
theorem Th2:
  for n being Ordinal, T being admissible TermOrder of n, b1,b2,b3
  being bag of n holds b1 <= b2,T implies b1 + b3 <= b2 + b3,T
proof
  let n be Ordinal, T be admissible TermOrder of n, b1,b2,b3 be bag of n;
  assume b1 <= b2,T;
  then [b1,b2] in T by TERMORD:def 2;
  then [b1+b3,b2+b3] in T by BAGORDER:def 5;
  hence thesis by TERMORD:def 2;
end;
