∀ {l : Type u_1} {R : Type u_2} [inst : DecidableEq l] [inst_1 : Fintype l] [inst_2 : CommRing R]
  {A : Matrix (l ⊕ l) (l ⊕ l) R}, A ∈ Matrix.symplecticGroup l R → -(Matrix.J l R * A.transpose * Matrix.J l R * A) = 1