(* *)
(**************************************************************************)
-set "baseuri" "cic:/matita/nat/permutation".
-
include "nat/compare.ma".
include "nat/sigma_and_pi.ma".
[ true \Rightarrow i
| false \Rightarrow n]].
-notation < "(❲i↹j❳)n"
- right associative with precedence 71
+notation < "(❲i↹j❳)n" with precedence 71
for @{ 'transposition $i $j $n}.
-notation < "(❲i \atop j❳)n"
- right associative with precedence 71
+notation < "(❲i \atop j❳)n" with precedence 71
for @{ 'transposition $i $j $n}.
interpretation "natural transposition" 'transposition i j n =
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.