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