reserve a,b,c,x,y,z for object,X,Y,Z for set,
  n for Nat,
  i,j for Integer,
  r,r1,r2,r3,s for Real,
  c1,c2 for Complex,
  p for Point of TOP-REAL n;

theorem Th1:
  0 <= r & 0 <= s & r^2 = s^2 implies r = s
  proof
    assume that
A1: 0 <= r and
A2: 0 <= s and
A3: r^2 = s^2 and
A4: r <> s;
    -Q >= --s by A1,A3,A4,SQUARE_1:40;
    hence contradiction by A4,A2,A3,SQUARE_1:40;
  end;
