(* predicate a is closed under "edge" relation e *)
Definition closed {T: finType} (e: rel T) (a: pred T) :=
  forall x y : T, e x y -> a x -> a y.

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