theorem Th55:
  for q being FinSubsequence holds dom Seq q = dom Seq Shift(q,i)
proof
  let q be FinSubsequence;
A1: len Seq q = card q by FINSEQ_3:158;
A2: len Seq Shift(q,i) = card Shift(q,i) by FINSEQ_3:158;
  thus dom Seq q = Seg len Seq q by FINSEQ_1:def 3
    .= dom Seq Shift(q,i) by Th41,A1,A2,FINSEQ_1:def 3;
end;
