<html><head><meta name="color-scheme" content="light dark"></head><body><pre style="word-wrap: break-word; white-space: pre-wrap;">\documentclass{article}
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\begin{document}



\begin{align*}
a &amp;\leq b
\\b &amp;\leq c
\\a &amp;\geq d
\\a &amp;= e
\end{align*}


\begin{align*}
b &amp;= c
\\b &amp;= d
\end{align*}


\begin{align*}
a = a
\end{align*}


\begin{align*}
&amp;&amp;c(v_a v_b \ldots v_c, v_x v_y \ldots v_z)  + c(v_d v_e \ldots v_f, v_x v_y  \ldots v_z) &amp;=  c(v_a v_b \ldots v_c v_d v_e \ldots v_f, v_x v_y  \ldots v_z)
\\ \textrm{if $m \geq n$,  } &amp;&amp;  c(v_1 v_2 \ldots v_{n-1} v_n) &amp;\geq c(v_1 v_2 \ldots v_{n-1} v_m)
\\&amp;&amp; c(v_a v_b \ldots v_c, v_x v_y \ldots v_z) + c(v_d v_e \ldots v_f, v_q v_r  \ldots v_s) &amp;\geq c(v_a v_b \ldots v_c, v_x v_y \ldots v_z)
\end{align*}



\begin{align*}
&amp;&amp;a + b &amp;= c
\\ \textrm{if $m \geq n$,  } &amp;&amp;  d &amp;\geq e
\\&amp;&amp; f &amp;\geq g
\end{align*}



\end{document}
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