Theorems · Theorem · logic and foundations

FirstOrder.Language.BoundedFormula.IsAtomic.realize_comp

∀ {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] {φ : L.BoundedFormula α n},
  φ.IsAtomic →
    ∀ [EmbeddingLike F M N] [L.HomClass F M N] (f : F) {v : α → M} {xs : Fin n → M},
      φ.Realize v xs → φ.Realize (⇑f ∘ v) (⇑f ∘ xs)

Defined in

Mathlib.ModelTheory.Complexity

Cited by

0 results in Mathlib

Foundations

Depth 24 from the axioms · uses propext, Quot.sound

Assumes

FirstOrder.Language.StructureFirstOrder.Language.StructureFunLikeEmbeddingLikeFirstOrder.Language.HomClass