reserve i,j,k,n,m for Nat,
        b,b1,b2 for bag of n;

theorem Th9:
  for L being non empty ZeroStr,
    p being Series of n,L, b being bag of n+1 st b.n = 0 holds
  b in Support (p extended_by_0) iff (0,n)-cut b in Support p
proof
  let L be non empty ZeroStr,
  p be Series of n,L, b be bag of n+1;
  assume
A1: b.n = 0;
  A2: n-'0 = n by NAT_D:40;
  b = ((0,n)-cut b) bag_extend 0 by A1,Th4;
  hence thesis by Th8,A2;
end;
