Theorems · Theorem · logic and foundations

FirstOrder.Language.BoundedFormula.realize_relabel

∀ {L : FirstOrder.Language} {M : Type w} [inst : L.Structure M] {α : Type u'} {β : Type v'} {m n : ℕ}
  {φ : L.BoundedFormula α n} {g : α → β ⊕ Fin m} {v : β → M} {xs : Fin (m + n) → M},
  (FirstOrder.Language.BoundedFormula.relabel g φ).Realize v xs ↔
    φ.Realize (Sum.elim v (xs ∘ Fin.castAdd n) ∘ g) (xs ∘ Fin.natAdd m)

Defined in

Mathlib.ModelTheory.Semantics

Cited by

3 results in Mathlib

Foundations

Depth 54 from the axioms · uses propext, Quot.sound

Assumes

FirstOrder.Language.Structure