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

theorem Th38:
  for c,d being Element of k-chain-space(p), x being Element of (k
-1)-polytopes(p) holds Sum incidence-sequence(x,c+d) = (Sum incidence-sequence(
  x,c)) + (Sum incidence-sequence(x,d))
proof
  let c,d be Element of k-chain-space(p), x be Element of (k-1)-polytopes(p);
  Sum incidence-sequence(x,c+d) = Sum (incidence-sequence(x,c) +
  incidence-sequence(x,d)) by Th36
    .= (Sum incidence-sequence(x,c)) + (Sum incidence-sequence(x,d)) by Th37;
  hence thesis;
end;
