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

theorem Th67:
  for x,y being Element of dim(p)-chain-space(p) st x <> y holds
  x = 0.(dim(p)-chain-space(p)) or y = 0.(dim(p)-chain-space(p))
proof
  set V = dim(p)-chain-space(p);
  let x,y be Element of V such that
A1: x <> y;
  assume x <> 0.V;
  then
A2: x = {p} by Th66;
  assume y <> 0.V;
  hence contradiction by A1,A2,Th66;
end;
