let GF be non empty right_complementable associative well-unital distributive Abelian add-associative right_zeroed doubleLoopStr ; :: thesis: for V being non empty right_complementable VectSp-like Abelian add-associative right_zeroed VectSpStr of GF
for u being Element of V
for W being Subspace of V
for B, C being Coset of W st u in B & u in C holds
B = C
let V be non empty right_complementable VectSp-like Abelian add-associative right_zeroed VectSpStr of GF; :: thesis: for u being Element of V
for W being Subspace of V
for B, C being Coset of W st u in B & u in C holds
B = C
let u be Element of V; :: thesis: for W being Subspace of V
for B, C being Coset of W st u in B & u in C holds
B = C
let W be Subspace 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
A2: ex v1 being Element of V st B = v1 + W by Def6;
ex v2 being Element of V st C = v2 + W by Def6;
hence B = C by A1, A2, Th71; :: thesis: verum