let R be Ring; :: thesis: for V being RightMod of R
for L being Linear_Combination of V st Carrier L = {} holds
Sum L = 0. V
let V be RightMod of R; :: thesis: for L being Linear_Combination of V st Carrier L = {} holds
Sum L = 0. V
let L be Linear_Combination of V; :: thesis: ( Carrier L = {} implies Sum L = 0. V )
assume Carrier L = {} ; :: thesis: Sum L = 0. V
then L = ZeroLC V by Def4;
hence Sum L = 0. V by Lm3; :: thesis: verum