Theorems · Theorem · logic and foundations
FirstOrder.Language.Substructure.fg_iff_exists_fin_generating_family
∀ {L : FirstOrder.Language} {M : Type u_1} [inst : L.Structure M] {N : L.Substructure M},
N.FG ↔ ∃ n s, (FirstOrder.Language.Substructure.closure L).toFun (Set.range s) = N- Defined in
- Mathlib.ModelTheory.FinitelyGenerated
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites15
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- DFunLike.coeproof · cited by 62,936
- Setstatement and proof · cited by 53,352
- SetLike.coestatement · cited by 8,199
- Set.rangestatement and proof · cited by 4,705
- Set.Finiteproof · cited by 1,814
- FirstOrder.Languagestatement and proof · cited by 1,084
- Function.Embeddingproof · cited by 988
- FirstOrder.Language.Structurestatement and proof · cited by 775
- FirstOrder.Language.Substructurestatement and proof · cited by 242
- LowerAdjoint.toFunstatement and proof · cited by 105
- FirstOrder.Language.Substructure.closurestatement and proof · cited by 70
- Set.finite_rangeproof · cited by 58
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