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Theorems · Theorem · logic and foundations

FirstOrder.Language.definableFun_const

∀ {M : Type u_1} (L : FirstOrder.Language) [inst : L.Structure M] {A : Set M} {a : M} (γ : Type u_4),
  a ∈ A → Set.DefinableFun L A fun x => a

A constant function is a definable function.

Defined in
Mathlib.ModelTheory.Definability
Cited by
1 results in Mathlib
Foundations
Depth 34 from the axioms · uses propext, Quot.sound
Assumes
FirstOrder.Language.Structure
Mathlib docsSourceLoogleLeanSearch

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Set.DefinableFun.ofPred_eq_const · cited by 1DefinableFun.ofPred_eq_co…Set · cited by 53352SetFirstOrder.Language · cited by 1084FirstOrder.LanguageFirstOrder.Language.Structure · cited by 775Language.StructureFirstOrder.Language.con · cited by 21Language.conSet.DefinableFun · cited by 15Set.DefinableFunFirstOrder.Language.Constants.term · cited by 11Constants.termFirstOrder.Language.Term.definableFun_realize · cited by 3Term.definableFun_realizeSet.definableFun_iff_empty_definableFun_with_params · cited by 1Set.definableFun_iff_empt…Language.definableFun_constCITED BYCITES

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Cited by1

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