Theorems · Theorem · logic and foundations
FirstOrder.Language.Substructure.cg_iff_empty_or_exists_nat_generating_family
∀ {L : FirstOrder.Language} {M : Type u_1} [inst : L.Structure M] {N : L.Substructure M},
N.CG ↔ ↑N = ∅ ∨ ∃ s, (FirstOrder.Language.Substructure.closure L).toFun (Set.range s) = N- Defined in
- Mathlib.ModelTheory.FinitelyGenerated
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- 0 results in Mathlib
- Foundations
- Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound
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- Setstatement and proof · cited by 53,352
- SetLike.coestatement and proof · cited by 8,199
- Set.rangestatement and proof · cited by 4,705
- Set.Nonemptyproof · cited by 2,627
- FirstOrder.Languagestatement and proof · cited by 1,084
- FirstOrder.Language.Structurestatement and proof · cited by 775
- Set.Countableproof · cited by 545
- Set.eq_empty_or_nonemptyproof · cited by 248
- FirstOrder.Language.Substructurestatement and proof · cited by 242
- Set.singleton_subset_iffproof · cited by 206
- LowerAdjoint.toFunstatement and proof · cited by 105
- sup_eq_leftproof · cited by 71
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