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
  a <> 1 implies {v,a * v} is linearly-dependent
proof
  v = 1 * v by RLVECT_1:def 8;
  hence thesis by Th21;
end;
