Theorems · Theorem · commutative algebra
gcd_assoc
∀ {α : Type u_1} [inst : CommMonoidWithZero α] [inst_1 : NormalizedGCDMonoid α] (m n k : α),
gcd (gcd m n) k = gcd m (gcd n k)- Defined in
- Mathlib.Algebra.GCDMonoid.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 20 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommMonoidWithZerostatement and proof · cited by 913
- NormalizedGCDMonoidstatement and proof · cited by 159
- Dvd.dvd.transproof · cited by 148
- GCDMonoid.gcdstatement and proof · cited by 143
- GCDMonoid.gcd_dvd_leftproof · cited by 36
- GCDMonoid.gcd_dvd_rightproof · cited by 34
- GCDMonoid.dvd_gcdproof · cited by 23
- dvd_antisymm_of_normalize_eqproof · cited by 15
- normalize_gcdproof · cited by 13
Cited by3
Results whose statement or proof uses this declaration.
- Multiset.gcd_dedupproof · cited by 4
- Finset.gcd_unionproof · cited by 1
- Finset.gcd_eq_of_dvd_subproof · cited by 1