theorem
  for p being FinSequence holds card ProperPrefixes p = len p
proof
  let p be FinSequence;
A1: dom p = Seg len p by FINSEQ_1:def 3;
A2: ProperPrefixes p,dom p are_equipotent by Th33;
 card dom p = card len p by A1,FINSEQ_1:55;
  hence thesis by A2,CARD_1:5;
end;
