
theorem Th3:
  for n being Ordinal, T being TermOrder of n, b1,b2,b3 being bag
  of n holds b1 <= b2,T & b2 < b3,T implies b1 < b3,T
proof
  let n be Ordinal, T be TermOrder of n, b1,b2,b3 be bag of n;
  assume that
A1: b1 <= b2,T and
A2: b2 < b3,T;
A3: b2 <= b3,T by A2,TERMORD:def 3;
  then
A4: b1 <= b3,T by A1,TERMORD:8;
  b2 <> b3 by A2,TERMORD:def 3;
  then b1 <> b3 by A1,A3,TERMORD:7;
  hence thesis by A4,TERMORD:def 3;
end;
