(* *)
(**************************************************************************)
-set "baseuri" "cic:/matita/nat/permutation".
-
include "nat/compare.ma".
include "nat/sigma_and_pi.ma".
apply (trans_eq ? ? (map_iter_i (S k) (\lambda m. g
(transpose i (S(m1 + i)) (transpose (S(m1 + i)) (S(S(m1 + i))) m))) f n)).
apply (H2 O ? ? (S(m1+i))).
-unfold lt.apply le_S_S.apply le_O_n.
+unfold lt.apply le_S_S.apply le_O_n.id.
apply (trans_le ? i).assumption.
change with (i \le (S m1)+i).apply le_plus_n.
exact H4.