Theorems · Theorem · logic and foundations
FirstOrder.Language.Substructure.closure_eq
∀ {L : FirstOrder.Language} {M : Type w} [inst : L.Structure M] (S : L.Substructure M),
(FirstOrder.Language.Substructure.closure L).toFun ↑S = SClosure of a substructure S equals S.
- Defined in
- Mathlib.ModelTheory.Substructures
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- SetLike.coestatement · cited by 8,199
- FirstOrder.Languagestatement and proof · cited by 1,084
- FirstOrder.Language.Structurestatement and proof · cited by 775
- FirstOrder.Language.Substructurestatement and proof · cited by 242
- LowerAdjoint.toFunstatement · cited by 105
- FirstOrder.Language.Substructure.closurestatement · cited by 70
- GaloisInsertion.l_u_eqproof · cited by 37
- FirstOrder.Language.Substructure.giproof · cited by 4
Cited by7
Results whose statement or proof uses this declaration.
- FirstOrder.Language.Substructure.cg_iff_countableproof · cited by 1
- FirstOrder.Language.Substructure.FG.of_finiteproof · cited by 1
- FirstOrder.Language.dlo_isExtensionPairproof · cited by 1
- FirstOrder.Language.Substructure.mem_iSup_of_directedproof · cited by 1
- FirstOrder.Language.Substructure.closure_univproof · cited by 0
- FirstOrder.Language.Substructure.cg_of_countableproof · cited by 0
- FirstOrder.Language.Substructure.iSup_eq_closureproof · cited by 0