Theorems · Theorem · logic and foundations

FirstOrder.Language.BoundedFormula.realize_subst

∀ {L : FirstOrder.Language} {M : Type w} [inst : L.Structure M] {α : Type u'} {β : Type v'} {n : ℕ}
  {φ : L.BoundedFormula α n} {tf : α → L.Term β} {v : β → M} {xs : Fin n → M},
  (φ.subst tf).Realize v xs ↔ φ.Realize (fun a => FirstOrder.Language.Term.realize v (tf a)) xs

Defined in

Mathlib.ModelTheory.Semantics

Cited by

0 results in Mathlib

Foundations

Depth 24 from the axioms · uses propext, Quot.sound

Assumes

FirstOrder.Language.Structure