Theorems · Theorem · ring theory
AddMonoidAlgebra.mul_def
∀ {R : Type u_1} {M : Type u_4} [inst : Semiring R] [inst_1 : Add M] (x y : AddMonoidAlgebra R M),
x * y = x.coeff.sum fun m₁ r₁ => y.coeff.sum fun m₂ r₂ => AddMonoidAlgebra.single (m₁ + m₂) (r₁ * r₂)- Defined in
- Mathlib.Algebra.MonoidAlgebra.Defs
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Semiringstatement and proof · cited by 13,802
- AddMonoidAlgebrastatement and proof · cited by 649
- Finsupp.sumstatement · cited by 481
- AddMonoidAlgebra.coeffstatement · cited by 365
- AddMonoidAlgebra.singlestatement · cited by 250
Cited by9
Results whose statement or proof uses this declaration.
- AddMonoidAlgebra.single_mul_singleproof · cited by 20
- AddMonoidAlgebra.coeff_mulproof · cited by 13
- AddMonoidAlgebra.support_coeff_mul_subsetproof · cited by 5
- AddMonoidAlgebra.liftNC_mulproof · cited by 1
- MvPolynomial.mul_defproof · cited by 1
- AddMonoidAlgebra.mem_ideal_span_of'_imageproof · cited by 1
- AddMonoidAlgebra.map_mulproof · cited by 0
- Polynomial.mul_eq_sum_sumproof · cited by 0
- AddMonoidAlgebra.mapDomain_mulproof · cited by 0