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 Th38:
  for p being Permutation of Seg 3 st p is being_transposition
  holds p = <*2,1,3*> or p = <*1,3,2*> or p = <*3,2,1*>
proof
  let p be Permutation of Seg 3;
  p in Permutations 3 by MATRIX_1:def 12;
  then
A1: p=<*1,2,3*> or p=<*2,1,3*> or p=<*2,3,1*> or p=<*3,1,2*> or p=<*3,2,1*>
  or p=<*1,3,2*> by Th19,ENUMSET1:def 4;
  assume p is being_transposition;
  hence thesis by A1,Th33,Th34,Th35,FINSEQ_2:53;
end;
