reserve a,b,n for Element of NAT;

theorem Th39:
  for a,b,n being Element of NAT holds GenFib(a,b,n) + GenFib(a,b,
  n + 3) = 2*GenFib(a,b,n + 2)
proof
  let a,b,n be Element of NAT;
  GenFib(a,b,n)+GenFib(a,b,n+3)= GenFib(a,b,n)+(GenFib(a,b,n+1)+GenFib(a,b
  ,n+2)) by Th35
    .= GenFib(a,b,n) + GenFib(a,b,n+1) + GenFib(a,b,n+2)
    .= GenFib(a,b,n+2)+ GenFib(a,b,n+2) by Th34
    .= 2*GenFib(a,b,n + 2);
  hence thesis;
end;
