let V be ComplexLinearSpace; :: thesis: for v being VECTOR of V
for W being Subspace of V holds
( - v in v + W iff v in W )
let v be VECTOR of V; :: thesis: for W being Subspace of V holds
( - v in v + W iff v in W )
let W be Subspace of V; :: thesis: ( - v in v + W iff v in W )
(- 1r) * v = - v by Th3;
hence ( - v in v + W iff v in W ) by Th77, Th78; :: thesis: verum