Expressing functions using the arithmetic dictionary


i have seen in the “logic to cs” class i take – a theorem that states: “every recursive (computable) function $ f$ can be expressed using the arithmetic dictionary {$ C_0, C_1, f_+(,), f_x(,)$ }”

But we didnt prove this theorem because a part of the students didnt take the “computational models” course (i did take it though)

Where can i find a proof for this theorem? Thanks in advance!