Sheaf quantization of Legendrian isotopy

Let $\{\Lambda ^\infty _t\}$ be an isotopy of Legendrians (possibly singular) in a unit cosphere bundle $S^*M$ that arise as slices singular Legendrian $\Lambda _I^\infty \subset S^*M \times T^*I$ . $\mathcal {C}_t = Sh(M, \Lambda _t)$ the differential graded derived category constructible sheaves on $M$ with support at infinity contained _t$ We prove if embeds into Liouville hypersurfaces, then family categories $\{\mathcal {C}_t\}$ is constant $t$