reserve a,a1,a2,b,c,d for Ordinal,
  n,m,k for Nat,
  x,y,z,t,X,Y,Z for set;
reserve f,g for Function;
reserve A,B,C for array;
reserve O for connected non empty Poset;
reserve R,Q for array of O;
reserve T for non empty array of O;
reserve p,q,r,s for Element of dom T;

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;
