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

theorem Th72:
  for x being Element of (dim(p)-1)-polytopes(p), c being Element
  of dim(p)-chain-space(p) st c = {p} holds incidence-sequence(x,c) = <*1.Z_2*>
proof
  let x be Element of (dim(p)-1)-polytopes(p), c be Element of dim(p)
  -chain-space(p) such that
A1: c = {p};
  set iseq = incidence-sequence(x,c);
A2: iseq.1 = 1.Z_2
  proof
    reconsider egy = 1 as Nat;
    set z = egy-th-polytope(p,dim(p));
    egy <= num-polytopes(p,dim(p)) by Th29;
    then
A3: iseq.egy = (c@z)*(incidence-value(x,z)) by Def16;
    c@z = 1.Z_2 & incidence-value(x,z) = 1.Z_2 by A1,Th69,Th70,Th71;
    hence thesis by A3;
  end;
  num-polytopes(p,dim(p))= 1 by Th29;
  then len iseq = 1 by Def16;
  hence thesis by A2,FINSEQ_1:40;
end;
