Theorems · Theorem · commutative algebra
gcd_one_right
∀ {α : Type u_1} [inst : CommMonoidWithZero α] [inst_1 : NormalizedGCDMonoid α] (a : α), gcd a 1 = 1- Defined in
- Mathlib.Algebra.GCDMonoid.Basic
- Cited by
- 5 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 and proof · cited by 143
- one_dvdproof · cited by 37
- GCDMonoid.gcd_dvd_rightproof · cited by 34
- dvd_antisymm_of_normalize_eqproof · cited by 15
- normalize_gcdproof · cited by 13
- normalize_oneproof · cited by 10
Cited by5
Results whose statement or proof uses this declaration.
- RatFunc.num_zeroproof · cited by 5
- RatFunc.num_algebraMapproof · cited by 4
- RatFunc.denom_algebraMapproof · cited by 4
- RatFunc.denom_zeroproof · cited by 3
- RatFunc.numDenom_divproof · cited by 1