"The direct approach" for a proof of the generalized Ito-Wentzell formula for a generalized stochastic differential equation

This paper is complete proof of one method for obtaining the generalized Ito-Wentzell formula, its basic idea was announced earlier in a pre-print (arXiv:1309.3038v1). This proof sets the approach which uses the Ito formula and the stochastic approximation theory.