theorem Th42: :: VECTSP_4:42

for x being object
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 v being Element of V
for W being Subspace of V holds
( x in v + W iff ex u being Element of V st
( u in W & x = v + u ) )