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

theorem
  b < 0 & d < 0 & a*d < c*b implies a/b < c/d
proof
  assume that
A1: b<0 and
A2: d<0 and
A3: a*d<c*b;
  a*d/b>c by A1,A3,Th84;
  then a/b*d>c by XCMPLX_1:74;
  hence thesis by A2,Th84;
end;
