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

theorem
  0 < b & 0 < d & 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,Th83;
  then a/b*d<c by XCMPLX_1:74;
  hence thesis by A2,Th81;
end;
