Theorems · Theorem · number theory
Nat.Coprime.mul_injOn_divisors
∀ {m n : ℕ}, m.Coprime n → Set.InjOn (fun p => p.1 * p.2) ↑(m.divisors ×ˢ n.divisors)Products of divisors taken from coprime naturals are unique.
- Defined in
- Mathlib.Data.Finset.NatDivisors
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 66 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- Finsetstatement · cited by 13,712
- SetLike.coestatement and proof · cited by 8,199
- SProd.sprodstatement and proof · cited by 1,750
- Set.InjOnstatement · cited by 543
- Nat.divisorsstatement and proof · cited by 137
- dvd_antisymmproof · cited by 23
Cited by1
Results whose statement or proof uses this declaration.
- Nat.Coprime.divisors_mulstatement and proof · cited by 0