Theorems · Theorem · logic and foundations

FirstOrder.Language.BoundedFormula.realize_constantsVarsEquiv

∀ {L : FirstOrder.Language} {M : Type w} [inst : L.Structure M] {α : Type u'} {β : Type v'}
  [inst_1 : (L.withConstants α).Structure M] [(L.lhomWithConstants α).IsExpansionOn M] {n : ℕ}
  {φ : (L.withConstants α).BoundedFormula β n} {v : β → M} {xs : Fin n → M},
  (FirstOrder.Language.BoundedFormula.constantsVarsEquiv φ).Realize (Sum.elim (fun a => ↑(L.con a)) v) xs ↔
    φ.Realize v xs

Defined in

Mathlib.ModelTheory.Semantics

Cited by

1 results in Mathlib

Foundations

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

Assumes

FirstOrder.Language.StructureFirstOrder.Language.StructureFirstOrder.Language.LHom.IsExpansionOn