<?xml version="1.0"?>
<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E34">Th42</font></span>: <a NAME="T42"><span class="comment"><font color="firebrick">:: CAT_8:42</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">C</font> being   <a href="cat_8.html#V7" title="CAT_8:attr.7">with_binary_products</a>  <a href="cat_6.html#NM2" title="CAT_6:NM.2">category</a><br/>  for <font color="Olive" title="b2">a</font>, <font color="Olive" title="b3">b</font> being   <a href="cat_6.html#NM3" title="CAT_6:NM.3">Object</a> of <font color="Olive" title="b1">C</font> holds <br/> ( <font color="Olive" title="b2">a</font> <a href="cat_8.html#K4" title="CAT_8:func.4">[x]</a> <font color="Olive" title="b3">b</font>, <a href="cat_8.html#K5" title="CAT_8:func.5">pr1</a> (<font color="Olive" title="b2">a</font>,<font color="Olive" title="b3">b</font>), <a href="cat_8.html#K6" title="CAT_8:func.6">pr2</a> (<font color="Olive" title="b2">a</font>,<font color="Olive" title="b3">b</font>) <a href="cat_8.html#R1" title="CAT_8:pred.1">is_product_of</a> <font color="Olive" title="b2">a</font>,<font color="Olive" title="b3">b</font> &amp;  <a href="cat_7.html#K1" title="CAT_7:func.1">Hom</a> (<span class="p1">(<span class="default"><font color="Olive" title="b2">a</font> <a href="cat_8.html#K4" title="CAT_8:func.4">[x]</a> <font color="Olive" title="b3">b</font></span>)</span>,<font color="Olive" title="b2">a</font>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp;  <a href="cat_7.html#K1" title="CAT_7:func.1">Hom</a> (<span class="p1">(<span class="default"><font color="Olive" title="b2">a</font> <a href="cat_8.html#K4" title="CAT_8:func.4">[x]</a> <font color="Olive" title="b3">b</font></span>)</span>,<font color="Olive" title="b3">b</font>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  )</div></div>
