(** And here is the corresponding proof for [seq'].  Note that the tactic [pclearbot] simplifies all hypotheses of the form [upaco{n} gf bot{n}] to [paco{n} gf bot{n}]. *)

Theorem seq'_cons : forall n1 n2 s1 s2 (SEQ : seq' (cons n1 s1) (cons n2 s2)),
n1 = n2 /\ seq' s1 s2.