Theorems · Theorem · commutative algebra
Associates.prod_le_prod
∀ {M : Type u_2} [inst : CommMonoid M] {p q : Multiset (Associates M)}, p ≤ q → p.prod ≤ q.prod- Defined in
- Mathlib.Algebra.BigOperators.Associated
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 55 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- mul_oneproof · cited by 3,885
- Multisetstatement and proof · cited by 2,627
- CommMonoidstatement and proof · cited by 2,264
- le_reflproof · cited by 2,061
- Multiset.prodstatement and proof · cited by 528
- Associatesstatement and proof · cited by 210
- Classical.decEqproof · cited by 134
- add_tsub_cancel_of_leproof · cited by 79
- one_leproof · cited by 23
- Multiset.prod_addproof · cited by 18
- Associates.mul_monoproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- Associates.prod_monoproof · cited by 2
- Associates.prod_le_prod_iff_leproof · cited by 0