
theorem
  for L be add-associative right_zeroed right_complementable
left-distributive unital non empty doubleLoopStr for z0,z1,x be Element of L
  holds eval(<%0.L,z1%>,x) = z1*x
proof
  let L be add-associative right_zeroed right_complementable left-distributive
  unital non empty doubleLoopStr;
  let z0,z1,x be Element of L;
  thus eval(<%0.L,z1%>,x) = 0.L+z1*x by Th44
    .= z1*x by RLVECT_1:4;
end;
