unfold equal in |- *.
split.
apply ana_transpose_incl_transpose_ana.
apply
inclusion_trans with (transpose (transpose (analysis_def (transpose h)))).
apply inclusion_transpose_inclusion.
apply ana_incl_transpose_ana_transpose.
generalize (transpose_invol (analysis_def (transpose h))).
unfold equal in |- *.
tauto.
Qed.

(** I(transpose h)=transpose I(h) *)
Lemma irr_transpose_transpose_irr :
forall h : hedge,
equal (irreducible (transpose h)) (transpose (irreducible h)).