let GF be non empty right_complementable well-unital distributive Abelian add-associative right_zeroed associative doubleLoopStr ; :: thesis: for V being non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed ModuleStr over GF
for u, v1, v2 being Element of V
for W being Subspace of V st u in v1 + W & u in v2 + W holds
v1 + W = v2 + W
let V be non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed ModuleStr over GF; :: thesis: for u, v1, v2 being Element of V
for W being Subspace of V st u in v1 + W & u in v2 + W holds
v1 + W = v2 + W
let u, v1, v2 be Element of V; :: thesis: for W being Subspace of V st u in v1 + W & u in v2 + W holds
v1 + W = v2 + W
let W be Subspace 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, Th55
.= v2 + W by A2, Th55 ; :: thesis: verum