Theorems · Theorem · ring theory
SkewMonoidAlgebra.sum_zero
∀ {k : Type u_1} {G : Type u_2} [inst : AddCommMonoid k] {N : Type u_3} [inst_1 : AddCommMonoid N]
{f : SkewMonoidAlgebra k G}, (f.sum fun x x_1 => 0) = 0- Defined in
- Mathlib.Algebra.SkewMonoidAlgebra.Basic
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 61 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
- Finset.sum_const_zeroproof · cited by 219
- SkewMonoidAlgebrastatement and proof · cited by 216
- SkewMonoidAlgebra.sumstatement · cited by 46
Cited by6
Results whose statement or proof uses this declaration.
- SkewMonoidAlgebra.single_mul_singleproof · cited by 4
- SkewMonoidAlgebra.coeff_single_mul_auxproof · cited by 2
- SkewMonoidAlgebra.support_single_mul_eq_imageproof · cited by 1
- SkewPolynomial.sum_zeroproof · cited by 1
- SkewMonoidAlgebra.mapDomain_mulproof · cited by 0
- SkewMonoidAlgebra.coeff_single_mul_of_not_exists_mulproof · cited by 0