Theorems · Definition · logic and foundations
FirstOrder.Language.Substructure.closure
(L : FirstOrder.Language) → {M : Type w} → [inst : L.Structure M] → LowerAdjoint SetLike.coeThe L.Substructure generated by a set.
- Defined in
- Mathlib.ModelTheory.Substructures
- Cited by
- 70 results in Mathlib
- Foundations
- Depth 68 from the axioms · uses propext, Classical.choice, 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.
- Setstatement and proof · cited by 53,352
- SetLike.coestatement and proof · cited by 8,199
- Set.ofPredproof · cited by 6,101
- FirstOrder.Languagestatement and proof · cited by 1,084
- InfSet.sInfproof · cited by 935
- FirstOrder.Language.Structurestatement and proof · cited by 775
- FirstOrder.Language.Substructurestatement and proof · cited by 242
- LowerAdjointstatement · cited by 38
Cited by74
Results whose statement or proof uses this declaration.
- FirstOrder.Language.Substructure.FGproof · cited by 34
- FirstOrder.Language.Substructure.CGproof · cited by 18
- FirstOrder.Language.Substructure.subset_closurestatement and proof · cited by 12
- FirstOrder.Language.Substructure.closure_eqstatement · cited by 7
- FirstOrder.Language.Substructure.closure_lestatement and proof · cited by 7
- FirstOrder.Language.Substructure.fg_defstatement and proof · cited by 6
- FirstOrder.Language.Substructure.cg_defstatement · cited by 5
- FirstOrder.Language.Substructure.closure_eq_of_lestatement and proof · cited by 5
- FirstOrder.Language.Substructure.FG.supproof · cited by 5
- FirstOrder.Language.Substructure.closure_imagestatement · cited by 4
- FirstOrder.Language.Substructure.closure_unionstatement · cited by 4
- FirstOrder.Language.Substructure.fg_closure_singletonstatement · cited by 4