let V be RealUnitarySpace; :: thesis: for W being Subspace of V
for v being VECTOR of V holds
( - v in v + W iff v in W )
let W be Subspace of V; :: thesis: for v being VECTOR of V holds
( - v in v + W iff v in W )
let v be VECTOR of V; :: thesis: ( - v in v + W iff v in W )
(- jj) * v = - v by RLVECT_1:16;
hence ( - v in v + W iff v in W ) by Th52, Th53; :: thesis: verum