let R be Ring; :: thesis: for V being RightMod of R
for v being Vector of V
for W being Submodule of V holds
( 0. V in v + W iff v + W = the carrier of W )
let V be RightMod of R; :: thesis: for v being Vector of V
for W being Submodule of V holds
( 0. V in v + W iff v + W = the carrier of W )
let v be Vector of V; :: thesis: for W being Submodule of V holds
( 0. V in v + W iff v + W = the carrier of W )
let W be Submodule of V; :: thesis: ( 0. V in v + W iff v + W = the carrier of W )
( 0. V in v + W iff v in W ) by Th58;
hence ( 0. V in v + W iff v + W = the carrier of W ) by Lm3; :: thesis: verum