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doc: eval is a universal partial recursive function (#9703)
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hmonroe committed Jan 16, 2024
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3 changes: 2 additions & 1 deletion Mathlib/Computability/PartrecCode.lean
Expand Up @@ -695,7 +695,8 @@ theorem smn :
⟨curry, Primrec₂.to_comp curry_prim, eval_curry⟩
#align nat.partrec.code.smn Nat.Partrec.Code.smn

/-- A function is partial recursive if and only if there is a code implementing it. -/
/-- A function is partial recursive if and only if there is a code implementing it. Therefore,
`eval` is a **universal partial recursive function**. -/
theorem exists_code {f : ℕ →. ℕ} : Nat.Partrec f ↔ ∃ c : Code, eval c = f := by
refine ⟨fun h => ?_, ?_⟩
· induction h with
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