Theorems · Theorem · logic and foundations

Set.DefinableFun.ite

∀ {M : Type u_1} {L : FirstOrder.Language} [inst : L.Structure M] {α : Type u_2} {A : Set M} {f : (α → M) → M}
  {p : (α → M) → Prop} {g : (α → M) → M} [inst_1 : DecidablePred p],
  A.Definable L (Set.ofPred p) →
    Set.DefinableFun L A f → Set.DefinableFun L A g → Set.DefinableFun L A fun v => if p v then f v else g v

Defined in

Mathlib.ModelTheory.Definability

Cited by

0 results in Mathlib

Foundations

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

Assumes

FirstOrder.Language.StructureDecidablePred