match eqb n j with
[ true \Rightarrow i
| false \Rightarrow n]].
-
+
+notation < "(❲i↹j❳)n"
+ right associative with precedence 71
+for @{ 'transposition $i $j $n}.
+
+notation < "(❲i \atop j❳)n"
+ right associative with precedence 71
+for @{ 'transposition $i $j $n}.
+
+interpretation "natural transposition" 'transposition i j n =
+ (cic:/matita/nat/permutation/transpose.con i j n).
+
lemma transpose_i_j_i: \forall i,j:nat. transpose i j i = j.
intros.unfold transpose.
rewrite > (eqb_n_n i).simplify. reflexivity.