 reserve n,i,k,m for Nat;
 reserve p for Prime;

theorem
  for m,n being non zero Nat st
    SquarefreePart n = SquarefreePart m &
      TSqF m = TSqF n holds
        m = n
  proof
    let m,n be non zero Nat;
    assume
A1: SquarefreePart n = SquarefreePart m &
      TSqF m = TSqF n;
     m = (SquarefreePart m) * (SqF m) ^2 by Canonical
       .= (SquarefreePart m) * ((SqF m) |^2) by NEWTON:81
       .= (SquarefreePart n) * TSqF n by A1,Cosik
       .= (SquarefreePart n) * (SqF n) |^2 by Cosik
       .= (SquarefreePart n) * (SqF n) ^2 by NEWTON:81
       .= n by Canonical;
     hence thesis;
  end;
