reserve a,b,n for Element of NAT;

theorem Th13:
  for n being Nat holds Lucas(n+1) + Lucas(n+2) = Lucas(n+3)
proof
  let n be Nat;
  Lucas(n+1) + Lucas(n+2) = Lucas((n+1+1)+1) by Th11
    .= Lucas(n+3);
  hence thesis;
end;
