simplify in H1.
elim H1 (S n1).assumption.apply le_n.apply le_n.
apply bijn_n_Sn.
-apply H ?.
+apply H.
apply permut_S_to_permut_transpose.
assumption.simplify.
rewrite > eqb_n_n (f (S n1)).simplify.reflexivity.
intro.
apply nat_case m ?.
intros.
-apply eq_map_iter_transpose_i_Si f H H1 g n i.
+apply eq_map_iter_transpose_i_Si ? H H1.
exact H3.
intros.
apply trans_eq ? ? (map_iter (S n) (\lambda m. g (transpose i (S(m1 + i)) m)) f a).
-apply H2 m1 ? g.
+apply H2.
simplify. apply le_n.
apply trans_le ? (S(S (m1+i))).
apply le_S.apply le_n.assumption.
apply trans_eq ? ? (map_iter (S n) (\lambda m. g
(transpose i (S(m1 + i)) (transpose (S(m1 + i)) (S(S(m1 + i))) m))) f a).
-apply H2 O ? ? (S(m1+i)) ?.
+apply H2 O ? ? (S(m1+i)).
simplify.apply le_S_S.apply le_O_n.
exact H3.
apply trans_eq ? ? (map_iter (S n) (\lambda m. g