
theorem Th6:
for n be non zero Nat, X be non-empty (n+1)-element FinSequence holds
  CarProduct X = [: CarProduct SubFin(X,n),ElmFin(X,n+1) :]
proof
    let n be non zero Nat, X be non-empty (n+1)-element FinSequence;
A1: n < n+1 by NAT_1:13; then
A2: CarProduct X = [: (ProdFinSeq X).n,X.(n+1) :] by Def3;
    CarProduct SubFin(X,n) = (ProdFinSeq X).n by A1,Th4;
    hence thesis by A2,Def1;
end;
