reserve A for set, x,y,z for object,
  k for Element of NAT;
reserve n for Nat,
  x for object;
reserve V, C for set;

theorem Th26:
  for D being set, F being FinSequence of D* holds len FlattenSeq
  F = Sum Card F
proof
  let D be set;
  defpred P[FinSequence of D*] means len FlattenSeq $1 = Sum Card $1;
A1: now
    let F be FinSequence of D*, p be Element of D* such that
A2: P[F];
    len FlattenSeq (F^<*p*>) = len (FlattenSeq F ^ FlattenSeq <*p*>) by Th3
      .= (Sum Card F) + len FlattenSeq <*p*> by A2,FINSEQ_1:22
      .= (Sum Card F) + len p by Th1
      .= Sum ((Card F)^<*len p*>) by RVSUM_1:74
      .= Sum ((Card F) ^ Card <*p*>) by Th23
      .= Sum Card (F^<*p*>) by Th24;
    hence P[F^<*p*>];
  end;
A3: P[<*>(D*)] by RVSUM_1:72;
  thus for F be FinSequence of D* holds P[F] from FINSEQ_2:sch 2(A3, A1);
end;
