reserve i,j,k for Nat;

theorem
  for K being right_zeroed add-associative right_complementable Abelian
  non empty addLoopStr holds comp K is_distributive_wrt the addF of K
proof
  let K be right_zeroed add-associative right_complementable Abelian non
  empty addLoopStr;
  the addF of K is having_a_unity by Th8;
  then (the_inverseOp_wrt the addF of K) is_distributive_wrt the addF of K by
Th14,FINSEQOP:63;
  hence thesis by Th15;
end;
