reserve m,j,p,q,n,l for Element of NAT;
reserve e1,e2 for ExtReal;
reserve i for Nat,
        k,k1,k2,j1 for Element of NAT,
        x,x1,x2,y for set;
reserve p1,p2 for FinSequence;
reserve q,q1,q2,q3,q4 for FinSubsequence,
        p1,p2 for FinSequence;

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;
