theorem :: HILB10_4:36

for n being Nat
for i1, i2, i3 being Element of n holds { p where p is b₁ -element XFinSequence of NAT : p . i3 = Product (1 + (((p . i1) !) * (idseq (1 + (p . i2))))) } is diophantine Subset of (n -xtuples_of NAT)