let a be Element of (Group_of_Perm 3); ( a = <*2,3,1*> implies a " = <*3,1,2*> )
reconsider a1 = a as Element of Permutations 3 by MATRIX_1:def 13;
assume
a = <*2,3,1*>
; a " = <*3,1,2*>
then
a1 " = <*3,1,2*>
by Th28;
hence
a " = <*3,1,2*>
by MATRIX_7:27; verum