Quasilinear preference is defined to be:
$x \sim y \Rightarrow x+ae_1 \sim y+ae_1$ and $x + ae_1 \succ x$ with $e_1 = (1,0,0,...)$,
Given a quasilinear preference, if f $x \succeq y - ae_1$, does it mean $x + ae_1 \succeq y$?
I know that $x + ae_1 \succ x$ but how do I compare $x+ae_1$ with $y$? Drawing a diagram makes me see it but I can't prove it rigorously.
EDIT: Included the definition for quasilinear preference.