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

theorem Th52:
  0-polytopes(p) is non empty
proof
  set d = dim(p);
  per cases;
  suppose
    d = 0;
    then 0-polytopes(p) = {p} by Def5;
    hence thesis;
  end;
  suppose
    d > 0;
    hence thesis by Th23;
  end;
end;
