unfold equal in |- *.
unfold inclusion in |- *.
intros.
split.
unfold transpose in |- *.
intros.
induction  H
as
[M
N
H|
M
N
K
L
H1
HrecH1
H0
HrecH0|
M1
N1
M2
N2
H1
HrecH1
H0
HrecH0|
o
M
N
H
HrecH].
apply SynInc; trivial.
apply SynEnc; trivial.
apply SynPair; trivial.
apply SynOp; trivial.
unfold transpose in |- *.
intros.
induction  H
as
[M
N
H|
M
N
K
L
H1
HrecH1
H0
HrecH0|
M1
N1
M2
N2
H1
HrecH1
H0
HrecH0|
o
M
N
H
HrecH].
apply SynInc; trivial.
apply SynEnc; trivial.
apply SynPair; trivial.
apply SynOp; trivial.
Qed.

(** if g <= h then (transpose g) <= (transpose h) *)
Lemma le_h_transpose_le_h :
forall g h : hedge, le_h g h -> le_h (transpose g) (transpose h).