let GF be non empty right_complementable associative well-unital distributive Abelian add-associative right_zeroed doubleLoopStr ; :: thesis: for V being non empty right_complementable VectSp-like Abelian add-associative right_zeroed VectSpStr of GF holds V is Subspace of V
let V be non empty right_complementable VectSp-like Abelian add-associative right_zeroed VectSpStr of GF; :: thesis: V is Subspace of V
A1: ( the carrier of V c= the carrier of V & 0. V = 0. V ) ;
( the addF of V = the addF of V || the carrier of V & the lmult of V = the lmult of V | [:the carrier of GF,the carrier of V:] ) by RELSET_1:34;
hence V is Subspace of V by A1, Def2; :: thesis: verum