<img width="1878" height="676" alt="Image" src="https://github.com/user-attachments/assets/b2b0942b-0910-4fac-a8bb-eaec67e24094" /> In the second line should be: E[Y_i(1) T_i ... + Y_i(0)(1-T_i) ...] Otherwise the notation is not consistent, with the actual proof.