Theorems · Theorem · logic and foundations

FirstOrder.Language.withConstants_funMap_sumInl

∀ (L : FirstOrder.Language) {M : Type w} [inst : L.Structure M] {α : Type w'} [inst_1 : (L.withConstants α).Structure M]
  [(L.lhomWithConstants α).IsExpansionOn M] {n : ℕ} {f : L.Functions n} {x : Fin n → M},
  FirstOrder.Language.Structure.funMap (Sum.inl f) x = FirstOrder.Language.Structure.funMap f x

Defined in

Mathlib.ModelTheory.LanguageMap

Cited by

3 results in Mathlib

Foundations

Depth 19 from the axioms · uses no axioms

Assumes

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