let V be non empty CLSStruct ; :: thesis: for L being C_Linear_Combination of V holds L + (ZeroCLC V) = L
let L be C_Linear_Combination of V; :: thesis: L + (ZeroCLC V) = L
let v be VECTOR of V; :: according to CONVEX4:def 7 :: thesis: (L + (ZeroCLC V)) . v = L . v
thus (L + (ZeroCLC V)) . v = (L . v) + ((ZeroCLC V) . v) by Def8
.= (L . v) + 0c by Th2
.= L . v ; :: thesis: verum