
theorem P1:
for L being add-associative right_zeroed right_complementable
            right-distributive non empty doubleLoopStr,
    S being Subset of L st 0.L in S
for a being Element of L holds S c= S + a * S
proof
let L be add-associative right_zeroed right_complementable
         right-distributive non empty doubleLoopStr,
    S be Subset of L;
assume A: 0.L in S;
let a be Element of L;
a * 0.L in {a*i where i is Element of L : i in S} by A;
hence thesis by P0;
end;
