let V be non empty CLSStruct ; :: thesis: for L being C_Linear_Combination of V holds 0c * L = ZeroCLC V
let L be C_Linear_Combination of V; :: thesis: 0c * L = ZeroCLC V
let v be VECTOR of V; :: according to CONVEX4:def 7 :: thesis: (0c * L) . v = (ZeroCLC V) . v
thus (0c * L) . v = 0c * (L . v) by Def9
.= (ZeroCLC V) . v by Th2 ; :: thesis: verum