let V be RealUnitarySpace; :: thesis: for W being Subspace of V
for v being VECTOR of V holds
( 0. V in v + W iff v + W = the carrier of W )
let W be Subspace of V; :: thesis: for v being VECTOR of V holds
( 0. V in v + W iff v + W = the carrier of W )
let v be VECTOR of V; :: thesis: ( 0. V in v + W iff v + W = the carrier of W )
( 0. V in v + W iff v in W ) by Th36;
hence ( 0. V in v + W iff v + W = the carrier of W ) by Lm3; :: thesis: verum