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

theorem Th12:
  <*2,1*> is odd Permutation of Seg 2
proof
  reconsider g = <*2,1*> as Permutation of Seg 2 by Lm2,MATRIX_1:def 12;
  not ex l be FinSequence of Group_of_Perm 2 st (len l) mod 2 = 0 & g =
Product l & for i st i in dom l ex q being Element of Permutations 2 st l.i = q
  & q is being_transposition by Lm1,MATRIX_7:11;
  hence thesis by MATRIX_1:def 15;
end;
