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<div><div><a NAME="S3"><span class="kw">scheme  </span><span class="comment"><font color="firebrick">:: ZF_REFLE:sch 3</font></span><br/></a><span class="lab"><font color="Green" title="E3">UOSExist</font></span>{ <font color="Maroon">F<sub>1</sub></font>() <span class="kw">-&gt; </span>  <a href="classes2.html#NM1" title="CLASSES2:NM.1">Universe</a>, <font color="Maroon">F<sub>2</sub></font>() <span class="kw">-&gt; </span>  <a href="ordinal4.html#NM1" title="ORDINAL4:NM.1">Ordinal</a> of <font color="Maroon">F<sub>1</sub></font>(), <font color="Maroon">F<sub>3</sub></font>(  <a href="ordinal1.html#NM3" title="ORDINAL1:NM.3">Ordinal</a>,  <a href="ordinal1.html#NM3" title="ORDINAL1:NM.3">Ordinal</a>) <span class="kw">-&gt; </span>  <a href="ordinal4.html#NM1" title="ORDINAL4:NM.1">Ordinal</a> of <font color="Maroon">F<sub>1</sub></font>(), <font color="Maroon">F<sub>4</sub></font>(  <a href="ordinal1.html#NM3" title="ORDINAL1:NM.3">Ordinal</a>,  <a href="ordinal1.html#NM4" title="ORDINAL1:NM.4">Sequence</a>) <span class="kw">-&gt; </span>  <a href="ordinal4.html#NM1" title="ORDINAL4:NM.1">Ordinal</a> of <font color="Maroon">F<sub>1</sub></font>() } :<br/><div class="add"><a NAME="E1:9"/>
 ex <font color="Olive" title="b1">phi</font> being   <a href="ordinal4.html#NM2" title="ORDINAL4:NM.2">Ordinal-Sequence</a> of <font color="Maroon">F<sub>1</sub></font>() st <br/>( <font color="Olive" title="b1">phi</font> <a href="ordinal4.html#K4" title="ORDINAL4:func.4">.</a> <span class="p1">(<span class="default"><a href="ordinal4.html#K2" title="ORDINAL4:func.2">0-element_of</a> <font color="Maroon">F<sub>1</sub></font>()</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">F<sub>2</sub></font>() &amp; (  for <font color="Olive" title="b2">a</font> being   <a href="ordinal4.html#NM1" title="ORDINAL4:NM.1">Ordinal</a> of <font color="Maroon">F<sub>1</sub></font>() holds  <font color="Olive" title="b1">phi</font> <a href="ordinal4.html#K4" title="ORDINAL4:func.4">.</a> <span class="p1">(<span class="default"><a href="ordinal4.html#K6" title="ORDINAL4:func.6">succ</a> <font color="Olive" title="b2">a</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">F<sub>3</sub></font>(<font color="Olive" title="b2">a</font>,<span class="p1">(<span class="default"><font color="Olive" title="b1">phi</font> <a href="ordinal4.html#K4" title="ORDINAL4:func.4">.</a> <font color="Olive" title="b2">a</font></span>)</span>) ) &amp; (  for <font color="Olive" title="b2">a</font> being   <a href="ordinal4.html#NM1" title="ORDINAL4:NM.1">Ordinal</a> of <font color="Maroon">F<sub>1</sub></font>()  st <font color="Olive" title="b2">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="ordinal4.html#K2" title="ORDINAL4:func.2">0-element_of</a> <font color="Maroon">F<sub>1</sub></font>() &amp; <font color="Olive" title="b2">a</font> is  <a href="ordinal1.html#V4" title="ORDINAL1:attr.4">limit_ordinal</a>  holds <br/><font color="Olive" title="b1">phi</font> <a href="ordinal4.html#K4" title="ORDINAL4:func.4">.</a> <font color="Olive" title="b2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">F<sub>4</sub></font>(<font color="Olive" title="b2">a</font>,<span class="p1">(<span class="default"><font color="Olive" title="b1">phi</font> <a href="relset_1.html#K5" title="RELSET_1:func.5">|</a> <font color="Olive" title="b2">a</font></span>)</span>) ) )
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