let V be non empty right_complementable Abelian add-associative right_zeroed CLSStruct ; :: thesis: for L being C_Linear_Combination of V st Carrier L = {} holds
Sum L = 0. V
let L be C_Linear_Combination of V; :: thesis: ( Carrier L = {} implies Sum L = 0. V )
assume Carrier L = {} ; :: thesis: Sum L = 0. V
then L = ZeroCLC V by Def3;
hence Sum L = 0. V by Th11; :: thesis: verum