<?xml version="1.0"?>
<div><span class="kw">theorem </span><a NAME="T9"><span class="comment"><font color="firebrick">:: CAT_1:9</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">C</font> being   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   non  <a href="struct_0.html#V11" title="STRUCT_0:attr.11">void</a>   <a href="cat_1.html#L1" title="CAT_1:struct.1">CatStr</a> <br/>  for <font color="Olive" title="b2">a</font>, <font color="Olive" title="b3">b</font>, <font color="Olive" title="b4">c</font>, <font color="Olive" title="b5">d</font> being   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Olive" title="b1">C</font><br/>  for <font color="Olive" title="b6">f</font> being    <a href="cat_1.html#M1" title="CAT_1:mode.1">Morphism</a> of <font color="Olive" title="b2">a</font>,<font color="Olive" title="b3">b</font>  st  <a href="cat_1.html#K2" title="CAT_1:func.2">Hom</a> (<font color="Olive" title="b2">a</font>,<font color="Olive" title="b3">b</font>), <a href="cat_1.html#K2" title="CAT_1:func.2">Hom</a> (<font color="Olive" title="b4">c</font>,<font color="Olive" title="b5">d</font>) <a href="tarski.html#R3" title="TARSKI:pred.3">are_equipotent</a>  &amp;  <a href="cat_1.html#K2" title="CAT_1:func.2">Hom</a> (<font color="Olive" title="b2">a</font>,<font color="Olive" title="b3">b</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Olive" title="b6">f</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> holds <br/> ex <font color="Olive" title="b7">h</font> being    <a href="cat_1.html#M1" title="CAT_1:mode.1">Morphism</a> of <font color="Olive" title="b4">c</font>,<font color="Olive" title="b5">d</font> st  <a href="cat_1.html#K2" title="CAT_1:func.2">Hom</a> (<font color="Olive" title="b4">c</font>,<font color="Olive" title="b5">d</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Olive" title="b7">h</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></div></div>
