theorem Th37: :: HILB10_4:37

for n being Nat
for i1, i2, i3 being Element of n st n <> 0 holds
{ p where p is b₁ -element XFinSequence of NAT : ( p . i3 = Product (((p . i2) + 1) + (- (idseq (p . i1)))) & p . i2 > p . i1 ) } is diophantine Subset of (n -xtuples_of NAT)