let V be Z_Module; :: thesis: for W1, W2, W3 being Submodule of V st W1 is strict Submodule of W3 holds
W1 + (W2 /\ W3) = (W1 + W2) /\ W3
let W1, W2, W3 be Submodule of V; :: thesis: ( W1 is strict Submodule of W3 implies W1 + (W2 /\ W3) = (W1 + W2) /\ W3 )
assume A1: W1 is strict Submodule of W3 ; :: thesis: W1 + (W2 /\ W3) = (W1 + W2) /\ W3
thus (W1 + W2) /\ W3 = (W1 /\ W3) + (W3 /\ W2) by A1, Lm13, Th45
.= W1 + (W2 /\ W3) by A1, Th106 ; :: thesis: verum