theorem Th33: :: FIB_NUM3:33

for a, b being Element of NAT
for k being Nat holds ((GenFib (a,b,(k + 1))) + (GenFib (a,b,((k + 1) + 1)))) |^ 2 = (((GenFib (a,b,(k + 1))) |^ 2) + ((2 * (GenFib (a,b,(k + 1)))) * (GenFib (a,b,((k + 1) + 1))))) + ((GenFib (a,b,((k + 1) + 1))) |^ 2)