theorem :: ZMODUL01:115

for R being Ring
for V being LeftMod of R
for W1, W2, W3 being Submodule of V st W1 is Submodule of W2 holds
W2 /\ (W1 + W3) = (W1 /\ W2) + (W2 /\ W3) by Lm13, Th45;