theorem
  for i,j being Nat holds i <> j implies dl.(R,i) <> dl.(R,j)
proof
  let i,j be Nat;
  assume
A1: i <> j;
  dl.(R,j) = [1,j] & dl.(R,i) = [1,i] by Th1;
  hence thesis by A1,XTUPLE_0:1;
end;
