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Let M1,M2 be submodules of analytic Hilbert module X on Ω( Cn) such that M1 M2and dimM1/M2 = k ＜∞.If M2 is an AF-cosubmodule,then the codimension dimM1/M2 of M2 in M1 equals the cardinality of zeros of M2 related to M1 by counting multiplicities.The codimension formula has some interesting applications.In particular,the author calculates out the dimension of Rudin quotient module,which is raised in [14].