reserve X,x for set;

theorem Th2:
  for x,y being set, f,g being FinSequence st <*x*>^f = <*y*>^g holds f = g
proof
  let x,y be set, f,g be FinSequence;
  assume
A1: <*x*>^f = <*y*>^g;
  then x = (<*y*>^g).1 by FINSEQ_1:41
    .= y by FINSEQ_1:41;
  hence thesis by A1,FINSEQ_1:33;
end;
