∀ {S : Type u_2} {R : Type u_1} {c₁ c₂ c₃ : R} [inst : Monoid S] [inst_1 : MulAction S R] (x : S)
  (x_1 : QuaternionAlgebra R c₁ c₂ c₃),
  (QuaternionAlgebra.equivProd c₁ c₂ c₃) (x • x_1) = (QuaternionAlgebra.equivProd c₁ c₂ c₃) (x • x_1)