theorem Th63: :: VECTSP_4:63

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 v1, v2 being Element of V
for W being Subspace of V holds
( ex v being Element of V st
( v1 in v + W & v2 in v + W ) iff v1 - v2 in W )