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 vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed ModuleStr over GF
for v being Element of V holds {v} is Coset of (0). V
let V be non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed ModuleStr over GF; :: thesis: for v being Element of V holds {v} is Coset of (0). V
let v be Element of V; :: thesis: {v} is Coset of (0). V
v + ((0). V) = {v} by Th46;
hence {v} is Coset of (0). V by Def6; :: thesis: verum