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<div><span class="kw">theorem </span><a NAME="T42"><span class="comment"><font color="firebrick">:: CAT_4:42</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">C</font> being   <a href="cat_4.html#NM1" title="CAT_4:NM.1">Cartesian_category</a><br/>  for <font color="Olive" title="b2">a</font>, <font color="Olive" title="b3">b</font>, <font color="Olive" title="b4">c</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="b5">f</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="b2">a</font><br/>  for <font color="Olive" title="b6">g</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="b3">b</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="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_1.html#K2" title="CAT_1:func.2">Hom</a> (<font color="Olive" title="b4">c</font>,<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>  holds <br/><span class="p1"><a href="cat_4.html#K9" title="CAT_4:func.9">&lt;:</a><span class="default"><font color="Olive" title="b5">f</font>,<font color="Olive" title="b6">g</font></span><a href="cat_4.html#K9" title="CAT_4:func.9">:&gt;</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b5">f</font> <a href="cat_4.html#K18" title="CAT_4:func.18">[x]</a> <font color="Olive" title="b6">g</font></span>)</span> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <span class="p1">(<span class="default"><a href="cat_4.html#K15" title="CAT_4:func.15">Delta</a> <font color="Olive" title="b4">c</font></span>)</span></div></div>
