∀ {R : Type u_1} {S : Type u_2} [inst : NonUnitalNonAssocRing R] [inst_1 : NonUnitalNonAssocRing S]
  (s : NonUnitalSubring R) (t : NonUnitalSubring S) (x x_1 : ↥(s.prod t)),
  (Equiv.Set.prod ↑s ↑t).toFun (x * x_1) = (Equiv.Set.prod ↑s ↑t).toFun (x * x_1)