Theorems · Theorem · commutative algebra
gcd_mul_dvd_mul_gcd
∀ {α : Type u_1} [inst : CommMonoidWithZero α] [inst_1 : GCDMonoid α] (k m n : α), gcd k (m * n) ∣ gcd k m * gcd k n- Defined in
- Mathlib.Algebra.GCDMonoid.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 20 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.
Cites11
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 and proof · cited by 143
- GCDMonoidstatement and proof · cited by 96
- dvd_mul_rightproof · cited by 89
- dvd_mul_leftproof · cited by 47
- GCDMonoid.gcd_dvd_leftproof · cited by 36
- GCDMonoid.gcd_dvd_rightproof · cited by 34
- mul_dvd_mulproof · cited by 24
- GCDMonoid.dvd_gcdproof · cited by 23
- exists_dvd_and_dvd_of_dvd_mulproof · cited by 6
Cited by2
Results whose statement or proof uses this declaration.
- Polynomial.associated_content_mulproof · cited by 6
- gcd_pow_right_dvd_pow_gcdproof · cited by 1