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<div><span class="kw">theorem </span><a NAME="T25"><span class="comment"><font color="firebrick">:: ALTCAT_3:25</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">C</font> being    <a href="altcat_1.html#L1" title="ALTCAT_1:struct.1">AltGraph</a> <br/>  for <font color="Olive" title="b2">o</font> being   <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">Object</a> of <font color="Olive" title="b1">C</font> holds <br/> ( <font color="Olive" title="b2">o</font> is  <a href="altcat_3.html#V6" title="ALTCAT_3:attr.6">initial</a>  iff  for <font color="Olive" title="b3">o1</font> being   <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">Object</a> of <font color="Olive" title="b1">C</font>  ex <font color="Olive" title="b4">M</font> being   <a href="altcat_1.html#NM2" title="ALTCAT_1:NM.2">Morphism</a> of <font color="Olive" title="b2">o</font>,<font color="Olive" title="b3">o1</font> st <br/>( <font color="Olive" title="b4">M</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Olive" title="b2">o</font>,<font color="Olive" title="b3">o1</font></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span> &amp; (  for <font color="Olive" title="b5">M1</font> being   <a href="altcat_1.html#NM2" title="ALTCAT_1:NM.2">Morphism</a> of <font color="Olive" title="b2">o</font>,<font color="Olive" title="b3">o1</font>  st <font color="Olive" title="b5">M1</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Olive" title="b2">o</font>,<font color="Olive" title="b3">o1</font></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span> holds <br/><font color="Olive" title="b4">M</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b5">M1</font> ) ) )</div></div>
