<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">a</font> be   <a href="card_5.html#NM1">Aleph</a>;<br/>

<a NAME="E1:36"/>
 <a href="card_1.html#K2">nextcard</a> <font color="Maroon">a</font> <a href="zfrefle1.html#R4">is_cofinal_with</a>  <a href="card_5.html#K1" target="_self">cf</a> <span class="p1">(<span class="default"><a href="card_1.html#K2">nextcard</a> <font color="Maroon">a</font></span>)</span>
 
<b>by </b><i/>;<br/>
<b>then consider </b><font color="Maroon">xi</font> being   <a href="ordinal2.html#NM1">Ordinal-Sequence</a><b> such that </b><br/><a NAME="E3:36"/><i><font color="Green">E23</font></i>: 
(  <a href="relat_1.html#K1">dom</a> <font color="Maroon">xi</font> <a href="hidden.html#R1">=</a>  <a href="card_5.html#K1" target="_self">cf</a> <span class="p1">(<span class="default"><a href="card_1.html#K2">nextcard</a> <font color="Maroon">a</font></span>)</span> &amp;  <a href="relat_1.html#K2">rng</a> <font color="Maroon">xi</font> <a href="tarski.html#R1">c=</a>  <a href="card_1.html#K2">nextcard</a> <font color="Maroon">a</font> &amp; <font color="Maroon">xi</font> is <a href="ordinal2.html#V2">increasing</a> &amp;  <a href="card_1.html#K2">nextcard</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a>  <a href="ordinal2.html#K4">sup</a> <font color="Maroon">xi</font> )
 <b>by </b><i><a class="ref" href="zfrefle1.html#D5">ZFREFLE1:def 5</a></i>;<br/>
<a NAME="E4:36"/><i><font color="Green">E24</font></i>: 
(  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="card_3.html#K1">Card</a> <font color="Maroon">xi</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">xi</font> &amp;  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_5.html#K1" target="_self">cf</a> <span class="p3">(<span class="default"><a href="card_1.html#K2">nextcard</a> <font color="Maroon">a</font></span>)</span></span>)</span> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">a</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="card_5.html#K1" target="_self">cf</a> <span class="p1">(<span class="default"><a href="card_1.html#K2">nextcard</a> <font color="Maroon">a</font></span>)</span> )
 
