
theorem LmSumSc11:
  for L being Z_Lattice, v being Vector of L holds
  SumSc(v, ZeroLC(L)) = 0.F_Real
  proof
    let L be Z_Lattice, v be Vector of L;
    consider F be FinSequence of L such that
    A1: F is one-to-one & rng F = Carrier(ZeroLC(L)) &
    SumSc(v,ZeroLC(L)) = Sum(ScFS(v, ZeroLC(L),F)) by defSumSc;
    F = {} by A1,VECTSP_6:def 3;
    then len(ScFS(v, ZeroLC(L),F)) = 0 by defScFS;
    hence thesis by A1,RLVECT_1:75;
  end;
