Theorems · Theorem · logic and foundations

FirstOrder.Language.ElementaryEmbedding.map_boundedFormula

∀ {L : FirstOrder.Language} {M : Type u_1} {N : Type u_2} [inst : L.Structure M] [inst_1 : L.Structure N]
  (f : L.ElementaryEmbedding M N) {α : Type u_5} {n : ℕ} (φ : L.BoundedFormula α n) (v : α → M) (xs : Fin n → M),
  φ.Realize (⇑f ∘ v) (⇑f ∘ xs) ↔ φ.Realize v xs

Defined in

Mathlib.ModelTheory.ElementaryMaps

Cited by

2 results in Mathlib

Foundations

Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FirstOrder.Language.StructureFirstOrder.Language.Structure