Notation multi_fstep := (@multi_step Sem FineDilMem _ DryHybridMachine.DryHybridMachineSig).

Lemma maximal_competing:
forall i j tr evi evj
(Hij: i < j)
(Hi: nth_error tr i = Some evi)
(Hj: nth_error tr j = Some evj)
(Hcompetes: competes evi evj),
exists k evk, i <= k < j /\
nth_error tr k = Some evk /\
competes evk evj /\
(forall k' evk', k < k' < j ->
nth_error tr k' = Some evk' ->
~ competes evk' evj).