“…The inductive s m a l l s t e p s e m l defines a local reduction, that is execution of a communication routine or execution of a sequential control flow. We give here an interesting part of its Coq's definition: ( * I f t h e n e l s e s e m a n t i c s * ) | s m a l l s t e p s e m i f e l s e t r u e : ∀ e i 1 i 2 l 1 l 1 ' , ∀i · · · ni, Ei, Ci, Ri, skip · · · ⇒ · · · ni, Ei, Ci, Ri, skip · · · ∀i · · · ni, Ei, Ci, Ri, ci · · · ⇀ · · · n ′ i , We previously defined [11] (also in Coq) a natural semantics of the same PUB subset. This semantics has been proved (also using Coq) to be deterministic and we thus have the following lemmas by induction/co-induction:…”