no goals
S : Type ?u.416499
T : Type ?u.416502
R : Type u_1
inst✝ : CommRing R
r x y z : R
a b c : ℍ[R]
⊢ a.re * b.re + -1 * a.imI * b.imI + -1 * a.imJ * b.imJ - -1 * -1 * a.imK * b.imK =
    a.re * b.re - a.imI * b.imI - a.imJ * b.imJ - a.imK * b.imK
simp only [one_mul, neg_mul, sub_eq_add_neg, neg_neg]