reserve FS for non empty doubleLoopStr;
reserve F for Field;
reserve R for Abelian add-associative right_zeroed right_complementable non
  empty addLoopStr,
  x, y, z for Scalar of R;

theorem
  (x + y = z iff x = z - y) & (x + y = z iff y = z - x) by Lm2,Lm3;
