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

theorem
  a <= b iff c-b <= c-a
proof
  hereby
    assume a <= b;
    then -b <= -a by Lm14;
    then c+-b <= c+-a by Lm5;
    hence c-b <= c-a;
  end;
  assume c-b <= c-a;
  then c-b-c <= c-a-c by Th9;
  then -b <= -a;
  hence thesis by Lm15;
end;
