# things to say in proofs instead of “trivially”

• Obviously
• Clearly
• The proof is left to the reader that
• We all agree that
• I would wager 5 dollars that
• By the Axiom of Choice
• With p < 0.05, we conclude that
• By the Laws of Mathematics
• If you’ve been paying attention you’d realize that
• Terry Tao told me in a personal email that
• The voices insist that
• Somebody once told me

that

(source)

The following snippet may prove useful:


\pgfmathdeclarerandomlist{trivials}{
{Trivially, }
{Obviously, }
{The proof is left to the reader that }
{We all agree that }
{We assume without loss of generality that }
{We assume without any good reason that }
{Any undergraduate could see that }
{It's probably true that }
{I bet you can't disprove that }
{I would wager 5 dollars that }
{I would wager two and half cows that }
{\pgfmathrandominteger{\a}{2}{50000} I would wager .\a \leavevmode\vtop{\offinterlineskip
\setbox0=\hbox{B}
\setbox2=\hbox to\wd0{\hfil\hskip-.03em
\vrule height .3ex width .15ex\hskip .08em
\vrule height .3ex width .15ex\hfil}
\vbox{\copy2\box0}\box2} that }
{By the Axiom of Choice, }
{By the Laws of Mathematics, }
{By the power vested in me by the State of Massachusetts, }
{By the Hammer of Grabthar, }
{According to the IMU, }
{According to Hoyle, }
{According to this book I found (I can't remember the name but I think it had a sort of vapor-wave cover? It might've been blue? I think the author's name had an m in it somewhere, or possibly a g?), }
{In accordance with the Prophecy, }
{With p $<$ 0.05 we conclude that }
{If you'd been paying attention you'd have already realized that }
{Terry Tao told me in a personal email that }
{The ghost of Paul Erd\H{o}s told me via Ouija board that }
{A voice in a dream told me that }
{The voices insist that }
{As Srinivasa Ramanujan once said, }
{In the words of Emmy Noether, }
{As Dwayne "The Rock" Johnson said in his groundbreaking treatise \textit{1001 fun facts and formul\ae}, }
{$\twonotes\;\textit{Somebody once told me}\;\twonotes$ that }
}
\providecommand\trivially{}
\renewcommand\trivially{
\pgfmathrandomitem{\choice}{trivials}
\choice
}