
theorem hom1:
for R being add-associative right_zeroed right_complementable
            non empty doubleLoopStr,
    S being add-associative right_zeroed right_complementable
            right-distributive non empty doubleLoopStr,
    f being additive Function of R,S
holds f.(0.R) = 0.S
proof
let R be add-associative right_zeroed right_complementable
         non empty doubleLoopStr,
    S be add-associative right_zeroed right_complementable
         right-distributive non empty doubleLoopStr,
    f be additive Function of R,S;
f.(0.R) = f.(0.R + 0.R)
       .= f.(0.R) + f.(0.R) by VECTSP_1:def 20;
hence thesis by RLVECT_1:9;
end;
