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

theorem Th71:
  for x being Element of (dim(p)-1)-polytopes(p), c being Element
  of dim(p)-polytopes(p) st c = p holds incidence-value(x,c) = 1.Z_2
proof
  set f = [:(dim(p)-1)-polytopes(p),{p}:] --> 1.Z_2;
  let x be Element of (dim(p)-1)-polytopes(p), c be Element of dim(p)
  -polytopes(p);
  assume c = p;
  then dom f = [:(dim(p)-1)-polytopes(p),{p}:] & c in {p} by TARSKI:def 1;
  then [x,c] in dom f by ZFMISC_1:87;
  then f.(x,c) in rng f by FUNCT_1:3;
  then f.(x,c) in {1.Z_2} by FUNCOP_1:8;
  then
A1: f.(x,c) = 1.Z_2 by TARSKI:def 1;
  eta(p,dim(p)) = f by Def6;
  hence thesis by A1,Def13;
end;
