Theorems · Definition · logic and foundations
FirstOrder.Language.Substructure.gi
(L : FirstOrder.Language) → (M : Type w) → [inst : L.Structure M] → GaloisInsertion (FirstOrder.Language.Substructure.closure L).toFun SetLike.coe
closure forms a Galois insertion with the coercion to set.
- Defined in
- Mathlib.ModelTheory.Substructures
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 71 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
- FirstOrder.Languagestatement and proof · cited by 1,084
- FirstOrder.Language.Structurestatement and proof · cited by 775
- FirstOrder.Language.Substructurestatement · cited by 242
- LowerAdjoint.toFunstatement and proof · cited by 105
- FirstOrder.Language.Substructure.closurestatement and proof · cited by 70
- GaloisInsertionstatement · cited by 35
Cited by4
Results whose statement or proof uses this declaration.
- FirstOrder.Language.Substructure.closure_eqproof · cited by 7
- FirstOrder.Language.Substructure.closure_unionproof · cited by 4
- FirstOrder.Language.Substructure.closure_iUnionproof · cited by 3
- FirstOrder.Language.Substructure.closure_emptyproof · cited by 1