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

theorem
  a <= 0 & b <= a & c <= 0 & d <= c implies a*c <= b*d
proof
  assume that
A1: 0 >= a and
A2: a >= b and
A3: 0 >= c and
A4: c >= d;
A5: -c <= -d by A4,Lm14;
  -a <= -b by A2,Lm14;
  then (-a)*(-c) <= (-b)*(-d) by A1,A3,A5,Th66;
  hence thesis;
end;
