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))).
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))).