let R be comRing; :: thesis: for V being RightMod of R
for L1, L2 being Linear_Combination of V holds L1 + L2 = L2 + L1
let V be RightMod of R; :: thesis: for L1, L2 being Linear_Combination of V holds L1 + L2 = L2 + L1
let L1, L2 be Linear_Combination of V; :: thesis: L1 + L2 = L2 + L1
let v be Vector of V; :: according to RMOD_4:def 8 :: thesis: (L1 + L2) . v = (L2 + L1) . v
thus (L1 + L2) . v = (L2 . v) + (L1 . v) by Def9
.= (L2 + L1) . v by Def9 ; :: thesis: verum