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Conditioned on the jump-chain states, the successive holding times are independent exponentials with rates $q_{i_0},\dots ,q_{i_n}$. Henceequals the integral over $s_0,\dots ,s_{n-1}\ge 0$ with ${\sum }_{r<n}{s}_r\le t$ ofThis simplex integral is unchanged by reversing the $n+1$ time portions and the rates attached to them. It is thereforeas required. This is holding-time reversal along a fixed CTMC jump path.