reserve x for set;
reserve a,b,c,d,e,r1,r2,r3,r4,r5,r6 for Real;
reserve V for RealLinearSpace;
reserve u,v,v1,v2,v3,w,w1,w2,w3 for VECTOR of V;
reserve W,W1,W2 for Subspace of V;

theorem
  w1 in Lin{w1,w2,w3} & w2 in Lin{w1,w2,w3} & w3 in 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,RLVECT_3:15;
end;
