Definition added (c: clause) {s s'': clauseset} (step: trans s s'') :=
(c \notin s) && (c \in s'').

Lemma deriv_plus_eq_removed
(c: clause) (s1 s2: clauseset) (step1: trans s1 s2) (trace: deriv s2 s1) :
removed c step1 -> adds c trace.