Cut, Shoulder, Check, Push

Watch the method: press play to see the winning idea run, or step through it move by move.

The mid-line rule is a guide, not a law. When your king already escorts the pawn and the defending king is cut off, even a pawn short of the middle wins.

Cut, then shoulder. The rook on the c-file keeps the black king away from the pawn, and your king does the rest with its body: Ka4 pushes the defender back and prepares b4-b5.

The cut can be traded for a tempo. You do not have to hold the c-file forever. In the main line the rook leaves it (Rc6, then Ra6) to support the pawn from the side, and comes back with a check, Rc6+, the moment the black king steps to c4.

One tempo wide. The same position with Black to move is drawn. That is how narrow the winning zone is short of the mid-line.

In this drill the defense fights to reach the blockade. Cut, shoulder, check, push.