### You Can Only Cross The Same River Once

The formula $a \otimes b \multimap a$ is strange. For example, here’s a small proof fragment, where $C$ is an arbitrary goal formula:

$\frac{\frac{\overline{a \vdash a} \qquad \overline{b \vdash b}}{a,b \vdash a \otimes b} \qquad \Delta, a \vdash C}{\Delta, a,b,a \otimes b \multimap a \vdash C}$

Is the $a$ in the right premise of the loli-left rule the same as the one we started with in the conclusion?