reserve a,b,n for Element of NAT;

theorem
  for a,b,n being Element of NAT holds GenFib(a,b,n) + GenFib(a,b,n + 4)
  = 3*GenFib(a,b,n + 2)
proof
  let a,b,n be Element of NAT;
  GenFib(a,b,n) + GenFib(a,b,n + 4) = GenFib(a,b,n)+(GenFib(a,b,n+2) +
  GenFib(a,b,n+3)) by Th36
    .=GenFib(a,b,n) + GenFib(a,b,n+2) + GenFib(a,b,n+3)
    .=GenFib(a,b,n) + GenFib(a,b,n+2) + (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) + GenFib(a,b,n+2) + GenFib(a,b,n+2) by Th34
    .= 3*GenFib(a,b,n + 2);
  hence thesis;
end;
