Theorems · Theorem · logic and foundations

FirstOrder.Language.ElementaryEmbedding.ofModelsElementaryDiagram_toFun

∀ (L : FirstOrder.Language) (M : Type u_1) [inst : L.Structure M] (N : Type u_5) [inst_1 : L.Structure N]
  [inst_2 : (L.withConstants M).Structure N] [inst_3 : (L.lhomWithConstants M).IsExpansionOn N]
  [inst_4 : N ⊨ L.elementaryDiagram M] (a : M),
  (FirstOrder.Language.ElementaryEmbedding.ofModelsElementaryDiagram L M N) a =
    (FirstOrder.Language.constantMap ∘ Sum.inr) a

Defined in

Mathlib.ModelTheory.ElementaryMaps

Cited by

0 results in Mathlib

Foundations

Depth 57 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FirstOrder.Language.StructureFirstOrder.Language.StructureFirstOrder.Language.StructureFirstOrder.Language.LHom.IsExpansionOnFirstOrder.Language.Theory.Model