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

theorem Tk1:
  a-b <= c-d implies a-c <= b-d
proof
  assume a-b <= c-d;
  then a-b+b <= c-d+b by Lm5;
  then a-c <= c-d+b-c by Th9;
  hence thesis;
end;
