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

theorem Th76:
  dim ((dim(p)-1)-bounding-chain-space(p)) = 1
proof
  set d = dim(p);
  set T = d-boundary(p);
  set U = d-chain-space(p);
  set V = (d-1)-bounding-chain-space(p);
A1: card [#]V = card (T .: [#]U) by RANKNULL:def 2
    .= card (rng T) by RELSET_1:22;
A2: card (dom T) = card [#]U by RANKNULL:7
    .= 2 by Th61;
  T is one-to-one by Th75;
  then card [#]V = 2 by A1,A2,CARD_1:70;
  hence thesis by RANKNULL:6;
end;
