Let C and D are inductions, assumptions or known results. I want to show that '$A$ holds if and only if $B$ holds'. Is the following proof structure true?
"Indeed, it suffices to see that $C$ to prove the if direction. Conversely, assume that $B$ holds. Since we have $D$, it follows that $A$ holds.
Are there other suggestions to improve the proof?
Generally speaking, if you want prove that $A \iff B $, you need to show that $A\implies B$ and B$\implies A$