
theorem Th11:
  for n being Ordinal, T being TermOrder of n, b1,b2 being bag of
  n holds min(b1,b2,T) = b1 or min(b1,b2,T) = b2
proof
  let n be Ordinal, T be TermOrder of n, b1,b2 be bag of n;
  assume
A1: min(b1,b2,T) <> b1;
  now
    per cases by A1,Def4;
    case
      not b1 <= b2,T;
      hence thesis by Def4;
    end;
    case
      b1 = b2;
      then b1 <= b2,T by Lm2;
      hence contradiction by A1,Def4;
    end;
  end;
  hence thesis;
end;
