Theorems · Definition · logic and foundations
FirstOrder.Language.Substructure.inclusion
{L : FirstOrder.Language} → {M : Type w} → [inst : L.Structure M] → {S T : L.Substructure M} → S ≤ T → L.Embedding ↥S ↥TThe embedding associated to an inclusion of substructures.
- Defined in
- Mathlib.ModelTheory.Substructures
- Cited by
- 26 results in Mathlib
- Foundations
- Depth 25 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- FirstOrder.Language.Substructure.subtypeproof · cited by 40
- FirstOrder.Language.Embedding.codRestrictproof · cited by 6
Cited by30
Results whose statement or proof uses this declaration.
- FirstOrder.Language.PartialEquiv.dom_le_domproof · cited by 8
- FirstOrder.Language.DirectLimit.partialEquivLimitproof · cited by 6
- FirstOrder.Language.PartialEquiv.cod_le_codproof · cited by 6
- FirstOrder.Language.DirectLimit.Equiv_iSupstatement and proof · cited by 4
- FirstOrder.Language.PartialEquiv.subtype_toEquiv_inclusionstatement and proof · cited by 3
- FirstOrder.Language.PartialEquiv.le_defstatement · cited by 2
- FirstOrder.Language.PartialEquiv.toEquiv_inclusion_applystatement and proof · cited by 2
- FirstOrder.Language.age.jointEmbeddingproof · cited by 2
- FirstOrder.Language.DirectLimit.liftInclusionstatement and proof · cited by 2
- FirstOrder.Language.PartialEquiv.domRestrictproof · cited by 2
- FirstOrder.Language.PartialEquiv.le_domRestrictproof · cited by 1
- FirstOrder.Language.PartialEquiv.le_iffstatement and proof · cited by 1