reserve a,b,c,d for Real;
reserve r,s for Real;

theorem
  a >= 1/2 implies 0 >= 1-2*a
proof
  assume a >= 1/2;
  then 2 * a >= 2 * (1/2) by Lm12;
  then 2 * a + 0 >= 1;
  hence thesis by Lm18;
end;
