reserve x,y for object,
        i,j,k,m,n for Nat;

theorem Th14:
  for p1,p2 be one-to-one a_partition of n st
    Euler_transformation p1 = Euler_transformation p2
  holds p1 = p2
proof
  let p1,p2 be one-to-one a_partition of n;
  assume
  Euler_transformation p1 = Euler_transformation p2;
  then A1:rng p1 = rng p2 by Lm4;
  then p1 is FinSequence of REAL & p2 is FinSequence of REAL
    by FINSEQ_1:def 4;
  hence thesis by INTEGRA3:6,A1;
end;
