reserve p,q,r for FinSequence;
reserve u,v,x,y,y1,y2,z for object, A,D,X,Y for set;
reserve i,j,k,l,m,n for Nat;
reserve J for Nat;
reserve n for Nat;
reserve x,y,y1,y2,z,a,b for object, X,Y,Z,V1,V2 for set,
  f,g,h,h9,f1,f2 for Function,
  i for Nat,
  P for Permutation of X,
  D,D1,D2,D3 for non empty set,
  d1 for Element of D1,
  d2 for Element of D2,
  d3 for Element of D3;
reserve n for Nat;

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;
