Theorems · Theorem · commutative algebra
gcd_mul_left
∀ {α : Type u_1} [inst : CommMonoidWithZero α] [inst_1 : StrongNormalizedGCDMonoid α] (a b c : α),
gcd (a * b) (a * c) = normalize a * gcd b c- Defined in
- Mathlib.Algebra.GCDMonoid.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 47 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- MulZeroClass.zero_mulproof · cited by 1,625
- CommMonoidWithZerostatement and proof · cited by 913
- GCDMonoid.gcdstatement and proof · cited by 143
- normalizestatement and proof · cited by 137
- dvd_mul_rightproof · cited by 89
- GCDMonoid.gcd_dvd_leftproof · cited by 36
- mul_dvd_mul_leftproof · cited by 34
- GCDMonoid.gcd_dvd_rightproof · cited by 34
- by_casesproof · cited by 31
- mul_dvd_mul_iff_leftproof · cited by 24
- GCDMonoid.dvd_gcdproof · cited by 23
- normalize_zeroproof · cited by 16
Cited by2
Results whose statement or proof uses this declaration.
- Finset.gcd_mul_leftproof · cited by 2
- gcd_mul_rightproof · cited by 0