let R be Ring; :: thesis: for V being RightMod of R
for u, v being Vector of V
for W being Submodule of V st u in W & v in W holds
u - v in W
let V be RightMod of R; :: thesis: for u, v being Vector of V
for W being Submodule of V st u in W & v in W holds
u - v in W
let u, v be Vector of V; :: thesis: for W being Submodule of V st u in W & v in W holds
u - v in W
let W be Submodule of V; :: thesis: ( u in W & v in W implies u - v in W )
assume that
A1: u in W and
A2: v in W ; :: thesis: u - v in W
- v in W by A2, Th22;
hence u - v in W by A1, Th20; :: thesis: verum