Theorems · Theorem · commutative algebra
normalize_gcd
∀ {α : Type u_1} [inst : CommMonoidWithZero α] [inst_1 : NormalizedGCDMonoid α] (a b : α), normalize (gcd a b) = gcd a b- Defined in
- Mathlib.Algebra.GCDMonoid.Basic
- Cited by
- 13 results in Mathlib
- Foundations
- Depth 8 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- GCDMonoid.gcdstatement · cited by 143
- normalizestatement · cited by 137
- NormalizedGCDMonoid.normalize_gcdproof · cited by 2
Cited by13
Results whose statement or proof uses this declaration.
- gcd_commproof · cited by 6
- gcd_eq_normalizeproof · cited by 6
- gcd_one_rightproof · cited by 5
- gcd_assocproof · cited by 3
- Multiset.normalize_gcdproof · cited by 3
- gcd_mul_leftproof · cited by 2
- gcd_one_leftproof · cited by 2
- Associated.gcd_eq_leftproof · cited by 2
- Associated.gcd_eq_rightproof · cited by 2
- gcd_eq_of_dvd_sub_rightproof · cited by 2
- gcd_eq_left_iffproof · cited by 1
- neg_gcdproof · cited by 0