let V be ComplexLinearSpace; :: 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 ((- 1r) * v) + W = the carrier of W ) by Th68, Th69;
hence ( v in W iff (- v) + W = the carrier of W ) by Th3; :: thesis: verum