Theorems · Theorem · logic and foundations
FirstOrder.Language.ClosedUnder.sInf
∀ {L : FirstOrder.Language} {M : Type w} [inst : L.Structure M] {n : ℕ} {f : L.Functions n} {S : Set (Set M)},
(∀ s ∈ S, FirstOrder.Language.ClosedUnder f s) → FirstOrder.Language.ClosedUnder f (sInf S)- Defined in
- Mathlib.ModelTheory.Substructures
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- Foundations
- Depth 5 from the axioms · uses no axioms
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Cites6
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- Setstatement and proof · cited by 53,352
- FirstOrder.Languagestatement and proof · cited by 1,084
- InfSet.sInfstatement and proof · cited by 935
- FirstOrder.Language.Structurestatement and proof · cited by 775
- FirstOrder.Language.Functionsstatement and proof · cited by 153
- FirstOrder.Language.ClosedUnderstatement and proof · cited by 13
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