Definition seqn := seqn_rec id.(* Sequence catenation "cat".                                               *)

Fixpoint cat s1 s2 := if s1 is x :: s1' then x :: s1' ++ s2 else s2
where "s1 ++ s2" := (cat s1 s2) : seq_scope.(* Sequence catenation "cat".                                               *)

Fixpoint cat s1 s2 := if s1 is x :: s1' then x :: s1' ++ s2 else s2
where "s1 ++ s2" := (cat s1 s2) : seq_scope.

Lemma cat_nseq n x s : nseq n x ++ s = ncons n x s.