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<div><div><a NAME="S1"><span class="kw">scheme  </span><span class="comment"><font color="firebrick">:: ORDERS_5:sch 1</font></span><br/></a><span class="lab"><font color="Green" title="E1">Finite2</font></span>{ <font color="Maroon">F<sub>1</sub></font>() <span class="kw">-&gt; </span>   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> , <font color="Maroon">F<sub>2</sub></font>() <span class="kw">-&gt; </span>  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon">F<sub>1</sub></font>(), <font color="Maroon">P<sub>1</sub></font>[   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> ] } :<br/><div class="add"><a NAME="E4:9"/>
<font color="Maroon">P<sub>1</sub></font>[<font color="Maroon">F<sub>1</sub></font>()]
 </div><span class="kw">provided</span><div class="add"><a NAME="E1:9"/><span class="lab"><font color="Green" title="E3">A1</font></span>: 
<font color="Maroon">F<sub>1</sub></font>() is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> 
 <span class="kw">and </span><br/><a NAME="E2:9"/><span class="lab"><font color="Green" title="E4">A2</font></span>: 
<font color="Maroon">P<sub>1</sub></font>[<font color="Maroon">F<sub>2</sub></font>()]
 <span class="kw">and </span><br/><a NAME="E3:9"/><span class="lab"><font color="Green" title="E5">A3</font></span>: 
 for <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">C</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>   st <font color="Olive" title="b1">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon">F<sub>1</sub></font>() <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <font color="Maroon">F<sub>2</sub></font>() &amp; <font color="Maroon">F<sub>2</sub></font>() <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b2">C</font> &amp; <font color="Olive" title="b2">C</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon">F<sub>1</sub></font>() &amp; <font color="Maroon">P<sub>1</sub></font>[<font color="Olive" title="b2">C</font>] holds <br/><font color="Maroon">P<sub>1</sub></font>[<font color="Olive" title="b2">C</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Olive" title="b1">x</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>]
 </div></div></div>
