let V be RealLinearSpace; :: thesis: for v being VECTOR of V
for W being Subspace of V holds
( 0. V in v + W iff v + W = the carrier of W )
let v be VECTOR of V; :: thesis: for W being Subspace of V holds
( 0. V in v + W iff v + W = the carrier of W )
let W be Subspace of V; :: thesis: ( 0. V in v + W iff v + W = the carrier of W )
( ( 0. V in v + W implies v in W ) & ( v in W implies 0. V in v + W ) & ( v in W implies v + W = the carrier of W ) & ( v + W = the carrier of W implies v in W ) ) by Lm3, Th58;
hence ( 0. V in v + W iff v + W = the carrier of W ) ; :: thesis: verum