Theorems · Theorem · commutative algebra
gcd_eq_left_iff
∀ {α : Type u_1} [inst : CommMonoidWithZero α] [inst_1 : NormalizedGCDMonoid α] (a b : α),
normalize a = a → (gcd a b = a ↔ a ∣ b)- Defined in
- Mathlib.Algebra.GCDMonoid.Basic
- Cited by
- 1 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.
Cites10
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
- normalizestatement and proof · cited by 137
- dvd_reflproof · cited by 97
- GCDMonoid.gcd_dvd_leftproof · cited by 36
- GCDMonoid.gcd_dvd_rightproof · cited by 34
- GCDMonoid.dvd_gcdproof · cited by 23
- dvd_antisymm_of_normalize_eqproof · cited by 15
- normalize_gcdproof · cited by 13
Cited by1
Results whose statement or proof uses this declaration.
- gcd_eq_right_iffproof · cited by 1