let V be non empty CLSStruct ; :: thesis: for v being VECTOR of V
for L1, L2 being C_Linear_Combination of V holds (L1 - L2) . v = (L1 . v) - (L2 . v)
let v be VECTOR of V; :: thesis: for L1, L2 being C_Linear_Combination of V holds (L1 - L2) . v = (L1 . v) - (L2 . v)
let L1, L2 be C_Linear_Combination of V; :: thesis: (L1 - L2) . v = (L1 . v) - (L2 . v)
thus (L1 - L2) . v = (L1 . v) + ((- L2) . v) by Def8
.= (L1 . v) - (L2 . v) by Th31 ; :: thesis: verum