Что такое "behalf to show"?

В контексте:

Red Turnip Senior shot up with a gasp. His son nervously disentangled from him as the father looked across the suddenly crowded village. A wide-eyed mare stood with a hoof over her mouth above a bundle of dropped supplies. Several young ponies stood at her side, also gaping. It only took two or three steps on Red Turnip Senior's behalf to show that he was alive, and she was galloping towards him. The two collided with a twirling embrace, falling to their knees and nuzzling each other as quickly as they could dry each other's joyful tears. Red Turnip Junior and the other young ponies clustered around the two, followed by a bouncing and giggling Rockspot.