
theorem P2:
for L being add-associative right_zeroed right_complementable
            right_unital right-distributive non empty doubleLoopStr,
    S being Subset of L st 0.L in S & 1.L in S
for a being Element of L holds a in S + a * S
proof
let L be add-associative right_zeroed right_complementable right_unital
         right-distributive non empty doubleLoopStr, S be Subset of L;
assume AS: 0.L in S & 1.L in S;
let a be Element of L;
a * 1.L in {a*i where i is Element of L : i in S} by AS;
then 0.L + a * 1.L in
            {c+b where c,b is Element of L : c in S & b in a*S} by AS;
hence thesis;
end;
