Sheaf Quantization of Legendrian Isotopy

Let $\{\Lambda^\infty_t\}$ be an isotopy of Legendrians (possibly singular) in a unit cosphere bundle $S^*M$. Let $Sh(M, \Lambda^\infty_t)$ be the differential graded (dg) derived category of constructible sheaves on $M$ with singular support at infinity contained in $\Lambda^\infty_t$. We prove that if the isotopy of Legendrians embeds into an isotopy of Weinstein hypersurfaces, then the categories $Sh(M, \Lambda^\infty_t)$ are invariant.