Theorems · Theorem · commutative algebra

UniqueFactorizationMonoid.factors_mul

∀ {α : Type u_1} [inst : CommMonoidWithZero α] [inst_1 : UniqueFactorizationMonoid α] {x y : α},
  x ≠ 0 →
    y ≠ 0 →
      Multiset.Rel Associated (UniqueFactorizationMonoid.factors (x * y))
        (UniqueFactorizationMonoid.factors x + UniqueFactorizationMonoid.factors y)

Defined in: Mathlib.RingTheory.UniqueFactorizationDomain.Basic
Cited by: 1 results in Mathlib
Foundations: Depth 27 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommMonoidWithZero UniqueFactorizationMonoid

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Cites15

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

Multisetstatement · cited by 2,627
CommMonoidWithZerostatement and proof · cited by 913
Associatedstatement and proof · cited by 296
UniqueFactorizationMonoidstatement and proof · cited by 279
mul_ne_zeroproof · cited by 178
Associated.symmproof · cited by 87
UniqueFactorizationMonoid.factorsstatement and proof · cited by 55
Multiset.Relstatement · cited by 47
Associated.transproof · cited by 22
UniqueFactorizationMonoid.factors_prodproof · cited by 18
Multiset.prod_addproof · cited by 18
Multiset.mem_addproof · cited by 16

Cited by1

Results whose statement or proof uses this declaration.

IsRelPrime.moebius_mulproof · cited by 0