{𝕜 : Type u_1} →
  {E : Type u_2} →
    [inst : RCLike 𝕜] →
      [inst_1 : SeminormedAddCommGroup E] →
        [inst_2 : InnerProductSpace 𝕜 E] →
          {T : E →ₗ[𝕜] E} →
            {motive : T.IsSymmetricProjection → Sort u} →
              ((isIdempotentElem : IsIdempotentElem T) → (isSymmetric : T.IsSymmetric) → motive ⋯) →
                (t : T.IsSymmetricProjection) → motive t