Theorems · Theorem · ring theory

AddMonoidAlgebra.coeff_mul

∀ {R : Type u_1} {M : Type u_4} [inst : Semiring R] [inst_1 : Add M] [inst_2 : DecidableEq M]
  (x y : AddMonoidAlgebra R M) (m : M),
  (x * y).coeff m = x.coeff.sum fun m₁ r₁ => y.coeff.sum fun m₂ r₂ => if m₁ + m₂ = m then r₁ * r₂ else 0

Defined in

Mathlib.Algebra.MonoidAlgebra.Defs

Cited by

13 results in Mathlib

Foundations

Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringAddDecidableEq