let R be Ring; :: thesis: for V being RightMod of R
for u, v being Vector of V
for W being Submodule of V holds
( v - u in v + W iff u in W )
let V be RightMod of R; :: thesis: for u, v being Vector of V
for W being Submodule of V holds
( v - u in v + W iff u in W )
let u, v be Vector of V; :: thesis: for W being Submodule of V holds
( v - u in v + W iff u in W )
let W be Submodule of V; :: thesis: ( v - u in v + W iff u in W )
A1: v - u = (- u) + v ;
A2: ( - u in W implies - (- u) in W ) by Th22;
( u in W implies - u in W ) by Th22;
hence ( v - u in v + W iff u in W ) by A1, A2, Th57, RLVECT_1:17; :: thesis: verum