reserve r1,r2,r3 for non negative Real;
reserve n,m1 for Nat;
reserve s for Real;
reserve cn,cd,i1,j1 for Integer;
reserve r for irrational Real;
reserve q for Rational;

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;
