Theorems · Theorem · group theory
Multiset.prod_dvd_prod_of_dvd
∀ {M : Type u_5} {N : Type u_6} [inst : CommMonoid N] {S : Multiset M} (g1 g2 : M → N),
(∀ a ∈ S, g1 a ∣ g2 a) → (Multiset.map g1 S).prod ∣ (Multiset.map g2 S).prod- Cited by
- 1 results in Mathlib
- Foundations
- Depth 21 from the axioms · uses propext, Quot.sound
- Assumes
- CommMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Multisetstatement and proof · cited by 2,627
- CommMonoidstatement and proof · cited by 2,264
- Multiset.mapstatement and proof · cited by 876
- Multiset.prodstatement and proof · cited by 528
- Multiset.map_consproof · cited by 93
- Multiset.prod_consproof · cited by 68
- mul_dvd_mulproof · cited by 24
- Multiset.induction_on'proof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- Finset.prod_dvd_prod_of_dvdproof · cited by 8