https://imgur.com/a/bFdEfxA
Here's the thing I'm having an issue with. I understand that the force multiplied by the probability of survival is equal to the probability of death at the time of the force.

I don't understand the jump from the second line to the third line. Wouldn't tP'(1)x * ux+t be equal to tq'(1)x? Why are we jumping to the conclusion that it's a constant q'(1)x? The video just says it's constant because UDD, but I'm having trouble making the connection.

Thank you in advance!