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

theorem Th77:
  p is simply-connected implies dim ((dim(p)-1)-circuit-space(p)) = 1
proof
  set d = dim(p);
  set U = (d-1)-bounding-chain-space(p);
  set V = (d-1)-circuit-space(p);
  assume p is simply-connected;
  then U = V by Th48;
  hence thesis by Th76;
end;
