reserve V for non empty RLSStruct;
reserve x,y,y1 for set;
reserve v for VECTOR of V;
reserve a,b for Real;

theorem Th12:
  for V being add-associative right_zeroed right_complementable
  non empty addLoopStr holds - 0.V = 0.V
proof
  let V be add-associative right_zeroed right_complementable non empty
  addLoopStr;
  thus 0.V = 0.V + (- 0.V) by Def10
    .= - 0.V;
end;
