Theorems · Theorem · logic and foundations
RecursiveIn.partrec_of_const
∀ {α : Type u_1} {σ : Type u_4} [inst : Primcodable α] [inst_1 : Primcodable σ] {f : α →. σ} {s : Part ℕ},
RecursiveIn {fun x => s} f → Partrec fIf a function is recursive in a constant partial function, then it is partial recursive.
- Defined in
- Mathlib.Computability.RecursiveIn
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 92 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PrimcodablePrimcodable
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Primcodablestatement and proof · cited by 325
- Partstatement and proof · cited by 325
- PFunstatement and proof · cited by 207
- Set.mem_singleton_iffproof · cited by 172
- Partrecstatement and proof · cited by 48
- RecursiveInstatement and proof · cited by 15
- RecursiveIn.partrec_of_oracleproof · cited by 2
- Partrec.const'proof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- TuringReducible.partrec_of_constproof · cited by 1
- partrec_iff_forall_recursiveIn_singletonproof · cited by 0