∀ {R : Type u_1} {M : Type u_2} [inst : CommRing R] [inst_1 : AddCommGroup M] [inst_2 : Module R M]
  (B : LinearMap.BilinMap R M R) (motive : LinearMap.IsSymm B → Prop) (x : LinearMap.IsSymm B),
  (∀ (hB : ∀ (x y : M), (RingHom.id R) ((B x) y) = (B y) x), motive ⋯) → motive x