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
  for V be Abelian add-associative right_zeroed right_complementable
  non empty addLoopStr, v be Element of V holds Sum{v} = v
proof
  let V be Abelian add-associative right_zeroed right_complementable non
  empty addLoopStr, v be Element of V;
A1: Sum<* v *> = v by RLVECT_1:44;
  rng<* v *> = {v} & <* v *> is one-to-one by FINSEQ_1:39,FINSEQ_3:93;
  hence thesis by A1,Def2;
end;
