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

theorem Th22:
  -1 < k & k < dim(p) implies k + 1 is Nat & 1 <= k + 1 & k + 1 <= dim(p)
proof
A1: -1 + 1 = 0;
  assume -1 < k;
  then
A2: 0 < k + 1 by A1,XREAL_1:6;
  then reconsider n = k + 1 as Element of NAT by INT_1:3;
A3: n is Nat & 0 + 1 = 1;
  assume k < dim(p);
  hence thesis by A2,A3,INT_1:7;
end;
