<?xml version="1.0"?>
<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E59">Th41</font></span>: <a NAME="T40"><span class="comment"><font color="firebrick">:: CAT_6:40</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">A</font> being   <a href="cat_1.html#NM4" title="CAT_1:NM.4">Category</a><br/>  for <font color="Olive" title="b2">a1</font>, <font color="Olive" title="b3">a2</font> being   <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <font color="Olive" title="b1">A</font><br/>  for <font color="Olive" title="b4">f1</font>, <font color="Olive" title="b5">f2</font> being   <a href="cat_6.html#NM1" title="CAT_6:NM.1">morphism</a> of <span class="p1">(<span class="default"><a href="cat_6.html#K18" title="CAT_6:func.18">alter</a> <font color="Olive" title="b1">A</font></span>)</span>  st <font color="Olive" title="b2">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">f1</font> &amp; <font color="Olive" title="b3">a2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b5">f2</font> &amp; <span class="p1"><a href="cat_2.html#K8" title="CAT_2:func.8">[</a><span class="default"><font color="Olive" title="b2">a1</font>,<font color="Olive" title="b3">a2</font></span><a href="cat_2.html#K8" title="CAT_2:func.8">]</a></span> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a>  the <a href="cat_1.html#U1" title="CAT_1:sel.1">Comp</a> of <font color="Olive" title="b1">A</font> holds <br/><font color="Olive" title="b2">a1</font> <a href="cat_1.html#K1" title="CAT_1:func.1">(*)</a> <font color="Olive" title="b3">a2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">f1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Olive" title="b5">f2</font></div></div>
