let R be Ring; :: thesis: for V being RightMod of R
for L being Linear_Combination of V holds L - L = ZeroLC V
let V be RightMod of R; :: thesis: for L being Linear_Combination of V holds L - L = ZeroLC V
let L be Linear_Combination of V; :: thesis: L - L = ZeroLC V
let v be Vector of V; :: according to RMOD_4:def 8 :: thesis: (L - L) . v = (ZeroLC V) . v
thus (L - L) . v = (L . v) - (L . v) by Th54
.= 0. R by RLVECT_1:15
.= (ZeroLC V) . v by Th18 ; :: thesis: verum