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<div><span class="kw">theorem </span><a NAME="T12"><span class="comment"><font color="firebrick">:: ORDERS_3:12</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">P</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="orders_3.html#NM1" title="ORDERS_3:NM.1">POSet_set</a><br/>  for <font color="Olive" title="b2">o1</font>, <font color="Olive" title="b3">o2</font> being   <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">Object</a> of <span class="p1">(<span class="default"><a href="orders_3.html#K4" title="ORDERS_3:func.4">POSAltCat</a> <font color="Olive" title="b1">P</font></span>)</span><br/>  for <font color="Olive" title="b4">A</font>, <font color="Olive" title="b5">B</font> being    <a href="orders_3.html#M1" title="ORDERS_3:mode.1">Element</a> of <font color="Olive" title="b1">P</font>  st <font color="Olive" title="b2">o1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">A</font> &amp; <font color="Olive" title="b3">o2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b5">B</font> holds <br/><span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Olive" title="b2">o1</font>,<font color="Olive" title="b3">o2</font></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="funct_2.html#K9" title="FUNCT_2:func.9">Funcs</a> ( the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b4">A</font>, the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b5">B</font>)</div></div>
