Theorems · Definition · number theory
Nat.equivProdNatSmoothNumbers
{p : ℕ} → Nat.Prime p → ℕ × ↑p.smoothNumbers ≃ ↑(p + 1).smoothNumbersWe establish the bijection from ℕ × smoothNumbers p to smoothNumbers (p+1)
given by (e, n) ↦ p^e * n when p is a prime. See Nat.smoothNumbers_succ for
when p is not prime.
- Defined in
- Mathlib.NumberTheory.SmoothNumbers
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 95 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Equivstatement · cited by 8,337
- Set.Elemstatement · cited by 7,166
- Nat.Primestatement and proof · cited by 2,059
- Equiv.transproof · cited by 337
- Nat.smoothNumbersstatement · cited by 32
- Finset.notMem_range_selfproof · cited by 18
- Nat.smoothNumbers_eq_factoredNumbersproof · cited by 16
- Equiv.setCongrproof · cited by 13
- Equiv.prodCongrRightproof · cited by 12
- Nat.equivProdNatFactoredNumbersproof · cited by 4
Cited by2
Results whose statement or proof uses this declaration.
- Nat.equivProdNatSmoothNumbers_apply'statement · cited by 0
- Nat.equivProdNatSmoothNumbers_applystatement · cited by 0