∀ {S : Type u_1} {T : Type u_2} {R : Type u_3} {M : Type u_4} {N : Type u_5} [inst : CommSemiring R]
  [inst_1 : AddCommMonoid M] [inst_2 : Module R M] [inst_3 : AddCommMonoid N] [inst_4 : Module R N] [inst_5 : Monoid S]
  [inst_6 : Monoid T] [inst_7 : DistribMulAction S N] [inst_8 : DistribMulAction T N] [inst_9 : SMulCommClass S R N]
  [inst_10 : SMulCommClass T R N] [SMulCommClass S T N], SMulCommClass S T (QuadraticMap R M N)