
theorem Th17:
  for n, m being Ordinal, b being bag of n st m in n holds b|m is bag of m
proof
  let n, m be Ordinal, b be bag of n;
  assume m in n;
  then
A1: m c= n by ORDINAL1:def 2;
  dom b = n by PARTFUN1:def 2;
  then dom (b|m) = m by A1,RELAT_1:62;
  hence thesis by PARTFUN1:def 2;
end;
