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<div><span class="kw">theorem </span><a NAME="T39"><span class="comment"><font color="firebrick">:: PCS_0:39</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">P</font>, <font color="Olive" title="b2">Q</font> being    <a href="pcs_0.html#L2" title="PCS_0:struct.2">pcs-Str</a> <br/>  for <font color="Olive" title="b3">p</font>, <font color="Olive" title="b4">q</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><font color="Olive" title="b1">P</font> <a href="pcs_0.html#K24" title="PCS_0:func.24">--&gt;</a> <font color="Olive" title="b2">Q</font></span>)</span><br/>  for <font color="Olive" title="b5">p1</font>, <font color="Olive" title="b6">p2</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">P</font><br/>  for <font color="Olive" title="b7">q1</font>, <font color="Olive" title="b8">q2</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b2">Q</font>  st <font color="Olive" title="b3">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b5">p1</font>,<font color="Olive" title="b7">q1</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> &amp; <font color="Olive" title="b4">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b6">p2</font>,<font color="Olive" title="b8">q2</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> holds <br/>( <font color="Olive" title="b3">p</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Olive" title="b4">q</font> iff ( <font color="Olive" title="b6">p2</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Olive" title="b5">p1</font> &amp; <font color="Olive" title="b7">q1</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Olive" title="b8">q2</font> ) )</div></div>
