unfold is_irreducible in |- *.
intros.
apply equal_trans with (transpose (irreducible h)).
apply equal_transpose_equal.
trivial.
apply equal_sym.
apply irr_transpose_transpose_irr.
Qed.

(** if g <= h, g is irreducible and h is consistent then g is consistent *)
Theorem irr_le_h_consistent_impl_consistent :
forall g h : hedge,
is_irreducible g -> is_consistent h -> le_h g h -> is_consistent g.