
theorem Th10:
for m,n,k be non zero Nat, X be non-empty m-element FinSequence st
  k <= n & n <= m holds (Pt2FinSeq X).k = (Pt2FinSeq SubFin(X,n)).k
proof
    let m,n,k be non zero Nat, X be non-empty m-element FinSequence;
    assume
A1: k <= n & n <= m;
A2: len X = m by FINSEQ_3:153;
    SubFin(X,m) = X|m by MEASUR13:def 5; then
    SubFin(X,m) = X by A2,FINSEQ_1:58;
    hence (Pt2FinSeq X).k = (Pt2FinSeq SubFin(X,n)).k by A1,Th9;
end;
