$\succsim$ is a countinuous and convex weak order.
$x,y,a$ are vectors in $\mathbb R^n$
We say $a\geq0$ if all directions of the vector $a$ is greater or equal to zero.
We want to prove (or disprove by counterexample) that:
Suppose $x\sim y$ implies $x+a\sim y+a$ for any $a\geq0$ and $x,y\in\mathbb R^n$,
Then the preference is linear.
One definition of linear preference is that $x\sim y$ implies $x+a\sim y+a$ for any $x,y,a$.