no goals
l : Type u_1
R : Type u_2
inst✝² : DecidableEq l
inst✝¹ : Fintype l
inst✝ : CommRing R
A : Matrix (l ⊕ l) (l ⊕ l) R
⊢ A ∈ symplecticGroup l R ↔ Aᵀ ⬝ J l R ⬝ A = J l R
rw [← transpose_mem_iff, mem_iff, transpose_transpose]