let R be domRing; :: thesis: for V being RightMod of R
for L1, L2 being Linear_Combination of V holds Sum (L1 - L2) = (Sum L1) - (Sum L2)
let V be RightMod of R; :: thesis: for L1, L2 being Linear_Combination of V holds Sum (L1 - L2) = (Sum L1) - (Sum L2)
let L1, L2 be Linear_Combination of V; :: thesis: Sum (L1 - L2) = (Sum L1) - (Sum L2)
thus Sum (L1 - L2) = (Sum L1) + (Sum (- L2)) by Th58
.= (Sum L1) + (- (Sum L2)) by Th60
.= (Sum L1) - (Sum L2) by RLVECT_1:def 11 ; :: thesis: verum