Rewrite conditional distribution that is an inequality as a function

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How do I rewrite a conditional distribution that is an inequality as a function of another variable?

The problem I have been posed is the following:

Given

$F_u(y) = \mathbb{P}[A-u \le y | A > u]$

Show that this can be rewritten as

$F(x) = 1 - (1-F(u))(1-F_u(x-u))$