let R be Ring; :: thesis: for V being RightMod of R
for u, v1, v2 being Vector of V
for W being Submodule of V st u in v1 + W & u in v2 + W holds
v1 + W = v2 + W
let V be RightMod of R; :: thesis: for u, v1, v2 being Vector of V
for W being Submodule of V st u in v1 + W & u in v2 + W holds
v1 + W = v2 + W
let u, v1, v2 be Vector of V; :: thesis: for W being Submodule of V st u in v1 + W & u in v2 + W holds
v1 + W = v2 + W
let W be Submodule of V; :: thesis: ( u in v1 + W & u in v2 + W implies v1 + W = v2 + W )
assume that
A1: u in v1 + W and
A2: u in v2 + W ; :: thesis: v1 + W = v2 + W
thus v1 + W = u + W by A1, Th53
.= v2 + W by A2, Th53 ; :: thesis: verum