.Definable L {v | f v = g v}

The set where two definable functions agree is definable.

Defined in

Mathlib.ModelTheory.Definability

Cited by

2 results in Mathlib

Foundations

Depth 63 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FirstOrder.Language.Structure