reserve a,b,n for Element of NAT;

theorem
  for n being Element of NAT holds Lucas(n) + Lucas(n + 3) = 2*Lucas(n + 2)
proof
  let n be Element of NAT;
A1: 2*GenFib(2,1,n + 2)=2*Lucas(n+2) by Th38;
  GenFib(2,1,n)= Lucas(n) & GenFib(2,1,n + 3) =Lucas(n+3) by Th38;
  hence thesis by A1,Th39;
end;
