theorem Th1: :: VECTSP_5:1

for GF being non empty right_complementable well-unital distributive Abelian add-associative right_zeroed associative doubleLoopStr
for M being non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed ModuleStr over GF
for W1, W2 being Subspace of M
for x being object holds
( x in W1 + W2 iff ex v1, v2 being Element of M st
( v1 in W1 & v2 in W2 & x = v1 + v2 ) )