unfold le_h in |- *.
unfold inclusion in |- *.
intros.
induction  H0
as
[M
N
H0|
M
N
K
L
H0_1
HrecH0_1
H0_0
HrecH0_0|
M1
N1
M2
N2
H0_1
HrecH0_1
H0_0
HrecH0_0|
o
M
N
H0
HrecH0].
apply H; trivial.
apply SynEnc; trivial.
apply SynPair; trivial.
apply SynOp; trivial.
Qed.

(** g <= h iff g is included in S(h) *)
Theorem le_h_iff_incl_syn :
forall g h : hedge, le_h g h <-> inclusion g (synthesis h).