Theorems · Definition · commutative algebra
GCDMonoid.gcd
{α : Type u_2} → {inst : CommMonoidWithZero α} → [self : GCDMonoid α] → α → α → αThe greatest common divisor between two elements.
- Defined in
- Mathlib.Algebra.GCDMonoid.Basic
- Cited by
- 143 results in Mathlib
- Foundations
- Depth 2 from the axioms, rests on 3 definitions · uses no axioms
- Assumes
- GCDMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommMonoidWithZerostatement and proof · cited by 913
- GCDMonoidstatement and proof · cited by 96
Cited by156
Results whose statement or proof uses this declaration.
- Finset.gcdproof · cited by 49
- GCDMonoid.gcd_dvd_leftstatement · cited by 36
- GCDMonoid.gcd_dvd_rightstatement · cited by 34
- GCDMonoid.dvd_gcdstatement · cited by 23
- Multiset.gcdproof · cited by 21
- RatFunc.num_div_denomproof · cited by 18
- normalize_gcdstatement · cited by 13
- Finset.gcd_insertstatement and proof · cited by 9
- gcd_samestatement · cited by 8
- dvd_gcd_iffstatement and proof · cited by 8
- gcd_dvd_gcdstatement · cited by 8
- RatFunc.denom_divstatement and proof · cited by 7