let R be Ring; :: thesis: for V being RightMod of R
for L being Linear_Combination of V holds L * (1_ R) = L
let V be RightMod of R; :: thesis: for L being Linear_Combination of V holds L * (1_ R) = L
let L be Linear_Combination of V; :: thesis: L * (1_ R) = L
let v be Vector of V; :: according to RMOD_4:def 8 :: thesis: (L * (1_ R)) . v = L . v
thus (L * (1_ R)) . v = (L . v) * (1_ R) by Def10
.= L . v ; :: thesis: verum