theorem Th101:
  x <= y & z <= 0 implies y*z <= x*z
proof
  assume x <= y & z <= 0;
  then
A1: x*(-z) <= y*(-z) by Th71;
  -x*z = x*(-z) & -y*z = y*(-z) by Th92;
  hence thesis by A1,Th38;
end;
