
theorem Th4:
for m,n be non zero Nat, X be non-empty m-element FinSequence
 st n <= m holds
  (ProdFinSeq X).n = (ProdFinSeq SubFin(X,n)).n
proof
    let m,n be non zero Nat, X be non-empty m-element FinSequence;
    assume
A1:  n <= m;

    len X = m by FINSEQ_3:153; then
    X = X|m by FINSEQ_1:58; then
    X = SubFin(X,m) by Def5;
    hence (ProdFinSeq X).n = (ProdFinSeq SubFin(X,n)).n by A1,Th3;
end;
