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 v + 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 v + W
let v be Vector of V; :: thesis: for W being Submodule of V st v in W holds
- v in v + W
let W be Submodule of V; :: thesis: ( v in W implies - v in v + W )
assume v in W ; :: thesis: - v in v + W
then v * (- (1_ R)) in v + W by Th55;
hence - v in v + W by VECTSP_2:32; :: thesis: verum