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Theorems · Theorem · logic and foundations

FirstOrder.Language.Term.definableFun_realize

∀ {M : Type u_1} {L : FirstOrder.Language} [inst : L.Structure M] {α : Type u_2} (t : L.Term α),
  Set.DefinableFun L ∅ fun v => FirstOrder.Language.Term.realize v t

A term is a definable function.

Defined in
Mathlib.ModelTheory.Definability
Cited by
3 results in Mathlib
Foundations
Depth 33 from the axioms · uses propext, Quot.sound
Assumes
FirstOrder.Language.Structure
Mathlib docsSourceLoogleLeanSearch

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FirstOrder.Language.definableFun_var · cited by 1Language.definableFun_varFirstOrder.Language.definableFun_const · cited by 1Language.definableFun_con…Set.DefinableFun.fun_symbol · cited by 0DefinableFun.fun_symbolSet · cited by 53352SetSet.ext · cited by 2266Set.extFirstOrder.Language · cited by 1084FirstOrder.LanguageFirstOrder.Language.Structure · cited by 775Language.StructureFirstOrder.Language.Term · cited by 166Language.TermFirstOrder.Language.Term.realize · cited by 81Term.realizeFirstOrder.Language.Term.relabel · cited by 27Term.relabelFirstOrder.Language.Term.realize_relabel · cited by 15Term.realize_relabelSet.DefinableFun · cited by 15Set.DefinableFunFirstOrder.Language.Term.equal · cited by 14Term.equalSet.empty_definableFun_iff · cited by 1Set.empty_definableFun_iffTerm.definableFun_realizeCITED BYCITES

Cites11

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Cited by3

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