Theorems · Theorem · logic and foundations
FirstOrder.Language.Substructure.FG.sup
∀ {L : FirstOrder.Language} {M : Type u_1} [inst : L.Structure M] {N₁ N₂ : L.Substructure M},
N₁.FG → N₂.FG → (N₁ ⊔ N₂).FG- Defined in
- Mathlib.ModelTheory.FinitelyGenerated
- Cited by
- 5 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.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- 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
- LowerAdjoint.toFunproof · cited by 105
- Set.Finite.unionproof · cited by 74
- FirstOrder.Language.Substructure.closureproof · cited by 70
- FirstOrder.Language.Substructure.FGstatement and proof · cited by 34
- FirstOrder.Language.Substructure.fg_defproof · cited by 6
- FirstOrder.Language.Substructure.closure_unionproof · cited by 4
Cited by5
Results whose statement or proof uses this declaration.
- FirstOrder.Language.age.jointEmbeddingproof · cited by 2
- FirstOrder.Language.IsFraisseLimit.isExtensionPairproof · cited by 1
- FirstOrder.Language.isUltrahomogeneous_iff_IsExtensionPairproof · cited by 1
- FirstOrder.Language.IsUltrahomogeneous.amalgamation_ageproof · cited by 1