theorem Th6:
  for V be Abelian right_zeroed non empty addLoopStr for A be Subset of V
    holds 0.V + A = A
 proof
   let V be Abelian right_zeroed non empty addLoopStr;
   let A be Subset of V;
   thus 0.V+A c=A
   proof
     let x be object;
     assume x in 0.V+A;
     then ex s be Element of V st x=0.V+s & s in A;
     hence thesis by RLVECT_1:def 4;
   end;
   let x be object;
   assume A1: x in A;
   then reconsider v=x as Element of V;
   0.V+v=v by RLVECT_1:def 4;
   hence thesis by A1;
 end;
