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;
reserve K,L,L1,L2,L3 for Linear_Combination of V;

theorem Th20:
  for V be non empty addLoopStr, v be Element of V holds ZeroLC(V) .v = 0
proof
  let V be non empty addLoopStr, v be Element of V;
  Carrier (ZeroLC(V)) = {} & not v in {} by Def5;
  hence thesis;
end;
