[F(a,b):F]=[F(b)(a):F(b)][F(b):F]=[F(a)(b):F(a)][F(a):F],所以[F(a):F]=n[F(b)(a):F(b)]=m[F(a)(b):F(a)]
因为F是F(b)的子空间,所以[F(b)(a):F(b)]<=[F(a):F]=m,所以[F(a,b):F]<=mn
若(m,n)=1则m│[F(a)(b):F(b)],所以[F(a)(b):F(b)]=m,故[F(a,b):F]=mn
因为F是F(b)的子空间,所以[F(b)(a):F(b)]<=[F(a):F]=m,所以[F(a,b):F]<=mn
若(m,n)=1则m│[F(a)(b):F(b)],所以[F(a)(b):F(b)]=m,故[F(a,b):F]=mn