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 implies v in W ) & ( v in W implies 0. V in v + W ) & ( v in W implies v + W = the carrier of W ) & ( v + W = the carrier of W implies v in W ) ) by Lm3, Th58;
hence ( 0. V in v + W iff v + W = the carrier of W ) ; :: thesis: verum