theorem Th55:
  the carrier of bool G = bool the carrier of G & the multF of
  bool G = (the multF of G).:^2
proof
  bool G = multLoopStr(#bool carr(G), op(G).:^2,{the_unity_wrt op(G)}#) or
  bool G = multMagma(#bool the carrier of G, op(G).:^2#) by Def9;
  hence thesis;
end;
