reserve W,X,Y,Z for set,
  f,g for Function,
  a,x,y,z for set;
reserve u,v for Element of Tarski-Class(X),
  A,B,C for Ordinal,
  L for Sequence;
reserve n for Element of omega;
reserve e,u for set;

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;
