theorem
  for p being FinSubsequence holds card p = len Seq p
proof
  let p be FinSubsequence;
A2: Seq p = p*(Sgm dom p) by FINSEQ_1:def 15;
A3: rng Sgm dom p = dom p by FINSEQ_1:50;
  then
A4: dom Seq p = dom Sgm dom p by A2,RELAT_1:27;
  rng Sgm dom p, dom Sgm dom p are_equipotent by WELLORD2:def 4;
  then
A5: card dom p = card dom Sgm dom p by A3,CARD_1:5;
  card dom p = card p by CARD_1:62;
  hence thesis by A4,A5,CARD_1:62;
end;
