Theorems · Theorem · logic and foundations

FirstOrder.Language.Substructure.closure_image

∀ {L : FirstOrder.Language} {M : Type w} {N : Type u_1} [inst : L.Structure M] [inst_1 : L.Structure N] {s : Set M}
  (f : L.Hom M N),
  (FirstOrder.Language.Substructure.closure L).toFun (⇑f '' s) =
    FirstOrder.Language.Substructure.map f ((FirstOrder.Language.Substructure.closure L).toFun s)

Defined in

Mathlib.ModelTheory.Substructures

Cited by

4 results in Mathlib

Foundations

Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FirstOrder.Language.StructureFirstOrder.Language.Structure