theorem Th79:
  for A being 0-based finite array of X st A <> {} holds last A in X
  proof
    let A be 0-based finite array of X;
    assume A <> {}; then
    consider n such that
A1: dom A = n+1 by NAT_1:6;
    Segm(n+1) = succ Segm n by NAT_1:38; then
    n in dom A & union dom A = n by A1,ORDINAL1:6,ORDINAL2:2;
    hence last A in X by FUNCT_1:102;
  end;