<b>by </b><i><a class="ref" href="card_3.html#D2">CARD_3:def 2</a>, <a class="ref" href="funcop_1.html#T19">FUNCOP_1:19</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="36_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:36_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="card_5.html#K1" target="_self">cf</a> <span class="p1">(<span class="default"><a href="card_1.html#K2">nextcard</a> <font color="Maroon">a</font></span>)</span>
 ;<br/><a NAME="E2:36_1"/><b>then </b><i><font color="Green">E25</font></i>: 
( <span class="p1">(<span class="default"><a href="card_3.html#K1">Card</a> <font color="Maroon">xi</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="card_1.html#K1">Card</a> <span class="p1">(<span class="default"><font color="Maroon">xi</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font></span>)</span> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_5.html#K1" target="_self">cf</a> <span class="p3">(<span class="default"><a href="card_1.html#K2">nextcard</a> <font color="Maroon">a</font></span>)</span></span>)</span> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">a</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> &amp; <font color="Maroon">xi</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">xi</font> )
 <b>by </b><i><a class="txt" href="card_5.html#E2:36_1"><i><font color="Green">E25</font></i></a>, <a class="ref" href="card_3.html#D2">CARD_3:def 2</a>, <a class="ref" href="funcop_1.html#T13">FUNCOP_1:13</a>, <a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/><b>then reconsider </b><font color="Maroon">A</font> = <font color="Maroon">xi</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> as   <a href="ordinal1.html#NM2">Ordinal</a> <b>by </b><i><a class="txt" href="card_5.html#E2:36_1"><i><font color="Green">E25</font></i></a>, <a class="ref" href="ordinal1.html#T23">ORDINAL1:23</a></i>;<br/><a NAME="E4:36_1"/>
 <a href="card_1.html#K1">Card</a> <font color="Maroon">A</font> <a href="ordinal1.html#R1">c=</a> <font color="Maroon">A</font>
 <b>by </b><i><a class="ref" href="card_1.html#T24">CARD_1:24</a></i>;<br/><a NAME="E5:36_1"/><b>then </b>
 <a href="card_1.html#K1">Card</a> <span class="p1">(<span class="default"><font color="Maroon">xi</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font></span>)</span> <a href="card_1.html#NR2" target="_self">&lt;`</a>  <a href="card_1.html#K2">nextcard</a> <font color="Maroon">a</font>
 <b>by </b><i><a class="txt" href="card_5.html#E2:36_1"><i><font color="Green">E25</font></i></a>, , <a class="ref" href="ordinal1.html#T22">ORDINAL1:22</a></i>;<br/><b>hence </b><a NAME="E6:36_1"/>
<span class="p1">(<span class="default"><a href="card_3.html#K1">Card</a> <font color="Maroon">xi</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_5.html#K1" target="_self">cf</a> <span class="p3">(<span class="default"><a href="card_1.html#K2">nextcard</a> <font color="Maroon">a</font></span>)</span></span>)</span> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">a</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
 <b>by </b><i>, <a class="ref" href="card_4.html#T23">CARD_4:23</a></i>;<br/></div><b>end;</b></div>
<a NAME="E6:36"/><b>then </b><i><font color="Green">E26</font></i>: 
(  <a href="card_1.html#K1">Card</a> <span class="p1">(<span class="default"><a href="card_3.html#K3">Union</a> <font color="Maroon">xi</font></span>)</span> <a href="card_1.html#NR1" target="_self">&lt;=`</a>  <a href="card_3.html#K6">Sum</a> <span class="p1">(<span class="default"><a href="card_3.html#K1">Card</a> <font color="Maroon">xi</font></span>)</span> &amp;  <a href="card_3.html#K6">Sum</a> <span class="p1">(<span class="default"><a href="card_3.html#K1">Card</a> <font color="Maroon">xi</font></span>)</span> <a href="card_1.html#NR1" target="_self">&lt;=`</a>  <a href="card_3.html#K6">Sum</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_5.html#K1" target="_self">cf</a> <span class="p3">(<span class="default"><a href="card_1.html#K2">nextcard</a> <font color="Maroon">a</font></span>)</span></span>)</span> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">a</font></span>)</span> &amp;  <a href="card_3.html#K6">Sum</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_5.html#K1" target="_self">cf</a> <span class="p3">(<span class="default"><a href="card_1.html#K2">nextcard</a> <font color="Maroon">a</font></span>)</span></span>)</span> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">a</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="card_5.html#K1" target="_self">cf</a> <span class="p2">(<span class="default"><a href="card_1.html#K2">nextcard</a> <font color="Maroon">a</font></span>)</span></span>)</span> <a href="card_2.html#K2">*`</a> <font color="Maroon">a</font> )
 
<b>by </b><i>, <a class="txt" href="card_5.html#E6:36"><i><font color="Green">E26</font></i></a>, <a class="ref" href="card_3.html#T43">CARD_3:43</a>, <a class="ref" href="card_3.html#T52">CARD_3:52</a>, <a class="ref" href="card_3.html#T54">CARD_3:54</a></i>;<br/>
<a NAME="E7:36"/>
 ex <font color="Olive">A</font> being  <a href="ordinal1.html#NM2">Ordinal</a> st  <a href="relat_1.html#K2">rng</a> <font color="Maroon">xi</font> <a href="tarski.html#R1">c=</a> <font color="Olive">A</font>
 
<b>by </b><i><a class="ref" href="ordinal2.html#D8">ORDINAL2:def 8</a></i>;<br/>
<a NAME="E8:36"/><b>then </b>
(  <a href="ordinal1.html#K3">On</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> <font color="Maroon">xi</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">xi</font> &amp;  <a href="ordinal2.html#K3">sup</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> <font color="Maroon">xi</font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="ordinal1.html#K1">succ</a> <span class="p1">(<span class="default"><a href="tarski.html#K3">union</a> <span class="p2">(<span class="default"><a href="ordinal1.html#K3">On</a> <span class="p3">(<span class="default"><a href="relat_1.html#K2">rng</a> <font color="Maroon">xi</font></span>)</span></span>)</span></span>)</span> &amp;  <a href="tarski.html#K3">union</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> <font color="Maroon">xi</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="card_3.html#K3">Union</a> <font color="Maroon">xi</font> &amp;  <a href="card_1.html#K1">Card</a> <span class="p1">(<span class="default"><a href="card_3.html#K3">Union</a> <font color="Maroon">xi</font></span>)</span> <a href="card_1.html#NR1" target="_self">&lt;=`</a> <span class="p1">(<span class="default"><a href="card_5.html#K1" target="_self">cf</a> <span class="p2">(<span class="default"><a href="card_1.html#K2">nextcard</a> <font color="Maroon">a</font></span>)</span></span>)</span> <a href="card_2.html#K2">*`</a> <font color="Maroon">a</font> &amp;  <a href="ordinal2.html#K3">sup</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> <font color="Maroon">xi</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="ordinal2.html#K4">sup</a> <font color="Maroon">xi</font> )
 
