∀ {R : Type u_1} {G : Type u_2} [inst : CommSemiring R] [inst_1 : Group G] [inst_2 : MulAction G R]
  [SMulCommClass G R R] [IsScalarTower G R R] (x : G) (y z : R), IsCoprime y (x • z) ↔ IsCoprime y z