How can I prove this?

[Matt]

Originally Posted by SAump

I have no argument if a substitute player fills in as pinch runner for the DH.
I would allow the DH to return to DH.

BRD 62 Batter: DH: Player returns offensively
FED: A player may leave the line-up and return offensively and/or defensively under the reentry rule. (3-1-3)

BRD 67 Batter: DH: Pinch hitter/runner for DH
FED: A pinch hitter or pinch runner for the DH becomes the DH. (3-1-4; 3-1-4 b) Except: The DH is terminated if the player for whom the DH currently hits (or any player for whom he has batted), pinch hits or pinch runs for him. (3-1-4a and c).

Connecting the dots, can both of them continue in the ballgame in their previous roles?

No, and there's no requirement stating that they have to do so.