<b>by </b><i>, <a class="ref" href="ordinal3.html#T8">ORDINAL3:8</a>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a>, <a class="ref" href="zf_refle.html#T27">ZF_REFLE:27</a></i>;<br/>
<a NAME="E9:36"/><b>then </b><i><font color="Green">E42</font></i>: 
(  <a href="card_1.html#K1">Card</a> <span class="p1">(<span class="default"><a href="card_1.html#K2">nextcard</a> <font color="Maroon">a</font></span>)</span> <a href="card_1.html#NR1" target="_self">&lt;=`</a>  <a href="card_1.html#K1">Card</a> <span class="p1">(<span class="default"><a href="ordinal1.html#K1">succ</a> <span class="p2">(<span class="default"><a href="card_3.html#K3">Union</a> <font color="Maroon">xi</font></span>)</span></span>)</span> &amp;  <a href="card_1.html#K1">Card</a> <span class="p1">(<span class="default"><a href="card_1.html#K2">nextcard</a> <font color="Maroon">a</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="card_1.html#K2">nextcard</a> <font color="Maroon">a</font> &amp;  <a href="ordinal1.html#K1">succ</a> <span class="p1">(<span class="default"><a href="card_3.html#K3">Union</a> <font color="Maroon">xi</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="card_3.html#K3">Union</a> <font color="Maroon">xi</font></span>)</span> <a href="ordinal2.html#K10">+^</a> 1 &amp; <span class="p1">(<span class="default"><a href="card_1.html#K1">Card</a> <span class="p2">(<span class="default"><a href="card_3.html#K3">Union</a> <font color="Maroon">xi</font></span>)</span></span>)</span> <a href="card_2.html#K1">+`</a> 1 <a href="card_1.html#NR1" target="_self">&lt;=`</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_5.html#K1" target="_self">cf</a> <span class="p3">(<span class="default"><a href="card_1.html#K2">nextcard</a> <font color="Maroon">a</font></span>)</span></span>)</span> <a href="card_2.html#K2">*`</a> <font color="Maroon">a</font></span>)</span> <a href="card_2.html#K1">+`</a> 1 &amp;  <a href="card_1.html#K1">Card</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_3.html#K3">Union</a> <font color="Maroon">xi</font></span>)</span> <a href="ordinal2.html#K10">+^</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="card_1.html#K1">Card</a> <span class="p2">(<span class="default"><a href="card_3.html#K3">Union</a> <font color="Maroon">xi</font></span>)</span></span>)</span> <a href="card_2.html#K1">+`</a> <span class="p1">(<span class="default"><a href="card_1.html#K1">Card</a> 1</span>)</span> )
 
<b>by </b><i>, <a class="ref" href="card_1.html#T27">CARD_1:27</a>, <a class="ref" href="card_1.html#D5">CARD_1:def 5</a>, <a class="ref" href="card_2.html#T24">CARD_2:24</a>, <a class="ref" href="card_4.html#T42">CARD_4:42</a>, <a class="ref" href="ordinal2.html#T48">ORDINAL2:48</a></i>;<br/>
<a NAME="E10:36"/><b>then </b><i><font color="Green">E43</font></i>: 
(  <a href="card_1.html#K2">nextcard</a> <font color="Maroon">a</font> <a href="card_1.html#NR1" target="_self">&lt;=`</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_5.html#K1" target="_self">cf</a> <span class="p3">(<span class="default"><a href="card_1.html#K2">nextcard</a> <font color="Maroon">a</font></span>)</span></span>)</span> <a href="card_2.html#K2">*`</a> <font color="Maroon">a</font></span>)</span> <a href="card_2.html#K1">+`</a> 1 &amp;  <a href="card_5.html#K1" target="_self">cf</a> <span class="p1">(<span class="default"><a href="card_1.html#K2">nextcard</a> <font color="Maroon">a</font></span>)</span> <a href="card_1.html#NR1" target="_self">&lt;=`</a>  <a href="card_1.html#K2">nextcard</a> <font color="Maroon">a</font> )
 
