Theorems · Definition · logic and foundations

FirstOrder.Language.Embedding.substructureEquivMap

{L : FirstOrder.Language} →
  {M : Type w} →
    {N : Type u_1} →
      [inst : L.Structure M] →
        [inst_1 : L.Structure N] →
          (f : L.Embedding M N) → (s : L.Substructure M) → L.Equiv ↥s ↥(FirstOrder.Language.Substructure.map f.toHom s)

The equivalence between a substructure s and its image s.map f.toHom, where f is an embedding.

Defined in

Mathlib.ModelTheory.Substructures

Cited by

2 results in Mathlib

Foundations

Depth 26 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FirstOrder.Language.StructureFirstOrder.Language.Structure