reserve x for set,
  i,j,k,n for Nat,
  K for Field;
reserve a,b,c,d for Element of K;
reserve D for non empty set;

theorem Th42:
  <*3,2,1*> is odd Permutation of Seg 3
proof
  reconsider f = <*3,2,1*> as Permutation of Seg 3 by Th27,MATRIX_1:def 12;
  not ex l be FinSequence of Group_of_Perm 3 st (len l) mod 2 = 0 & f =
Product l & for i st i in dom l ex q being Element of Permutations 3 st l.i = q
  & q is being_transposition by Lm3,Lm7,Lm17;
  hence thesis by MATRIX_1:def 15;
end;
