reserve K for Ring,
  V1,W1 for VectSp of K;
reserve F for Field,
  V,W for VectSp of F;

theorem Th4:
  [#]V is finite implies V is finite-dimensional
proof
  set B = the Basis of V;
  assume [#]V is finite;
  then reconsider B as finite Subset of V;
  take B;
  thus thesis;
end;
