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Theorems · Theorem · logic and foundations

Nat.Partrec.recursiveIn

∀ {f : ℕ →. ℕ} {O : Set (ℕ →. ℕ)}, Nat.Partrec f → Nat.RecursiveIn O f

If a function is partial recursive, then it is recursive in every partial function.

Defined in
Mathlib.Computability.RecursiveIn
Cited by
2 results in Mathlib
Foundations
Depth 27 from the axioms · uses propext

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Cites4

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
  • PFunstatement and proof · cited by 207
  • Nat.Partrecstatement and proof · cited by 19
  • Nat.RecursiveInstatement and proof · cited by 8

Cited by2

Results whose statement or proof uses this declaration.