let V be non empty CLSStruct ; :: thesis: for a, b being Complex
for L being C_Linear_Combination of V holds a * (b * L) = (a * b) * L
let a, b be Complex; :: thesis: for L being C_Linear_Combination of V holds a * (b * L) = (a * b) * L
let L be C_Linear_Combination of V; :: thesis: a * (b * L) = (a * b) * L
let v be VECTOR of V; :: according to CONVEX4:def 7 :: thesis: (a * (b * L)) . v = ((a * b) * L) . v
thus (a * (b * L)) . v = a * ((b * L) . v) by Def9
.= a * (b * (L . v)) by Def9
.= (a * b) * (L . v)
.= ((a * b) * L) . v by Def9 ; :: thesis: verum