Theorems · Theorem · logic and foundations

FirstOrder.Language.BoundedFormula.IsQF.realize_embedding

∀ {L : FirstOrder.Language} {α : Type u'} {n : ℕ} {M : Type u_1} [inst : L.Structure M] {N : Type u_2}
  [inst_1 : L.Structure N] {F : Type u_3} [inst_2 : FunLike F M N] [EmbeddingLike F M N] [L.StrongHomClass F M N]
  {φ : L.BoundedFormula α n},
  φ.IsQF → ∀ (f : F) {v : α → M} {xs : Fin n → M}, φ.Realize (⇑f ∘ v) (⇑f ∘ xs) ↔ φ.Realize v xs

Defined in

Mathlib.ModelTheory.Complexity

Cited by

2 results in Mathlib

Foundations

Depth 23 from the axioms · uses propext, Quot.sound

Assumes

FirstOrder.Language.StructureFirstOrder.Language.StructureFunLikeEmbeddingLikeFirstOrder.Language.StrongHomClass