∀ {R : Type u_1} {M : Type u_2} {N : Type u_3} [inst : CommSemiring R] [inst_1 : AddCommMonoid M]
  [inst_2 : AddCommMonoid N] [inst_3 : Module R M] [inst_4 : Module R N] (f : M ≃ₗ[R] N) (a : Module.Dual R M × M),
  (QuadraticForm.dualProdIsometry f) a = (f.symm.dualMap.toAddEquiv.prodCongr f.toAddEquiv) a