<b>by </b><i>, <a class="ref" href="card_2.html#T19">CARD_2:19</a>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>
<a NAME="E11:36"/><i><font color="Green">E44</font></i>: 
<font color="Maroon">a</font>, <a href="card_5.html#K1" target="_self">cf</a> <span class="p1">(<span class="default"><a href="card_1.html#K2">nextcard</a> <font color="Maroon">a</font></span>)</span> <a href="xboole_0.html#R3">are_c=-comparable</a> 
 
<b>by </b><i><a class="ref" href="ordinal1.html#T25">ORDINAL1:25</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="36_2"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="36_2_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:36_2_1"/>
(  <a href="card_5.html#K1" target="_self">cf</a> <span class="p1">(<span class="default"><a href="card_1.html#K2">nextcard</a> <font color="Maroon">a</font></span>)</span> <a href="hidden.html#R1">=</a> 0 or  <a href="card_5.html#K1" target="_self">cf</a> <span class="p1">(<span class="default"><a href="card_1.html#K2">nextcard</a> <font color="Maroon">a</font></span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0 )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="36_2_1_1"><b>suppose </b></a><a NAME="E1:36_2_1_1"/>
 <a href="card_5.html#K1" target="_self">cf</a> <span class="p1">(<span class="default"><a href="card_1.html#K2">nextcard</a> <font color="Maroon">a</font></span>)</span> <a href="hidden.html#R1">=</a> 0
 ;<br/><div class="add"><a NAME="E2:36_2_1_1"/><b>then </b>
( <span class="p1">(<span class="default"><a href="card_5.html#K1" target="_self">cf</a> <span class="p2">(<span class="default"><a href="card_1.html#K2">nextcard</a> <font color="Maroon">a</font></span>)</span></span>)</span> <a href="card_2.html#K2">*`</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> 0 &amp; 0 <a href="card_2.html#K1">+`</a> 1 <a href="hidden.html#R1">=</a> 1 &amp; 1 <a href="card_1.html#NR2" target="_self">&lt;`</a>  <a href="card_1.html#K2">nextcard</a> <font color="Maroon">a</font> )
 <b>by </b><i>, , <a class="ref" href="card_2.html#T29">CARD_2:29</a>, <a class="ref" href="card_2.html#T32">CARD_2:32</a></i>;<br/><b>hence </b><a NAME="E3:36_2_1_1"/>
 <a href="card_5.html#K1" target="_self">cf</a> <span class="p1">(<span class="default"><a href="card_1.html#K2">nextcard</a> <font color="Maroon">a</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="card_1.html#K2">nextcard</a> <font color="Maroon">a</font>
 <b>by </b><i>, <a class="ref" href="card_1.html#T14">CARD_1:14</a>, <a class="ref" href="card_2.html#T19">CARD_2:19</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="36_2_1_2"><b>suppose </b></a><a NAME="E1:36_2_1_2"/><i><font color="Green">E45</font></i>: 
 <a href="card_5.html#K1" target="_self">cf</a> <span class="p1">(<span class="default"><a href="card_1.html#K2">nextcard</a> <font color="Maroon">a</font></span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 ;<br/><div class="add"><a NAME="E2:36_2_1_2"/>
0 <a href="card_1.html#NR1" target="_self">&lt;=`</a>  <a href="card_5.html#K1" target="_self">cf</a> <span class="p1">(<span class="default"><a href="card_1.html#K2">nextcard</a> <font color="Maroon">a</font></span>)</span>
 <b>by </b><i><a class="ref" href="xboole_1.html#T2">XBOOLE_1:2</a></i>;<br/><a NAME="E3:36_2_1_2"/><b>then </b>
( 0 <a href="card_1.html#NR2" target="_self">&lt;`</a>  <a href="card_5.html#K1" target="_self">cf</a> <span class="p1">(<span class="default"><a href="card_1.html#K2">nextcard</a> <font color="Maroon">a</font></span>)</span> &amp; 1 <a href="card_1.html#NR2" target="_self">&lt;`</a> <font color="Maroon">a</font> &amp; (  <a href="card_5.html#K1" target="_self">cf</a> <span class="p1">(<span class="default"><a href="card_1.html#K2">nextcard</a> <font color="Maroon">a</font></span>)</span> <a href="card_1.html#NR1" target="_self">&lt;=`</a> <font color="Maroon">a</font> or <font color="Maroon">a</font> <a href="card_1.html#NR1" target="_self">&lt;=`</a>  <a href="card_5.html#K1" target="_self">cf</a> <span class="p1">(<span class="default"><a href="card_1.html#K2">nextcard</a> <font color="Maroon">a</font></span>)</span> ) )
