Theorems · Theorem · ring theory

AddMonoidAlgebra.smul_apply_addAction

∀ {G : Type u_1} {P : Type u_2} {R : Type u_3} {V : Type u_4} [inst : AddGroup G] [inst_1 : AddAction G P]
  [inst_2 : Semiring R] [inst_3 : AddCommMonoid V] [inst_4 : SMulWithZero R V] (f : AddMonoidAlgebra R G) (x : P → V)
  (p : P), (f • x) p = ∑ i ∈ f.coeff.support, f.coeff i • x (-i +ᵥ p)

Defined in

Mathlib.Algebra.MonoidAlgebra.PointwiseSMul

Cited by

1 results in Mathlib

Foundations

Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddGroupAddActionSemiringAddCommMonoidSMulWithZero