My professor wants me to write the proof method of every proof at the beginning. Something of the form
$\textbf{proof. }\textit{[proof method.]} \\ [\text{body}] \\ [\text{conclusion}] \\ \square$
What do I call my method if I use something like the AM-GM inequality or absolute value identities? Are those still direct proofs? Or are they indirect proofs? My understanding right now is if I use facts/assumptions pertaining to the proposition, then it's a direct proof. For example, showing if $a|b$ and $b|c$ then $a|c$ by showing that by substitution $c=aln$ for integers $l,n$, therefore $a|c$. Otherwise its an indirect proof. I'm not too sure about the semantic differences overall though.