Theorems · Theorem · commutative algebra
lcm_eq_one_iff
∀ {α : Type u_1} [inst : CommMonoidWithZero α] [inst_1 : NormalizedGCDMonoid α] (a b : α), lcm a b = 1 ↔ a ∣ 1 ∧ b ∣ 1- Defined in
- Mathlib.Algebra.GCDMonoid.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 21 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Units.valproof · cited by 1,966
- CommMonoidWithZerostatement and proof · cited by 913
- NormalizedGCDMonoidstatement and proof · cited by 159
- GCDMonoid.lcmstatement and proof · cited by 78
- dvd_lcm_leftproof · cited by 17
- dvd_lcm_rightproof · cited by 17
- Units.mkOfMulEqOneproof · cited by 15
- lcm_units_coe_leftproof · cited by 3
- normalize_coe_unitsproof · cited by 2
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