Theorems · Definition · logic and foundations
FirstOrder.Language.Substructure.subtype
{L : FirstOrder.Language} → {M : Type w} → [inst : L.Structure M] → (S : L.Substructure M) → L.Embedding (↥S) MThe natural embedding of an L.Substructure of M into M.
- Defined in
- Mathlib.ModelTheory.Substructures
- Cited by
- 40 results in Mathlib
- Foundations
- Depth 19 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- FirstOrder.Languagestatement and proof · cited by 1,084
- FirstOrder.Language.Structurestatement and proof · cited by 775
- FirstOrder.Language.Substructurestatement and proof · cited by 242
- FirstOrder.Language.Embeddingstatement · cited by 128
Cited by48
Results whose statement or proof uses this declaration.
- FirstOrder.Language.Substructure.inclusionproof · cited by 26
- FirstOrder.Language.Substructure.fg_iff_structure_fgproof · cited by 12
- FirstOrder.Language.PartialEquiv.dom_le_domproof · cited by 8
- FirstOrder.Language.PartialEquiv.cod_le_codproof · cited by 6
- FirstOrder.Language.IsUltrahomogeneousproof · cited by 5
- FirstOrder.Language.Substructure.topEquivproof · cited by 4
- FirstOrder.Language.PartialEquiv.extstatement and proof · cited by 3
- FirstOrder.Language.Substructure.range_subtypestatement · cited by 3
- FirstOrder.Language.PartialEquiv.subtype_toEquiv_inclusionstatement and proof · cited by 3
- FirstOrder.Language.PartialEquiv.le_defstatement · cited by 2
- FirstOrder.Language.Embedding.subtype_equivRangestatement and proof · cited by 2
- FirstOrder.Language.Embedding.toPartialEquiv_toEmbeddingproof · cited by 2