theorem Th4:
  (P * ASeq).n >= 0
proof
A1: n in NAT by ORDINAL1:def 12;
  dom (P * ASeq) = NAT by SEQ_1:1;
  then (P * ASeq).n = P.(ASeq.n) by A1,FUNCT_1:12;
  hence thesis by PROB_1:def 8;
end;
