Definition removes (c: clause) (s s': clauseset) (trace: deriv s s') :=
[&& c \in s & c \notin s'].

(* Specifications: *)
Lemma deriv_plus_eq_added
(c: clause) (s1 s2: clauseset) (step1: trans s1 s2) (trace: deriv s2 s1) :
added c step1 -> removes c trace.