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

theorem
  for n1, n2 being Nat st n1 ^2 = n2 ^2 holds
    n1 = n2
  proof
    let n1, n2 be Nat;
    assume n1 ^2 = n2 ^2; then
    n1 = sqrt (n2 ^2) by SQUARE_1:22;
    hence thesis by SQUARE_1:22;
  end;
