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 )
( ( v in W implies (- 1) * v in v + W ) & (- 1) * v = - v & ( - 1 <> 1 & (- 1) * v in v + W implies v in W ) ) by Th52, Th53, RLVECT_1:29;
hence ( - v in v + W iff v in W ) ; :: thesis: verum