
theorem prod4:
for R being add-associative right_zeroed right_complementable
            distributive well-unital non empty doubleLoopStr,
    F being FinSequence of R
st ex i being Nat st i in dom F & F.i = 0.R holds Product F = 0.R
proof
let R be add-associative right_zeroed right_complementable
         distributive well-unital non empty doubleLoopStr;
let m be FinSequence of R;
given i being Nat such that
A: i in dom m & m.i = 0.R;
m/.i = m.i by A,PARTFUN1:def 6;
hence thesis by A,POLYNOM2:4;
end;
