Theorems · Theorem · commutative algebra
Associates.factors_prod
∀ {α : Type u_1} [inst : CommMonoidWithZero α] [inst_1 : UniqueFactorizationMonoid α] (a : Associates α),
a.factors.prod = a- Cited by
- 9 results in Mathlib
- Foundations
- Depth 32 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- eq_or_neproof · cited by 1,117
- CommMonoidWithZerostatement and proof · cited by 913
- Multiset.prodproof · cited by 528
- UniqueFactorizationMonoidstatement and proof · cited by 279
- Associatesstatement and proof · cited by 210
- Associates.mkproof · cited by 137
- Associates.factorsstatement · cited by 97
- Associates.FactorSet.prodstatement and proof · cited by 20
- Associates.factors_mkproof · cited by 12
- Associates.factors_zeroproof · cited by 7
- Associates.mk_surjectiveproof · cited by 7
- Associates.prod_mkproof · cited by 6
Cited by9
Results whose statement or proof uses this declaration.
- Associates.factors_oneproof · cited by 6
- Associates.factors_mulproof · cited by 4
- Associates.eq_of_factors_eq_factorsproof · cited by 4
- Associates.prod_factorsproof · cited by 3
- Associates.factors_leproof · cited by 2
- Associates.factors_prime_powproof · cited by 2
- Associates.dvd_of_mem_factorsproof · cited by 2
- Associates.factors_eq_top_iff_zeroproof · cited by 1
- Associates.factors_selfproof · cited by 1