reserve x,y for set;
reserve a,b for Real;
reserve i,j for Integer;
reserve V for RealLinearSpace;
reserve W1,W2,W3 for Subspace of V;
reserve v,v1,v2,v3,u,w,w1,w2,w3 for VECTOR of V;
reserve A,B,C for Subset of V;
reserve L,L1,L2 for Linear_Combination of V;
reserve l,l1,l2 for Linear_Combination of A;

theorem Th11:
  0.V in Z_Lin(A)
proof
  reconsider l = ZeroLC(V) as Linear_Combination of A by RLVECT_2:22;
A1: Sum(l) = 0.V by RLVECT_2:30;
  rng l c= INT by Th7;
  hence thesis by A1;
end;
