Theorems · Definition · ring theory
SkewMonoidAlgebra.sum
{k : Type u_1} →
{G : Type u_2} →
[inst : AddCommMonoid k] → {N : Type u_3} → [AddCommMonoid N] → SkewMonoidAlgebra k G → (G → k → N) → Nsum f g is the sum of g a (f.coeff a) over the support of f.
- Defined in
- Mathlib.Algebra.SkewMonoidAlgebra.Basic
- Cited by
- 46 results in Mathlib
- Foundations
- Depth 60 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddCommMonoidAddCommMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddCommMonoidstatement and proof · cited by 12,281
- Finsupp.sumproof · cited by 481
- SkewMonoidAlgebrastatement and proof · cited by 216
- SkewMonoidAlgebra.coeffproof · cited by 110
Cited by48
Results whose statement or proof uses this declaration.
- SkewPolynomial.sumproof · cited by 22
- SkewMonoidAlgebra.sum_single_indexstatement · cited by 12
- SkewMonoidAlgebra.mapDomainproof · cited by 12
- SkewMonoidAlgebra.coeff_mulstatement and proof · cited by 9
- SkewMonoidAlgebra.coeff_sum'statement · cited by 8
- SkewMonoidAlgebra.sum_singlestatement and proof · cited by 7
- SkewMonoidAlgebra.sum_zerostatement · cited by 6
- SkewMonoidAlgebra.single_mul_singleproof · cited by 4
- SkewMonoidAlgebra.sum_ite_eq'statement · cited by 4
- SkewMonoidAlgebra.coeff_sumstatement and proof · cited by 3
- SkewMonoidAlgebra.sum_congrstatement · cited by 3
- SkewMonoidAlgebra.sum_sum_indexstatement and proof · cited by 3