let V be RealLinearSpace; :: thesis: for v being VECTOR of V
for W being Subspace of V holds
( v in W iff (- v) + W = the carrier of W )
let v be VECTOR of V; :: thesis: for W being Subspace of V holds
( v in W iff (- v) + W = the carrier of W )
let W be Subspace of V; :: thesis: ( v in W iff (- v) + W = the carrier of W )
( v in W iff ((- jj) * v) + W = the carrier of W ) by Th49, Th50;
hence ( v in W iff (- v) + W = the carrier of W ) by RLVECT_1:16; :: thesis: verum