Theorems · Theorem · ring theory
SkewPolynomial.sum_def
∀ {R : Type u_1} [inst : Semiring R] {S : Type u_5} [inst_1 : AddCommMonoid S] (p : SkewPolynomial R) (f : ℕ → R → S),
p.sum f = ∑ n ∈ p.support, f n (p.coeff n)- Defined in
- Mathlib.Algebra.SkewPolynomial.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SemiringAddCommMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- Finset.sumstatement and proof · cited by 5,195
- Finset.sum_congrproof · cited by 2,323
- Multiplicativeproof · cited by 875
- Finsupp.supportproof · cited by 828
- Function.Injective.injOnproof · cited by 280
- Multiplicative.ofAddproof · cited by 237
- Multiplicative.toAddproof · cited by 161
- SkewPolynomialstatement and proof · cited by 124
- SkewMonoidAlgebra.coeffproof · cited by 110
Cited by3
Results whose statement or proof uses this declaration.
- SkewPolynomial.sum_add'proof · cited by 1
- SkewPolynomial.sum_negproof · cited by 1
- SkewPolynomial.sum_eq_of_subsetproof · cited by 0