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