Which of the following is equivalent to "PUSH $\{$r$7\}"?$

$(1)$ SP$=$ SP $-4,$ and then memory$[$ SP$]=$ r$7$

$(2)$ SP$=$ SP$+4,$ and then memory$[$SP$]=$ r$7$

$(3)$ memory$[$SP$]=$ r$7,$ and then SP$=$ SP $-4$

$(4)$ memory$[$SP$]=$ r$7,$ and then SP$=$ SP$+4$