Theorems · Theorem · logic and foundations

FirstOrder.Language.Term.realize_constantsToVars

∀ {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] {t : (L.withConstants α).Term β}
  {v : β → M},
  FirstOrder.Language.Term.realize (Sum.elim (fun a => ↑(L.con a)) v) t.constantsToVars =
    FirstOrder.Language.Term.realize v t

Defined in

Mathlib.ModelTheory.Semantics

Cited by

1 results in Mathlib

Foundations

Depth 20 from the axioms · uses propext, Quot.sound

Assumes

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