Theorems · Theorem · logic and foundations
FirstOrder.Language.Substructure.reduct_withConstants
∀ {L : FirstOrder.Language} {M : Type w} [inst : L.Structure M] {S : L.Substructure M} {A : Set M} (h : A ⊆ ↑S),
(L.lhomWithConstants ↑A).substructureReduct (S.withConstants h) = S- Defined in
- Mathlib.ModelTheory.Substructures
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 28 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Setstatement and proof · cited by 53,352
- SetLike.coestatement and proof · cited by 8,199
- Set.Elemstatement and proof · cited by 7,166
- FirstOrder.Languagestatement and proof · cited by 1,084
- FirstOrder.Language.Structurestatement and proof · cited by 775
- OrderEmbeddingstatement · cited by 619
- FirstOrder.Language.Substructurestatement and proof · cited by 242
- FirstOrder.Language.withConstantsstatement · cited by 108
- FirstOrder.Language.lhomWithConstantsstatement and proof · cited by 39
- FirstOrder.Language.LHom.substructureReductstatement · cited by 6
- FirstOrder.Language.Substructure.extproof · cited by 6
Cited by1
Results whose statement or proof uses this declaration.
- FirstOrder.Language.Substructure.closure_withConstants_eqproof · cited by 0