theorem Thm31: :: SRINGS_4:32

for n being non zero Nat
for Xn being non-empty b₁ -element FinSequence
for X1 being non-empty 1 -element FinSequence
for Sn being SemiringFamily of Xn
for S1 being SemiringFamily of X1 st SemiringProduct Sn is semiring_of_sets of (product Xn) & SemiringProduct S1 is semiring_of_sets of (product X1) holds
SemiringProduct (Sn ^ S1) is semiring_of_sets of (product (Xn ^ X1))