let GF be non empty right_complementable well-unital distributive Abelian add-associative right_zeroed associative doubleLoopStr ; :: thesis: for V being non empty right_complementable strict vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed ModuleStr over GF
for W being strict Subspace of V st the carrier of W = the carrier of V holds
W = V
let V be non empty right_complementable strict vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed ModuleStr over GF; :: thesis: for W being strict Subspace of V st the carrier of W = the carrier of V holds
W = V
let W be strict Subspace of V; :: thesis: ( the carrier of W = the carrier of V implies W = V )
assume A1: the carrier of W = the carrier of V ; :: thesis: W = V
V is Subspace of V by Th24;
hence W = V by A1, Th29; :: thesis: verum