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*If [tex]U_\lambda = F_\lambda(U_0)[/tex] and [tex]U_\lambda\cap U_0\neq\emptyset[/tex], then [tex]F_\lambda |U_{-\lambda}\cap U_0 :U_{-\lambda}\cap U_0 \rightarrow U_0 \cap U_\lambda [/tex] is a diffeomorphism and its inverse is [tex]F_{-\lambda}|U_0 \cap U_\lambda[/tex].*

So what does the notation [tex]f|A[/tex] in [tex]f|A:A\rightarrow B[/tex] (where f is a function and A and B are sets) mean?