Not Understanding This Mortality Formula
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! 
Factoring out the q' requires the UDD assumption. Under UDD deaths are at a constant rate over the year. That constant rate is q'x.

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In other words, I don't see how if we're taking someone surviving t years (t<1), then they die at time t, then saying that's the same as the chances of someone dying in the first year. 
It's more intuitive to think of a cohort than an individual. Lets there are 1000000 lives at the beginning of the year with lets say q' = .02. The lives are dying at the rate of 20000/year with the number of deaths in any time interval proportional to the time interval. Over the year the number of survivors is decreasing by the force of mortality increases exactly enough to keep the rate of deaths constant.
UDD is equivalent to the product of the probability of survival and the force of mortality is constant. 
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