unfold weak_left_consistent in |- *.
unfold is_left_consistent in |- *.
tauto.
Qed.

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