Theorems · Theorem · commutative algebra
gcd_eq_right_iff
∀ {α : Type u_1} [inst : CommMonoidWithZero α] [inst_1 : NormalizedGCDMonoid α] (a b : α),
normalize b = b → (gcd a b = b ↔ b ∣ a)- Defined in
- Mathlib.Algebra.GCDMonoid.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 21 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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 and proof · cited by 137
- gcd_commproof · cited by 6
- gcd_eq_left_iffproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- Finset.gcd_insertproof · cited by 9