reserve n for Nat,
  k for Integer;
reserve p for polyhedron,
  k for Integer,
  n for Nat;

theorem Th66:
  for x being Element of dim(p)-chain-space(p) holds
  x = 0.(dim(p)-chain-space(p)) or x = {p}
proof
  set V = dim(p)-chain-space(p);
  let x be Element of V;
  x in [#]V;
  then x in { 0.V, {p} } by Th65;
  hence thesis by TARSKI:def 2;
end;
