#!/usr/bin/php


\subsection*{Common Notions}
\begin{alltt}
equalitytransitive
   hypotheses: EQAC EQBC 
   conclusion: EQAB
congruencetransitive
   hypotheses: EEPQBC EEPQDE 
   conclusion: EEBCDE
equalityreflexive
   hypotheses: none
   conclusion: EQAA
congruencereflexive
   hypotheses: none
   conclusion: EEABAB
equalityreverse
   hypotheses: none
   conclusion: EEABBA
stability
   hypotheses: NONEAB 
   conclusion: EQAB
equalitysub
   hypotheses: EQDA BEABC 
   conclusion: BEDBC
\end{alltt}
\subsection*{Definitions}
\begin{alltt}
unequal  {\em A and B are distinct points}
   <br />
<b>Fatal error</b>:  Uncaught TypeError: count(): Argument #1 ($value) must be of type Countable|array, string given in /usr/home/beeson/public_html/michaelbeeson/research/papers/programs/proofs/MakeAppendix (Michael Beeson's conflicted copy 2017-07-31).php:165
Stack trace:
#0 /usr/home/beeson/public_html/michaelbeeson/research/papers/programs/proofs/MakeAppendix (Michael Beeson's conflicted copy 2017-07-31).php(209): display_definition(Object(Definition))
#1 /usr/home/beeson/public_html/michaelbeeson/research/papers/programs/proofs/MakeAppendix (Michael Beeson's conflicted copy 2017-07-31).php(269): display_proposition(Object(Definition))
#2 {main}
  thrown in <b>/usr/home/beeson/public_html/michaelbeeson/research/papers/programs/proofs/MakeAppendix (Michael Beeson's conflicted copy 2017-07-31).php</b> on line <b>165</b><br />