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

theorem Th53:
  card [#]((-1)-chain-space(p)) = 2
proof
  (-1)-polytopes(p) = {{}} by Def5;
  then card ((-1)-polytopes(p)) = 1 by CARD_1:30;
  then card [#]((-1)-chain-space(p)) = exp(2,1) by BSPACE:42
    .= 2 by CARD_2:27;
  hence thesis;
end;
