theorem :: BINOM:27

for C, D being non empty set
for b being Element of D
for F being Function of [:D,C:],D ex g being Function of [:C,NAT:],D st
for a being Element of C holds
( g . (a,0) = b & ( for n being Element of NAT holds g . (a,(n + 1)) = F . ((g . (a,n)),a) ) ) by Lm2;