let V be RealLinearSpace; for u, v, w being VECTOR of V st {u,w,v} is linearly-independent & u <> v & u <> w & v <> w holds
{u,(w + u),(v + u)} is linearly-independent
let u, v, w be VECTOR of V; ( {u,w,v} is linearly-independent & u <> v & u <> w & v <> w implies {u,(w + u),(v + u)} is linearly-independent )
assume A1:
( {u,w,v} is linearly-independent & u <> v & u <> w & v <> w )
; {u,(w + u),(v + u)} is linearly-independent
hence
{u,(w + u),(v + u)} is linearly-independent
by Th7; verum