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<div><div><a NAME="S2"><span class="kw">scheme  </span><span class="comment"><font color="firebrick">:: ORDERS_5:sch 2</font></span><br/></a><span class="lab"><font color="Green" title="E2">RelStrMin</font></span>{ <font color="Maroon">F<sub>1</sub></font>() <span class="kw">-&gt; </span>  <a href="orders_2.html#V4" title="ORDERS_2:attr.4">transitive</a>   <a href="orders_5.html#V1" title="ORDERS_5:attr.1">connected</a>   <a href="orders_2.html#L1" title="ORDERS_2:struct.1">RelStr</a> , <font color="Maroon">F<sub>2</sub></font>() <span class="kw">-&gt; </span>  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon">F<sub>1</sub></font>(), <font color="Maroon">P<sub>1</sub></font>[  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon">F<sub>1</sub></font>()] } :<br/><div class="add"><a NAME="E2:57"/>
 ex <font color="Olive" title="b1">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon">F<sub>1</sub></font>() st <br/>( <font color="Olive" title="b1">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon">F<sub>2</sub></font>() &amp; <font color="Maroon">P<sub>1</sub></font>[<font color="Olive" title="b1">x</font>] &amp; (  for <font color="Olive" title="b2">y</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon">F<sub>1</sub></font>()  st <font color="Olive" title="b2">y</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon">F<sub>2</sub></font>() &amp; <font color="Olive" title="b2">y</font> <a href="orders_5.html#R4" title="ORDERS_5:pred.4">&lt;~</a> <font color="Olive" title="b1">x</font> holds <br/> not <font color="Maroon">P<sub>1</sub></font>[<font color="Olive" title="b2">y</font>] ) )
 </div><span class="kw">provided</span><div class="add"><a NAME="E1:57"/><span class="lab"><font color="Green" title="E19">A1</font></span>: 
 ex <font color="Olive" title="b1">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon">F<sub>1</sub></font>() st <br/>( <font color="Olive" title="b1">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon">F<sub>2</sub></font>() &amp; <font color="Maroon">P<sub>1</sub></font>[<font color="Olive" title="b1">x</font>] )
 </div></div></div>
