Theorems · Theorem · commutative algebra
dvd_gcd_mul_of_dvd_mul
∀ {α : Type u_1} [inst : CommMonoidWithZero α] [inst_1 : GCDMonoid α] {m n k : α}, k ∣ m * n → k ∣ gcd k m * n- Defined in
- Mathlib.Algebra.GCDMonoid.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 18 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommMonoidWithZeroGCDMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommMonoidWithZerostatement and proof · cited by 913
- Dvd.dvd.transproof · cited by 148
- GCDMonoid.gcdstatement · cited by 143
- GCDMonoidstatement and proof · cited by 96
- dvd_mul_rightproof · cited by 89
- Associated.dvdproof · cited by 38
- GCDMonoid.dvd_gcdproof · cited by 23
- gcd_mul_right'proof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- dvd_mul_gcd_of_dvd_mulproof · cited by 1
- pow_dvd_of_mul_eq_powproof · cited by 1
- dvd_gcd_mul_iff_dvd_mulproof · cited by 0