theorem Th18:
  r1*r2 <= r3 implies r1 <= sqrt r3 or r2 <= sqrt r3
   proof
     assume that
A1:  r1*r2 <= r3 and
A2:  not (r1 <= sqrt r3 or r2 <= sqrt r3);
     sqrt r3 >= 0 by SQUARE_1:def 2; then
     (sqrt r3)^2 < r1 * r2 by A2,XREAL_1:96;
     hence contradiction by A1,SQUARE_1:def 2;
   end;
