unfold irreducible in |- *.
intro.
apply equal_trans with (reduce (transpose (analysis_def h))).
apply equal_reduce_equal.
apply ana_transpose_transpose_ana.
apply reduce_transpose_transpose_reduce.
Qed.

(** if h is irreducible then (transpose h) is irreducible *)
Lemma is_irreducible_transpose_is_irreducible :
forall h : hedge, is_irreducible h -> is_irreducible (transpose h).