Theorems · Theorem · logic and foundations
FirstOrder.Language.Substructure.FG.finite
∀ {L : FirstOrder.Language} {M : Type u_1} [inst : L.Structure M] [L.IsRelational] {S : L.Substructure M},
S.FG → Finite ↥S- Defined in
- Mathlib.ModelTheory.FinitelyGenerated
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- Finsetproof · cited by 13,712
- SetLike.coeproof · cited by 8,199
- Finitestatement · cited by 3,029
- Set.Finiteproof · cited by 1,814
- FirstOrder.Languagestatement and proof · cited by 1,084
- FirstOrder.Language.Structurestatement and proof · cited by 775
- FirstOrder.Language.Substructurestatement and proof · cited by 242
- Finset.finite_toSetproof · cited by 210
- LowerAdjoint.toFunproof · cited by 105
- FirstOrder.Language.Substructure.closureproof · cited by 70
- FirstOrder.Language.Substructure.FGstatement and proof · cited by 34
Cited by3
Results whose statement or proof uses this declaration.
- FirstOrder.Language.Structure.FG.finiteproof · cited by 3
- FirstOrder.Language.empty.isFraisseLimit_of_countable_infiniteproof · cited by 1
- FirstOrder.Language.Substructure.fg_iff_finiteproof · cited by 0