let a be Real; :: thesis: for V being RealLinearSpace
for v, w being VECTOR of V st a <> 1 holds
not {v,(a * v),w} is linearly-independent
let V be RealLinearSpace; :: thesis: for v, w being VECTOR of V st a <> 1 holds
not {v,(a * v),w} is linearly-independent
let v, w be VECTOR of V; :: thesis: ( a <> 1 implies not {v,(a * v),w} is linearly-independent )
v = 1 * v by RLVECT_1:def 9;
hence ( a <> 1 implies not {v,(a * v),w} is linearly-independent ) by Th34; :: thesis: verum