
theorem
for m,n be non zero Nat, X be non-empty m-element FinSequence
 st n < m holds
 (ProdFinSeq SubFin(X,n+1)).(n+1)
  = [: (ProdFinSeq SubFin(X,n)).n, ElmFin(X,n+1) :]
proof
    let m,n be non zero Nat, X be non-empty m-element FinSequence;
    assume A1: n < m;
    CarProduct SubFin(X,n+1) = (ProdFinSeq SubFin(X,n+1)).(n+1); then
    (ProdFinSeq SubFin(X,n+1)).(n+1)
     = [: CarProduct SubFin(X,n),ElmFin(X,n+1) :] by A1,Th9;
    hence
 (ProdFinSeq SubFin(X,n+1)).(n+1)
  = [: (ProdFinSeq SubFin(X,n)).n, ElmFin(X,n+1) :];
end;
