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

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