theorem Th65: :: VECTSP_4:65

for GF being non empty right_complementable well-unital distributive Abelian add-associative right_zeroed associative doubleLoopStr
for V being non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed ModuleStr over GF
for u, v being Element of V
for W being Subspace of V st v + W = u + W holds
ex v1 being Element of V st
( v1 in W & v - v1 = u )