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Theorems · Theorem · logic and foundations

FirstOrder.Language.Substructure.closure_empty

∀ {L : FirstOrder.Language} {M : Type w} [inst : L.Structure M],
  (FirstOrder.Language.Substructure.closure L).toFun ∅ = ⊥
Defined in
Mathlib.ModelTheory.Substructures
Cited by
1 results in Mathlib
Foundations
Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
FirstOrder.Language.Structure
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

FirstOrder.Language.Substructure.fg_bot · cited by 2Substructure.fg_botSet · cited by 53352SetSetLike.coe · cited by 8199SetLike.coeBot.bot · cited by 4720Bot.botFirstOrder.Language · cited by 1084FirstOrder.LanguageFirstOrder.Language.Structure · cited by 775Language.StructureFirstOrder.Language.Substructure · cited by 242Language.SubstructureGaloisInsertion.gc · cited by 137GaloisInsertion.gcLowerAdjoint.toFun · cited by 105LowerAdjoint.toFunFirstOrder.Language.Substructure.closure · cited by 70Substructure.closureGaloisConnection.l_bot · cited by 63GaloisConnection.l_botFirstOrder.Language.Substructure.gi · cited by 4Substructure.giSubstructure.closure_emptyCITED BYCITES

Cites11

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Cited by1

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