
theorem
  for A, B, C, D being category st A, B are_opposite & C, D are_opposite
  holds A, C are_isomorphic implies B, D are_isomorphic
proof
  let A, B, C, D be category;
  assume that
A1: A, B are_opposite and
A2: C, D are_opposite;
  A, C are_isomorphic implies B, C are_anti-isomorphic by A1,Th17;
  hence thesis by A2,Th17;
end;
