Mathlib Map

Theorems · Definition · logic and foundations

FirstOrder.Language.Substructure.copy

{L : FirstOrder.Language} →
  {M : Type w} → [inst : L.Structure M] → (S : L.Substructure M) → (s : Set M) → s = ↑S → L.Substructure M

Copy a substructure replacing carrier with a set that is equal to it.

Defined in
Mathlib.ModelTheory.Substructures
Cited by
2 results in Mathlib
Foundations
Depth 11 from the axioms · uses no axioms
Assumes
FirstOrder.Language.Structure
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

FirstOrder.Language.Hom.range · cited by 30Hom.rangeFirstOrder.Language.Substructure.coe_copy · cited by 0Substructure.coe_copyFirstOrder.Language.Substructure.copy_eq · cited by 0Substructure.copy_eqSet · cited by 53352SetSetLike.coe · cited by 8199SetLike.coeFirstOrder.Language · cited by 1084FirstOrder.LanguageFirstOrder.Language.Structure · cited by 775Language.StructureFirstOrder.Language.Substructure · cited by 242Language.SubstructureSubstructure.copyCITED BYCITES

Cites5

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by3

Results whose statement or proof uses this declaration.