let V be Z_Module; :: 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 (- 1) * v in W by Th37;
hence - v in W by Th2; :: thesis: verum