let a, b, n be Element of NAT ; (GenFib (a,b,n)) + (GenFib (a,b,(n + 4))) = 3 * (GenFib (a,b,(n + 2)))
(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
(GenFib (a,b,n)) + (GenFib (a,b,(n + 4))) = 3 * (GenFib (a,b,(n + 2)))
; verum