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
 for V be RealLinearSpace, v1, v2, v3 be VECTOR of V,
     a, b, c be Real st
 v1 <> v2 & v1 <> v3 & v2 <> v3
 ex l being Linear_Combination of {v1,v2,v3} st l.v1 = a & l.v2 = b & l.v3 = c
 by Lm3;
