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
  w1 in Z_Lin{w1,w2,w3} & w2 in Z_Lin{w1,w2,w3} & w3 in Z_Lin{w1,w2,w3}
proof
A1: w3 in {w1,w2,w3} by ENUMSET1:def 1;
  w1 in {w1,w2,w3} & w2 in {w1,w2,w3} by ENUMSET1:def 1;
  hence thesis by A1,Th12;
end;
