Theorems · Theorem · commutative algebra
gcd_same
∀ {α : Type u_1} [inst : CommMonoidWithZero α] [inst_1 : NormalizedGCDMonoid α] (a : α), gcd a a = normalize a- Defined in
- Mathlib.Algebra.GCDMonoid.Basic
- Cited by
- 8 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.
Cites8
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
- dvd_reflproof · cited by 97
- GCDMonoid.gcd_dvd_leftproof · cited by 36
- GCDMonoid.dvd_gcdproof · cited by 23
- gcd_eq_normalizeproof · cited by 6
Cited by8
Results whose statement or proof uses this declaration.
- Multiset.gcd_dedupproof · cited by 4
- gcd_mul_leftproof · cited by 2
- Multiset.gcd_addproof · cited by 2
- Multiset.gcd_eq_zero_iffproof · cited by 2
- RatFunc.num_oneproof · cited by 2
- RatFunc.denom_oneproof · cited by 2
- Polynomial.content_eq_gcd_leadingCoeff_content_eraseLeadproof · cited by 1
- Finset.gcd_eq_gcd_filter_ne_zeroproof · cited by 0