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<div><span class="kw">theorem </span><a NAME="T32"><span class="comment"><font color="firebrick">:: CATALG_1:32</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">C</font> being   <a href="cat_1.html#NM4" title="CAT_1:NM.4">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>, <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>, <font color="Olive" title="b7">g</font>, <font color="Olive" title="b8">h</font> being   <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <font color="Olive" title="b1">C</font>  st <font color="Olive" title="b6">f</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <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>) &amp; <font color="Olive" title="b7">g</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="cat_1.html#K2" title="CAT_1:func.2">Hom</a> (<font color="Olive" title="b3">b</font>,<font color="Olive" title="b4">c</font>) &amp; <font color="Olive" title="b8">h</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <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>) holds <br/><span class="p1">(<span class="default"><a href="msualg_1.html#K5" title="MSUALG_1:func.5">Den</a> (<span class="p2">(<span class="default"><a href="catalg_1.html#K10" title="CATALG_1:func.10">compsym</a> (<font color="Olive" title="b2">a</font>,<font color="Olive" title="b4">c</font>,<font color="Olive" title="b5">d</font>)</span>)</span>,<span class="p2">(<span class="default"><a href="catalg_1.html#K13" title="CATALG_1:func.13">MSAlg</a> <font color="Olive" title="b1">C</font></span>)</span>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Olive" title="b8">h</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="msualg_1.html#K5" title="MSUALG_1:func.5">Den</a> (<span class="p4">(<span class="default"><a href="catalg_1.html#K10" title="CATALG_1:func.10">compsym</a> (<font color="Olive" title="b2">a</font>,<font color="Olive" title="b3">b</font>,<font color="Olive" title="b4">c</font>)</span>)</span>,<span class="p4">(<span class="default"><a href="catalg_1.html#K13" title="CATALG_1:func.13">MSAlg</a> <font color="Olive" title="b1">C</font></span>)</span>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><font color="Olive" title="b7">g</font>,<font color="Olive" title="b6">f</font></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span></span>)</span></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="msualg_1.html#K5" title="MSUALG_1:func.5">Den</a> (<span class="p2">(<span class="default"><a href="catalg_1.html#K10" title="CATALG_1:func.10">compsym</a> (<font color="Olive" title="b2">a</font>,<font color="Olive" title="b3">b</font>,<font color="Olive" title="b5">d</font>)</span>)</span>,<span class="p2">(<span class="default"><a href="catalg_1.html#K13" title="CATALG_1:func.13">MSAlg</a> <font color="Olive" title="b1">C</font></span>)</span>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="msualg_1.html#K5" title="MSUALG_1:func.5">Den</a> (<span class="p4">(<span class="default"><a href="catalg_1.html#K10" title="CATALG_1:func.10">compsym</a> (<font color="Olive" title="b3">b</font>,<font color="Olive" title="b4">c</font>,<font color="Olive" title="b5">d</font>)</span>)</span>,<span class="p4">(<span class="default"><a href="catalg_1.html#K13" title="CATALG_1:func.13">MSAlg</a> <font color="Olive" title="b1">C</font></span>)</span>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><font color="Olive" title="b8">h</font>,<font color="Olive" title="b7">g</font></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span></span>)</span>,<font color="Olive" title="b6">f</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span></div></div>
