∀ {𝕜 : Type u_1} {E : Type u_2} [inst : RCLike 𝕜] [inst_1 : NormedAddCommGroup E] [inst_2 : InnerProductSpace 𝕜 E]
  {S T : E →ₗ[𝕜] E}, S.IsSymmetricProjection → T.IsSymmetricProjection → S.range = T.range → S = T