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Theorems · Theorem · commutative algebra

lcm_eq_normalize

∀ {α : Type u_1} [inst : CommMonoidWithZero α] [inst_1 : NormalizedGCDMonoid α] {a b c : α},
  lcm a b ∣ c → c ∣ lcm a b → lcm a b = normalize c
Defined in
Mathlib.Algebra.GCDMonoid.Basic
Cited by
4 results in Mathlib
Foundations
Depth 19 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CommMonoidWithZeroNormalizedGCDMonoid
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

lcm_same · cited by 5lcm_samelcm_units_coe_left · cited by 3lcm_units_coe_leftlcm_mul_left · cited by 2lcm_mul_leftIdeal.sup_mul_inf · cited by 1Ideal.sup_mul_infCommMonoidWithZero · cited by 913CommMonoidWithZeroNormalizedGCDMonoid · cited by 159NormalizedGCDMonoidnormalize · cited by 137normalizeGCDMonoid.lcm · cited by 78GCDMonoid.lcmnormalize_lcm · cited by 8normalize_lcmnormalize_eq_normalize · cited by 5normalize_eq_normalizelcm_eq_normalizeCITED BYCITES

Cites6

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Cited by4

Results whose statement or proof uses this declaration.