 reserve K,F,E for Field,
         R,S for Ring;

theorem Th2:
   for S being Subring of R, F being FinSequence of R, G being FinSequence of S
   st F = G holds Sum F = Sum G
   proof
     let S be Subring of R, F be FinSequence of R, G be FinSequence of S;
     assume
A1:  F = G;
     the carrier of S c= the carrier of R by C0SP1:def 3; then
     In(Sum G,R) = Sum G by SUBSET_1:def 8;
     hence thesis by A1,ALGNUM_1:10;
   end;
