
theorem hom4:
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
for x,y being Element of R holds f.(x-y) = f.x - f.y
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 being additive Function of R,S;
let x,y being Element of R;
thus f.(x-y) = f.x + f.(-y) by VECTSP_1:def 20
            .= f.x - f.y by hom4a;
end;
