reserve x,y,y1,y2 for set,
  p for FinSequence,
  i,k,l,n for Nat,
  V for RealLinearSpace,
  u,v,v1,v2,v3,w for VECTOR of V,
  a,b for Real,
  F,G,H1,H2 for FinSequence of V,
  A,B for Subset of V,
  f for Function of the carrier of V, REAL;

theorem Th8:
  for V be Abelian add-associative right_zeroed non empty
  addLoopStr holds Sum({}V) = 0.V
proof
  let V be Abelian add-associative right_zeroed non empty addLoopStr;
  Sum(<*>(the carrier of V)) = 0.V by RLVECT_1:43;
  hence thesis by Def2,RELAT_1:38;
end;
