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<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[  <a href="ordinal1.html#NM2">Ordinal</a>] <b>means </b><font color="Maroon">f</font>,<font color="Maroon">a<sub>1</sub></font> <a href="knaster.html#K3" target="_self">+.</a> <font color="Maroon">a</font> is   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>;<br/>
<a NAME="E1:27_1_1"/><i><font color="Green">E17</font></i>: 
<font color="Maroon">S<sub>1</sub></font>[ <a href="xboole_0.html#K1">{}</a> ]
 
<b>by </b><i/>;<br/>
<div><i><font color="Green">E21</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="27_1_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">O1</font> be   <a href="ordinal1.html#NM2">Ordinal</a>;<br/><b>assume </b><a NAME="E1:27_1_1_1"/>
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon">O1</font>]
 ;<br/><b>then reconsider </b><font color="Maroon">fa</font> = <font color="Maroon">f</font>,<font color="Maroon">O1</font> <a href="knaster.html#K3" target="_self">+.</a> <font color="Maroon">a</font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font> ;<br/><a NAME="E3:27_1_1_1"/>
<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">fa</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font>,<span class="p1">(<span class="default"><a href="ordinal1.html#K1">succ</a> <font color="Maroon">O1</font></span>)</span> <a href="knaster.html#K3" target="_self">+.</a> <font color="Maroon">a</font>
 <b>by </b><i><a class="ref" href="knaster.html#T1" target="_self">Th1</a></i>;<br/><b>hence </b><a NAME="E4:27_1_1_1"/>
<font color="Maroon">S<sub>1</sub></font>[ <a href="ordinal1.html#K1">succ</a> <font color="Maroon">O1</font>]
 ;<br/></div><b>end;</b></div>
<b>deffunc </b><font color="Maroon">H<sub>1</sub></font>(  <a href="ordinal1.html#NM2">Ordinal</a>) <b>-&gt; </b>   <a href="hidden.html#M1">set</a>  = <font color="Maroon">f</font>,<font color="Maroon">a<sub>1</sub></font> <a href="knaster.html#K3" target="_self">+.</a> <font color="Maroon">a</font>;<br/>
<div><i><font color="Green">E22</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="27_1_1_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">O1</font> be   <a href="ordinal1.html#NM2">Ordinal</a>;<br/><b>assume </b><a NAME="E1:27_1_1_2"/><i><font color="Green">E23</font></i>: 
( <font color="Maroon">O1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  &amp; <font color="Maroon">O1</font> <a href="ordinal1.html#NR2" target="_self">is_limit_ordinal</a>  &amp; ( for <font color="Olive">O2</font> being  <a href="ordinal1.html#NM2">Ordinal</a>  st <font color="Olive">O2</font> <a href="hidden.html#R2">in</a> <font color="Maroon">O1</font> holds <br/><font color="Maroon">S<sub>1</sub></font>[<font color="Olive">O2</font>] ) )
 ;<br/><b>consider </b><font color="Maroon">Ls</font> being   <a href="ordinal1.html#NM3">T-Sequence</a><b> such that </b><br/><a NAME="E3:27_1_1_2"/><i><font color="Green">E24</font></i>: 
(  <a href="relat_1.html#K1">dom</a> <font color="Maroon">Ls</font> <a href="hidden.html#R1">=</a> <font color="Maroon">O1</font> &amp; ( for <font color="Olive">O2</font> being  <a href="ordinal1.html#NM2">Ordinal</a>  st <font color="Olive">O2</font> <a href="hidden.html#R2">in</a> <font color="Maroon">O1</font> holds <br/><font color="Maroon">Ls</font> <a href="funct_1.html#K1">.</a> <font color="Olive">O2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive">O2</font>) ) )
 <b>from </b><i><a class="ref" href="ordinal2.html#S2">ORDINAL2:sch 2</a>();<br/></i><a NAME="E4:27_1_1_2"/>
<font color="Maroon">f</font>,<font color="Maroon">O1</font> <a href="knaster.html#K3" target="_self">+.</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a>  <a href="lattice3.html#K15">"\/"</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> <font color="Maroon">Ls</font></span>)</span>,<font color="Maroon">L</font>
 <b>by </b><i><a class="txt" href="knaster.html#E1:27_1_1_2"><i><font color="Green">E23</font></i></a>, <a class="txt" href="knaster.html#E3:27_1_1_2"><i><font color="Green">E24</font></i></a>, </i>;<br/><b>hence </b><a NAME="E5:27_1_1_2"/>
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon">O1</font>]
 ;<br/></div><b>end;</b></div>
<a NAME="E4:27_1_1"/>
for <font color="Olive">O</font> being  <a href="ordinal1.html#NM2">Ordinal</a> holds  <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">O</font>]
 
<b>from </b><i><a class="ref" href="ordinal2.html#S1">ORDINAL2:sch 1</a>(, <a class="txt" href="knaster.html#E2:27_1_1"><i><font color="Green">E21</font></i></a>, <a class="txt" href="knaster.html#E3:27_1_1"><i><font color="Green">E22</font></i></a>);<br/></i>
<b>hence </b><a NAME="E5:27_1_1"/>
<font color="Maroon">f</font>,<font color="Maroon">O</font> <a href="knaster.html#K3" target="_self">+.</a> <font color="Maroon">a</font> is   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>
 ;<br/>


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