let R be comRing; :: thesis: for V being RightMod of R
for L being Linear_Combination of V holds
( L + (ZeroLC V) = L & (ZeroLC V) + L = L )
let V be RightMod of R; :: thesis: for L being Linear_Combination of V holds
( L + (ZeroLC V) = L & (ZeroLC V) + L = L )
let L be Linear_Combination of V; :: thesis: ( L + (ZeroLC V) = L & (ZeroLC V) + L = L )
thus L + (ZeroLC V) = L :: thesis: (ZeroLC V) + L = L

proof

let v be Vector of V; :: according to RMOD_4:def 8 :: thesis: (L + (ZeroLC V)) . v = L . v
thus (L + (ZeroLC V)) . v = (L . v) + ((ZeroLC V) . v) by Def9
.= (L . v) + (0. R) by Th18
.= L . v by RLVECT_1:4 ; :: thesis: verum

end;

hence (ZeroLC V) + L = L by Th39; :: thesis: verum