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;

theorem Th41:
  for q being FinSubsequence holds card q = card Shift(q,i)
proof
  let q be FinSubsequence;
  ex ss being FinSubsequence st ( dom ss = dom q)&( rng ss =
  dom Shift(q,i))&( for k st k in dom q holds ss.k = i+k)&( ss is one-to-one)
  by Th40;
  then
A1: dom q, dom Shift(q,i) are_equipotent;
A2: card dom q = card q by CARD_1:62;
  card dom Shift(q,i) = card Shift(q,i) by CARD_1:62;
  hence thesis by A1,A2,CARD_1:5;
end;
