  In a previous report, the second and third authors gave general theorems for
unique strong solutions of infinite-dimensional stochastic differential
equations (ISDEs) describing the dynamics of infinitely many interacting
Brownian particles. One of the critical assumptions is the \lq\lq IFC"
condition. The IFC condition requires that, for a given weak solution, the
scheme consisting of the finite-dimensional stochastic differential equations
(SDEs) related to the ISDEs exists. Furthermore, the IFC condition implies that
each finite-dimensional SDE has unique strong solutions. Unlike other
assumptions, the IFC condition is challenging to verify, and so the previous
report only verified solution for solutions given by quasi-regular Dirichlet
forms. In the present paper, we provide a sufficient condition for the IFC
requirement in more general situations. In particular, we prove the IFC
condition without assuming the quasi-regularity or symmetry of the associated
Dirichlet forms. As an application of the theoretical formulation, the results
derived in this paper are used to prove the uniqueness of Dirichlet forms and
the dynamical universality of random matrices.
