# how can we represent the following projection

how can we express the following correctly.

$$f:E\to F$$ $$E \subseteq C_1 \times C_2 \times C_3 \times C_4$$

$$f|_A:A\to F$$ $$A \subseteq C_1 \times C_4$$ here, I misused the notation of mathematical restriction. I am looking for some notation like $$f|_A$$