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Theorems · Theorem · logic and foundations

Set.Definable.compl

∀ {M : Type w} {A : Set M} {L : FirstOrder.Language} [inst : L.Structure M] {α : Type u₁} {s : Set (α → M)},
  A.Definable L s → A.Definable L sᶜ
Defined in
Mathlib.ModelTheory.Definability
Cited by
3 results in Mathlib
Foundations
Depth 23 from the axioms · uses propext, Quot.sound
Assumes
FirstOrder.Language.Structure
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

Set.DefinableFun.ite · cited by 0DefinableFun.iteSet.Definable.sdiff · cited by 0Definable.sdiffSet.Definable.himp · cited by 0Definable.himpSet · cited by 53352SetSet.Elem · cited by 7166Set.ElemSet.ofPred · cited by 6101Set.ofPredCompl.compl · cited by 2925Compl.complSet.ext · cited by 2266Set.extFirstOrder.Language · cited by 1084FirstOrder.LanguageFirstOrder.Language.Structure · cited by 775Language.StructureFirstOrder.Language.withConstants · cited by 108Language.withConstantsSet.mem_ofPred · cited by 104Set.mem_ofPredFirstOrder.Language.Formula · cited by 93Language.FormulaFirstOrder.Language.Formula.Realize · cited by 81Formula.RealizeSet.Definable · cited by 39Set.DefinableFirstOrder.Language.Formula.not · cited by 27Formula.notSet.compl_ofPred · cited by 4Set.compl_ofPredFirstOrder.Language.Formula.realize_not · cited by 1Formula.realize_notDefinable.complCITED BYCITES

Cites15

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Cited by3

Results whose statement or proof uses this declaration.