Theorems · Theorem · logic and foundations

FirstOrder.Language.BoundedFormula.realize_all

∀ {L : FirstOrder.Language} {M : Type w} [inst : L.Structure M] {α : Type u'} {l : ℕ} {θ : L.BoundedFormula α l.succ}
  {v : α → M} {xs : Fin l → M}, θ.all.Realize v xs ↔ ∀ (a : M), θ.Realize v (Fin.snoc xs a)

Defined in

Mathlib.ModelTheory.Semantics

Cited by

3 results in Mathlib

Foundations

Depth 21 from the axioms · uses no axioms

Assumes

FirstOrder.Language.Structure