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

theorem
  0 < b & d < 0 & a*b < c/d implies c/b < a*d
proof
  assume that
A1: b>0 and
A2: d<0;
  assume a*b<c/d;
  then a*b*d>c by A2,Th78;
  then a*d*b>c;
  hence thesis by A1,Th83;
end;
