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Theorems · Theorem · logic and foundations

Set.TermDefinable.definable_tupleGraph

∀ {M : Type w} (A : Set M) (L : FirstOrder.Language) [inst : L.Structure M] {α : Type u₁} {f : (α → M) → M},
  A.TermDefinable L f → A.Definable L (Function.tupleGraph f)

Every TermDefinable function has a tupleGraph that is definable.

Defined in
Mathlib.ModelTheory.Definability
Cited by
1 results in Mathlib
Foundations
Depth 25 from the axioms · uses propext, Quot.sound
Assumes
FirstOrder.Language.Structure
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Set.TermDefinable₁.definable₂_graph · cited by 0TermDefinable₁.definable₂…Set · cited by 53352SetSet.Elem · cited by 7166Set.ElemSet.ext · cited by 2266Set.extFirstOrder.Language · cited by 1084FirstOrder.LanguageFirstOrder.Language.Structure · cited by 775Language.StructureFirstOrder.Language.Term · cited by 166Language.TermFirstOrder.Language.withConstants · cited by 108Language.withConstantsFirstOrder.Language.Term.realize · cited by 81Term.realizeSet.Definable · cited by 39Set.DefinableFirstOrder.Language.Term.relabel · cited by 27Term.relabelFirstOrder.Language.Term.realize_relabel · cited by 15Term.realize_relabelFirstOrder.Language.Term.equal · cited by 14Term.equalSet.TermDefinable · cited by 12Set.TermDefinableFunction.tupleGraph · cited by 4Function.tupleGraphTermDefinable.definable_tuple…CITED BYCITES

Cites14

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