theorem
  for F,G,H be Function
  st F,G are_fiberwise_equipotent & F,H are_fiberwise_equipotent holds
  G,H are_fiberwise_equipotent
proof
  let F,G,H be Function;
  assume that
A1: F,G are_fiberwise_equipotent and
A2: F,H are_fiberwise_equipotent;
  let x be object;
  thus card Coim(G,x) = card Coim(F,x) by A1
    .= card Coim(H,x) by A2;
end;
