induction ls; intuition; simpl in *.
unfold sumList; simpl.
eapply refl.
intuition.
eapply trans.
eapply refl.
eapply sumList_cons.
eapply trans.
2:{
eapply refl.
symmetry.
eapply sumList_cons.
}
eapply add_proper.
intuition.
eapply IHls; intuition.
Qed.

(* Specifications: *)
Lemma rel_seq :
forall (A B C : Set)(c : Comp A)(f1 : A -> Comp B)(f2 : A -> Comp C) rel x1 x2,
RatRel rel ->
(forall a, In a (getSupport c) -> rel (evalDist (f1 a) x1) (evalDist (f2 a) x2)) ->
rel (evalDist (a <-$ c; f1 a) x1) (evalDist (a <-$ c; f2 a) x2).