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<div><div><a NAME="S22"><span class="kw">scheme  </span><span class="comment"><font color="firebrick">:: FRAENKEL:sch 22</font></span><br/></a><span class="lab"><font color="Green" title="E22">CartFin</font></span>{ <font color="Maroon">F<sub>1</sub></font>() <span class="kw">-&gt; </span>  non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> , <font color="Maroon">F<sub>2</sub></font>() <span class="kw">-&gt; </span>  non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> , <font color="Maroon">F<sub>3</sub></font>() <span class="kw">-&gt; </span>   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> , <font color="Maroon">F<sub>4</sub></font>() <span class="kw">-&gt; </span>   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> , <font color="Maroon">F<sub>5</sub></font>(   <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> ,   <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> ) <span class="kw">-&gt; </span>   <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>  } :<br/><div class="add"><a NAME="E3:27"/>
<span class="p1"> { <span class="default"> <font color="Maroon">F<sub>5</sub></font>(<font color="Olive" title="b1">u</font>,<font color="Olive" title="b2">v</font>) where <font color="Olive" title="b1">u</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon">F<sub>1</sub></font>(), <font color="Olive" title="b2">v</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon">F<sub>2</sub></font>() : ( <font color="Olive" title="b1">u</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon">F<sub>3</sub></font>() &amp; <font color="Olive" title="b2">v</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon">F<sub>4</sub></font>() ) </span> } </span>  is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> 
 </div><span class="kw">provided</span><div class="add"><a NAME="E1:27"/><span class="lab"><font color="Green" title="E6">A1</font></span>: 
<font color="Maroon">F<sub>3</sub></font>() is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> 
 <span class="kw">and </span><br/><a NAME="E2:27"/><span class="lab"><font color="Green" title="E7">A2</font></span>: 
<font color="Maroon">F<sub>4</sub></font>() is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> 
 </div></div></div>
