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

theorem Th27:
  for V being add-associative right_zeroed right_complementable
  non empty addLoopStr, v,u,w being Element of V holds
  v - (u + w) = (v - w) - u
proof
  let V be add-associative right_zeroed right_complementable non empty
  addLoopStr;
  let v,u,w be Element of V;
  thus v - (u + w) = v + (-w + -u) by Lm3
    .= (v - w) - u by Def3;
end;
