theorem Th18: :: HILB10_3:18

for n being Nat
for a, b, c 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)) + (c * (p . i3)) } is diophantine Subset of (n -xtuples_of NAT)