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

theorem Th9:
  a <= b iff a-c <= b-c
proof
  thus a <= b implies a-c <= b-c by Lm7;
  assume a-c <= b-c;
  then a+ (-c) + c <= b+ (-c)+c by Lm5;
  hence thesis;
end;
