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

theorem Th85:
  dim(p) = 0 implies p is eulerian
proof
  set d = dim(p);
  set apcs = alternating-proper-f-vector(p);
  assume
A1: d = 0;
  then (-1)|^(d+1) = -1;
  then
A2: 1 + (-1)|^(d+1) = 0;
  len apcs = 0 by A1,Def27;
  then apcs = <*>INT;
  hence thesis by A2,GR_CY_1:3;
end;
