let i be Nat; for q being FinSubsequence holds card q = card (Shift (q,i))
let q be FinSubsequence; card q = card (Shift (q,i))
ex ss being FinSubsequence st
( dom ss = dom q & rng ss = dom (Shift (q,i)) & ( for k being Element of NAT 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
card q = card (Shift (q,i))
by A1, A2, CARD_1:5; verum