theorem Th8: :: HILB10_3:8

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