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 vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr of GF
for v being Element of V holds v + ((Omega). V) = the carrier of V
let V be non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr of GF; :: thesis: for v being Element of V holds v + ((Omega). V) = the carrier of V
let v be Element of V; :: thesis: v + ((Omega). V) = the carrier of V
v in (Omega). V by RLVECT_1:1;
hence v + ((Omega). V) = the carrier of V by Lm4; :: thesis: verum