Theorems · Definition · logic and foundations
FirstOrder.Language.Substructure.topEquiv
{L : FirstOrder.Language} → {M : Type w} → [inst : L.Structure M] → L.Equiv (↥⊤) MThe equivalence between the maximal substructure of a structure and the structure itself.
- Defined in
- Mathlib.ModelTheory.Substructures
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 21 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Top.topstatement and proof · cited by 9,680
- FirstOrder.Languagestatement and proof · cited by 1,084
- FirstOrder.Language.Structurestatement and proof · cited by 775
- FirstOrder.Language.Substructurestatement · cited by 242
- FirstOrder.Language.Equivstatement · cited by 83
- FirstOrder.Language.Substructure.subtypeproof · cited by 40
- FirstOrder.Language.Substructure.mem_topproof · cited by 2
Cited by7
Results whose statement or proof uses this declaration.
- FirstOrder.Language.Embedding.toPartialEquivproof · cited by 6
- FirstOrder.Language.PartialEquiv.toEmbeddingOfEqTopproof · cited by 5
- FirstOrder.Language.PartialEquiv.toEquivOfEqTopproof · cited by 2
- FirstOrder.Language.Structure.cg_iff_countableproof · cited by 1
- FirstOrder.Language.Substructure.realize_boundedFormula_topproof · cited by 0
- FirstOrder.Language.Substructure.coe_topEquivstatement · cited by 0
- FirstOrder.Language.Substructure.realize_formula_topproof · cited by 0