reserve i,j,k for Nat;

theorem Th1:
  for K being Abelian non empty addLoopStr holds the addF of K is commutative
proof
  let K be Abelian non empty addLoopStr;
  now
    let a,b be Element of K;
    thus (the addF of K).(a,b)=a+b .=(the addF of K).(b,a) by RLVECT_1:2;
  end;
  hence thesis by BINOP_1:def 2;
end;
