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Theorems · Theorem · commutative algebra

lcm_assoc

∀ {α : Type u_1} [inst : CommMonoidWithZero α] [inst_1 : NormalizedGCDMonoid α] (m n k : α),
  lcm (lcm m n) k = lcm m (lcm n k)
Defined in
Mathlib.Algebra.GCDMonoid.Basic
Cited by
2 results in Mathlib
Foundations
Depth 20 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.

Multiset.lcm_dedup · cited by 3Multiset.lcm_dedupFinset.lcm_union · cited by 0Finset.lcm_unionCommMonoidWithZero · cited by 913CommMonoidWithZeroNormalizedGCDMonoid · cited by 159NormalizedGCDMonoidDvd.dvd.trans · cited by 148dvd.transGCDMonoid.lcm · cited by 78GCDMonoid.lcmdvd_lcm_left · cited by 17dvd_lcm_leftdvd_lcm_right · cited by 17dvd_lcm_rightdvd_antisymm_of_normalize_eq · cited by 15dvd_antisymm_of_normalize…lcm_dvd · cited by 14lcm_dvdnormalize_lcm · cited by 8normalize_lcmlcm_assocCITED BYCITES

Cites9

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by2

Results whose statement or proof uses this declaration.