theorem :: ZMODUL01:133

for R being Ring
for V being LeftMod of R
for W1, W2 being Submodule of V holds
( W1 + W2 = ModuleStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #) iff for v being Vector of V ex v1, v2 being Vector of V st
( v1 in W1 & v2 in W2 & v = v1 + v2 ) ) by Lm17;