theorem
  for E being non empty set, p,q being FinSequence of E st k in dom q
  holds (p ^ q)/.(len p + k) = q/.k
proof
  let E be non empty set, p,q be FinSequence of E;
  assume
A1: k in dom q;
  then len p + k in dom(p ^ q) by FINSEQ_1:28;
  hence (p ^ q)/.(len p + k) = (p ^ q).(len p + k) by PARTFUN1:def 6
    .= q.k by A1,FINSEQ_1:def 7
    .= q/.k by A1,PARTFUN1:def 6;
end;
