reserve
  X,x,y,z for set,
  k,n,m for Nat ,
  f for Function,
  p,q,r for FinSequence of NAT;
reserve p1,p2,p3 for FinSequence;
reserve T,T1 for Tree;
reserve fT,fT1 for finite Tree;
reserve t for Element of T;
reserve w for FinSequence;

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;
