no goals
S : Type ?u.421024
T : Type ?u.421027
R : Type u_1
inst✝ : CommRing R
r x y z : R
a b c : ℍ[R]
⊢ a.re * b.imJ + -1 * a.imI * b.imK + a.imJ * b.re - -1 * a.imK * b.imI =
    a.re * b.imJ - a.imI * b.imK + a.imJ * b.re + a.imK * b.imI
simp only [one_mul, neg_mul, sub_eq_add_neg, neg_neg]