Theorems · Theorem · logic and foundations
Partrec.cond
∀ {α : Type u_1} {σ : Type u_4} [inst : Primcodable α] [inst_1 : Primcodable σ] {c : α → Bool} {f g : α →. σ},
Computable c → Partrec f → Partrec g → Partrec fun a => bif c a then f a else g a- Defined in
- Mathlib.Computability.RE
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 100 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.
Cites29
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Primcodablestatement and proof · cited by 325
- Partstatement · cited by 325
- PFunstatement and proof · cited by 207
- Encodable.encodeproof · cited by 118
- Computablestatement and proof · cited by 80
- Encodable.decodeproof · cited by 77
- Part.bindproof · cited by 70
- Nat.Partrec.Codeproof · cited by 66
- Part.mapproof · cited by 65
- Part.bind_someproof · cited by 49
- Partrecstatement and proof · cited by 48
- Part.ofOptionproof · cited by 33
Cited by3
Results whose statement or proof uses this declaration.
- ComputablePred.riceproof · cited by 2
- ComputablePred.to_reproof · cited by 1
- Partrec.sumCasesOnproof · cited by 0