intros.
apply incl_syn_impl_le_h.
apply inclusion_trans with (transpose (synthesis h)).
apply inclusion_transpose_inclusion.
apply le_h_impl_incl_syn.
trivial.
generalize (synthesis_transpose_transpose_synthesis h).
unfold equal in |- *.
tauto.
Qed.

Lemma irr_le_h_left_consistent_impl_left_consistent_weak :
forall g h : hedge,
is_irreducible g ->
is_left_consistent h -> le_h g h -> weak_left_consistent g.