Theorems · Theorem · logic and foundations

FirstOrder.Language.BoundedFormula.realize_all_liftAt_one_self

∀ {L : FirstOrder.Language} {M : Type w} [inst : L.Structure M] {α : Type u'} [Nonempty M] {n : ℕ}
  {φ : L.BoundedFormula α n} {v : α → M} {xs : Fin n → M},
  (FirstOrder.Language.BoundedFormula.liftAt 1 n φ).all.Realize v xs ↔ φ.Realize v xs

Defined in

Mathlib.ModelTheory.Semantics

Cited by

1 results in Mathlib

Foundations

Depth 57 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FirstOrder.Language.StructureNonempty