Theorems · Theorem · commutative algebra
associated_gcd_left_iff
∀ {α : Type u_1} [inst : CommMonoidWithZero α] [inst_1 : GCDMonoid α] {x y : α}, Associated x (gcd x y) ↔ x ∣ y- Defined in
- Mathlib.Algebra.GCDMonoid.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 13 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommMonoidWithZeroGCDMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommMonoidWithZerostatement and proof · cited by 913
- Associatedstatement and proof · cited by 296
- Dvd.dvd.transproof · cited by 148
- GCDMonoid.gcdstatement and proof · cited by 143
- GCDMonoidstatement and proof · cited by 96
- dvd_rflproof · cited by 80
- Associated.dvdproof · cited by 38
- GCDMonoid.gcd_dvd_leftproof · cited by 36
- GCDMonoid.gcd_dvd_rightproof · cited by 34
- associated_of_dvd_dvdproof · cited by 28
- GCDMonoid.dvd_gcdproof · cited by 23
Cited by1
Results whose statement or proof uses this declaration.
- Irreducible.isUnit_gcd_iffproof · cited by 1