let R be Ring; :: thesis: for V being RightMod of R
for u being Vector of V
for W being Submodule of V
for B, C being Coset of W st u in B & u in C holds
B = C
let V be RightMod of R; :: thesis: for u being Vector of V
for W being Submodule of V
for B, C being Coset of W st u in B & u in C holds
B = C
let u be Vector of V; :: thesis: for W being Submodule of V
for B, C being Coset of W st u in B & u in C holds
B = C
let W be Submodule of V; :: thesis: for B, C being Coset of W st u in B & u in C holds
B = C
let B, C be Coset of W; :: thesis: ( u in B & u in C implies B = C )
assume A1: ( u in B & u in C ) ; :: thesis: B = C
( ex v1 being Vector of V st B = v1 + W & ex v2 being Vector of V st C = v2 + W ) by Def6;
hence B = C by A1, Th54; :: thesis: verum