Theorems · Theorem · logic and foundations
FirstOrder.Language.Substructure.fg_closure
∀ {L : FirstOrder.Language} {M : Type u_1} [inst : L.Structure M] {s : Set M},
s.Finite → ((FirstOrder.Language.Substructure.closure L).toFun s).FG- Defined in
- Mathlib.ModelTheory.FinitelyGenerated
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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 · cited by 8,199
- Set.Finitestatement and proof · cited by 1,814
- FirstOrder.Languagestatement and proof · cited by 1,084
- FirstOrder.Language.Structurestatement and proof · cited by 775
- Set.Finite.toFinsetproof · cited by 351
- FirstOrder.Language.Substructurestatement · cited by 242
- Set.Finite.coe_toFinsetproof · cited by 124
- LowerAdjoint.toFunstatement and proof · cited by 105
- FirstOrder.Language.Substructure.closurestatement and proof · cited by 70
- FirstOrder.Language.Substructure.FGstatement · cited by 34
Cited by3
Results whose statement or proof uses this declaration.
- FirstOrder.Language.Substructure.fg_closure_singletonproof · cited by 4
- FirstOrder.Language.age.nonemptyproof · cited by 2
- FirstOrder.Language.age.countable_quotientproof · cited by 2