Theorems · Theorem · logic and foundations

FirstOrder.Language.StrongHomClass.realize_boundedFormula

∀ {L : FirstOrder.Language} {M : Type w} {N : Type u_1} [inst : L.Structure M] [inst_1 : L.Structure N] {α : Type u'}
  {n : ℕ} {F : Type u_4} [inst_2 : EquivLike F M N] [L.StrongHomClass F M N] (g : F) (φ : L.BoundedFormula α n)
  {v : α → M} {xs : Fin n → M}, φ.Realize (⇑g ∘ v) (⇑g ∘ xs) ↔ φ.Realize v xs

Defined in

Mathlib.ModelTheory.Semantics

Cited by

2 results in Mathlib

Foundations

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

Assumes

FirstOrder.Language.StructureFirstOrder.Language.StructureEquivLikeFirstOrder.Language.StrongHomClass