reserve x,y,y1,y2 for object;
reserve GF for add-associative right_zeroed right_complementable Abelian
  associative well-unital distributive non empty doubleLoopStr,
  V,X,Y for Abelian add-associative right_zeroed right_complementable
  vector-distributive scalar-distributive scalar-associative scalar-unital non
  empty ModuleStr over GF;
reserve a for Element of GF;
reserve u,u1,u2,v,v1,v2 for Element of V;
reserve W,W1,W2 for Subspace of V;
reserve V1 for Subset of V;
reserve w,w1,w2 for Element of W;
reserve B,C for Coset of W;

theorem
  for W1,W2 being strict Subspace of V, C1 being Coset of W1, C2 being
  Coset of W2 st C1 = C2 holds W1 = W2
proof
  let W1,W2 be strict Subspace of V, C1 be Coset of W1, C2 be Coset of W2;
  ( ex v1 st C1 = v1 + W1)& ex v2 st C2 = v2 + W2 by Def6;
  hence thesis by Th67;
end;
