Before revision:  As the first application of the frameworks, we prove that the assumptions hold for the linear finite element discretization of Poisson problem with high contrast and oscillatory coefficient  .
After revision:  As the first application of the frameworks, we prove that the assumptions hold for the linear finite element discretization of Poisson problem with high contrast and oscillatory coefficient and the condition number of the TL-OS preconditioned system is robust with respect to the model and mesh parameters .