
theorem u5:
for R being Ring, S being Subring of R
for F being FinSequence of R
for G being FinSequence of S st F = G holds Product F = Product G
proof
let R be Ring, S be Subring of R; let F be FinSequence of R;
let G be FinSequence of S;
assume AS: F = G;
the carrier of S c= the carrier of R by C0SP1:def 3;
then In(Product G,R) = Product G by SUBSET_1:def 8;
hence thesis by AS,Th14;
end;
