Theorems · Theorem · logic and foundations
Denumerable.sigma_ofNat_val
∀ {α : Type u_1} [inst : Denumerable α] {γ : α → Type u_3} [inst_1 : (a : α) → Denumerable (γ a)] (n : ℕ),
Denumerable.ofNat (Sigma γ) n =
⟨Denumerable.ofNat α (Nat.unpair n).1,
Denumerable.ofNat (γ (Denumerable.ofNat α (Nat.unpair n).1)) (Nat.unpair n).2⟩- Defined in
- Mathlib.Logic.Denumerable
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DenumerableDenumerable
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Nat.unpairstatement and proof · cited by 67
- Denumerablestatement and proof · cited by 28
- Denumerable.ofNatstatement and proof · cited by 26
- Option.bind_congr'proof · cited by 23
- Denumerable.decode_eq_ofNatproof · cited by 9
- Encodable.decode_sigma_valproof · cited by 1
Cited by7
Results whose statement or proof uses this declaration.
- Primrec₂.natPairproof · cited by 4
- Nat.Partrec.Code.primrec_evalnproof · cited by 3
- Primrec₂.ofNat_iffproof · cited by 3
- Nat.Partrec.Code.fixed_point₂proof · cited by 1
- Nat.Partrec.Code.fixed_pointproof · cited by 1
- Denumerable.prod_ofNat_valproof · cited by 1
- Denumerable.prod_nat_ofNatproof · cited by 0