reserve x,y,z,x1,x2,y1,y2,z1,z2 for object,
  i,j,k,l,n,m for Nat,
  D for non empty set,
  K for Ring;

theorem Th11:
  for n being Nat
  for K being add-associative right_zeroed right_complementable
      non empty addLoopStr holds
    Sum (n |-> 0.K) = 0.K
proof
  let n be Nat;
  let K be add-associative right_zeroed right_complementable non empty
  addLoopStr;
  set p = n |-> 0.K;
  for i be Element of NAT st i in dom p holds p.i = 0.K
  proof
    let i be Element of NAT;
    assume i in dom p;
    then i in Seg n by FUNCOP_1:13;
    hence thesis by FUNCOP_1:7;
  end;
  hence thesis by Lm1;
end;
