let R be Ring; :: thesis: for V being RightMod of
for v being Vector of holds (ZeroLC V) . v = 0. R
let V be RightMod of ; :: thesis: for v being Vector of holds (ZeroLC V) . v = 0. R
let v be Vector of ; :: thesis: (ZeroLC V) . v = 0. R
( Carrier (ZeroLC V) = {} & not v in {} ) by Def6;
hence (ZeroLC V) . v = 0. R ; :: thesis: verum