 <b>by </b><i>, , , , <a class="ref" href="card_1.html#T13">CARD_1:13</a>, <a class="ref" href="xboole_0.html#D9">XBOOLE_0:def 9</a></i>;<br/><a NAME="E4:36_2_1_2"/><b>then </b>
( ( <span class="p1">(<span class="default"><a href="card_5.html#K1" target="_self">cf</a> <span class="p2">(<span class="default"><a href="card_1.html#K2">nextcard</a> <font color="Maroon">a</font></span>)</span></span>)</span> <a href="card_2.html#K2">*`</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> &amp; <font color="Maroon">a</font> <a href="card_2.html#K1">+`</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> &amp; <font color="Maroon">a</font> <a href="card_1.html#NR2" target="_self">&lt;`</a>  <a href="card_1.html#K2">nextcard</a> <font color="Maroon">a</font> ) or ( <span class="p1">(<span class="default"><a href="card_5.html#K1" target="_self">cf</a> <span class="p2">(<span class="default"><a href="card_1.html#K2">nextcard</a> <font color="Maroon">a</font></span>)</span></span>)</span> <a href="card_2.html#K2">*`</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a>  <a href="card_5.html#K1" target="_self">cf</a> <span class="p1">(<span class="default"><a href="card_1.html#K2">nextcard</a> <font color="Maroon">a</font></span>)</span> &amp;  <a href="card_5.html#K1" target="_self">cf</a> <span class="p1">(<span class="default"><a href="card_1.html#K2">nextcard</a> <font color="Maroon">a</font></span>)</span> is   <a href="card_5.html#NM1">Aleph</a> ) )
 <b>by </b><i>, , <a class="ref" href="card_1.html#T32">CARD_1:32</a>, <a class="ref" href="card_4.html#T34">CARD_4:34</a>, <a class="ref" href="card_4.html#T78">CARD_4:78</a></i>;<br/><a NAME="E5:36_2_1_2"/><b>then </b>
(  <a href="card_1.html#K2">nextcard</a> <font color="Maroon">a</font> <a href="card_1.html#NR1" target="_self">&lt;=`</a> <span class="p1">(<span class="default"><a href="card_5.html#K1" target="_self">cf</a> <span class="p2">(<span class="default"><a href="card_1.html#K2">nextcard</a> <font color="Maroon">a</font></span>)</span></span>)</span> <a href="card_2.html#K1">+`</a> 1 &amp;  <a href="card_5.html#K1" target="_self">cf</a> <span class="p1">(<span class="default"><a href="card_1.html#K2">nextcard</a> <font color="Maroon">a</font></span>)</span> is   <a href="card_5.html#NM1">Aleph</a> &amp; 1 <a href="card_1.html#NR2" target="_self">&lt;`</a>  <a href="card_5.html#K1" target="_self">cf</a> <span class="p1">(<span class="default"><a href="card_1.html#K2">nextcard</a> <font color="Maroon">a</font></span>)</span> )
 <b>by </b><i>, , , <a class="ref" href="card_1.html#T14">CARD_1:14</a>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/><a NAME="E6:36_2_1_2"/><b>then </b>
 <a href="card_1.html#K2">nextcard</a> <font color="Maroon">a</font> <a href="card_1.html#NR1" target="_self">&lt;=`</a>  <a href="card_5.html#K1" target="_self">cf</a> <span class="p1">(<span class="default"><a href="card_1.html#K2">nextcard</a> <font color="Maroon">a</font></span>)</span>
 <b>by </b><i><a class="ref" href="card_4.html#T34">CARD_4:34</a></i>;<br/><b>hence </b><a NAME="E7:36_2_1_2"/>
 <a href="card_5.html#K1" target="_self">cf</a> <span class="p1">(<span class="default"><a href="card_1.html#K2">nextcard</a> <font color="Maroon">a</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="card_1.html#K2">nextcard</a> <font color="Maroon">a</font>
 <b>by </b><i>, <a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E13:36"/>
 <a href="card_5.html#K1" target="_self">cf</a> <span class="p1">(<span class="default"><a href="card_1.html#K2">nextcard</a> <font color="Maroon">a</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="card_1.html#K2">nextcard</a> <font color="Maroon">a</font>
 ;<br/>


</div>
