Let $x_{1}$, $x_{2}$, $x_{3}$ three disctinct closed points of a curve $X$ over an algebraically closed field k.

Let G a connected reductive group and $\mathfrak{g}$ his Lie algebra. I fix a Borel $B_{x_{1}}$ and let $I_{x_{1}}$ the corresponding Iwahori.

For $l\in\mathfrak{g}(X-x_{3})\cap Lie(I_{x_{1}})$, is there a choice of a Borel $B_{x_{2}}$ such that there exists $u\in\mathfrak{g}(X-x_{3})\cap Lie(I_{x_{1}})$ and $v\in\mathfrak{g}(X-x_{3})\cap Lie(I_{x_{2}})$ such that:

$l+u=v$