theorem Th9: :: HILB10_3:9

for n being Nat
for a, b being Integer
for i1, i2, i3 being Element of n holds { p where p is b₁ -element XFinSequence of NAT : a * (p . i1) = (b * (p . i2)) * (p . i3) } is diophantine Subset of (n -xtuples_of NAT)