Theorems · Definition · logic and foundations
Set.DefinableFun
{M : Type u_1} → (L : FirstOrder.Language) → [L.Structure M] → {α : Type u_2} → Set M → ((α → M) → M) → PropA function from tuples of elements of M to M is definable if its graph is definable.
- Defined in
- Mathlib.ModelTheory.Definability
- Cited by
- 15 results in Mathlib
- Foundations
- Depth 23 from the axioms · uses Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- FirstOrder.Languagestatement and proof · cited by 1,084
- FirstOrder.Language.Structurestatement and proof · cited by 775
- Set.Definableproof · cited by 39
- Function.tupleGraphproof · cited by 4
Cited by16
Results whose statement or proof uses this declaration.
- Set.DefinableMapproof · cited by 3
- FirstOrder.Language.Term.definableFun_realizestatement · cited by 3
- Set.DefinableFun.ofPred_eqstatement and proof · cited by 2
- Set.empty_definableFun_iffstatement · cited by 1
- FirstOrder.Language.definableFun_conststatement · cited by 1
- FirstOrder.Language.definableFun_varstatement · cited by 1
- Set.definableFun_iff_empty_definableFun_with_paramsstatement · cited by 1
- Set.DefinableFun.ofPred_eq_conststatement and proof · cited by 1
- Set.DefinableFun.of_emptystatement and proof · cited by 1
- Set.DefinableFun.projstatement · cited by 1
- Set.DefinableFun.compstatement and proof · cited by 0
- Set.DefinableFun.fun_symbolstatement · cited by 0