Upper estimate conjecture for the coderivative of a differential inclusion's reachable map

Let $F$ define a differential inclusion on $[0,T]$ and let $R:\mathbb{R}^{n}\rightrightarrows\mathbb{R}^{n}$ be the reachable map, with reference points $(\bar{x},\bar{y})$. For the feasible-path set

$$\mathcal{F}(\bar{x},\bar{y})=\{x(\cdot)\in AC([0,T],\mathbb{R}^{n}):x(0)=\bar{x},\ x(T)=\bar{y},\ x^{\prime}(t)\in F(t,x(t))\text{ for almost every }t\in[0,T]\},$$

consider absolutely continuous adjoint paths $p(\cdot)$. Upper estimate of the coderivative of the reachable map. The convexified coderivative satisfies

$$\overline{\operatorname{co}}D^{*}R(\bar{x}\mid\bar{y})(v)\subset\left\{u:\begin{array}{l}\exists x(\cdot)\in\mathcal{F}(\bar{x},\bar{y}),\ p(\cdot)\in AC([0,T],\mathbb{R}^{n})\text{ such that}\\ p^{\prime}(t)\in-\overline{\operatorname{co}}D_{x}^{*}F\bigl(t,x(t)\mid x^{\prime}(t)\bigr)\bigl(p(t)\bigr),\\ p(0)=u\text{ and }p(T)=v\end{array}\right\}$$

for all $v\in\mathbb{R}^{n}$. This conjectural estimate would give a continuous-time upper bound for the coderivative of the reachable map in terms of feasible trajectories and their adjoint differential inclusions; the supplied text does not establish its resolution.