let V be non empty addLoopStr ; :: thesis: for l being C_Linear_Combination of {} the carrier of V holds l = ZeroCLC V
let l be C_Linear_Combination of {} the carrier of V; :: thesis: l = ZeroCLC V
Carrier l c= {} by Def4;
then Carrier l = {} ;
hence l = ZeroCLC V by Def3; :: thesis: verum