Theorems · Theorem · commutative algebra
DividedPowerAlgebra.prod_dp
∀ {R : Type u_2} {M : Type u_3} [inst : CommSemiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] {ι : Type u_4}
{s : Finset ι} {n : ι → ℕ} {m : M},
∏ i ∈ s, DividedPowerAlgebra.dp R (n i) m = ↑(Nat.multinomial s n) * DividedPowerAlgebra.dp R (s.sum n) m- Cited by
- 1 results in Mathlib
- Foundations
- Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites26
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Modulestatement and proof · cited by 20,661
- Finsetstatement and proof · cited by 13,712
- AddCommMonoidstatement and proof · cited by 12,281
- CommSemiringstatement and proof · cited by 10,911
- Finsuppstatement · cited by 5,255
- Finset.sumstatement and proof · cited by 5,195
- one_mulproof · cited by 2,841
- Nat.cast_oneproof · cited by 2,501
- Finset.prodstatement and proof · cited by 2,356
- mul_commproof · cited by 2,262
- MvPolynomialstatement · cited by 2,140
- mul_assocproof · cited by 1,667
Cited by1
Results whose statement or proof uses this declaration.
- DividedPowerAlgebra.pow_dpproof · cited by 0