let R be Ring; :: thesis: for V being RightMod of R
for v being Vector of V
for W being Submodule of V st v in W holds
- v in W
let V be RightMod of R; :: thesis: for v being Vector of V
for W being Submodule of V st v in W holds
- v in W
let v be Vector of V; :: thesis: for W being Submodule of V st v in W holds
- v in W
let W be Submodule of V; :: thesis: ( v in W implies - v in W )
assume v in W ; :: thesis: - v in W
then v * (- (1_ R)) in W by Th21;
hence - v in W by VECTSP_2:32; :: thesis: verum