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

<b>let </b><font color="Maroon" title="c2">M</font> be   <a href="card_1.html#NM1" title="CARD_1:NM.1">Cardinal</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( not <font color="Maroon" title="c2">M</font> is <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> implies <font color="Maroon" title="c2">M</font> <a href="card_2.html#K1" title="CARD_2:func.1">+`</a> <font color="Maroon" title="c2">M</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">M</font> )</span><br/>

<b>assume </b><a NAME="E1:21"/>
not <font color="Maroon" title="c2">M</font> is <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">M</font> <a href="card_2.html#K1" title="CARD_2:func.1">+`</a> <font color="Maroon" title="c2">M</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">M</font></span><br/>

<a NAME="E2:21"/><b>then </b>
<font color="Maroon" title="c2">M</font> <a href="ordinal1.html#NR2" title="ORDINAL1:NR.2">is_limit_ordinal</a> 
 
<b>by </b><i><a class="ref" href="card_4.html#T32" target="_self" title="CARD_4:th.32">Th32</a></i>;<br/>
<a NAME="E3:21"/><b>then </b>
<font color="Maroon" title="c2">M</font> <a href="ordinal2.html#K11" title="ORDINAL2:func.11">*^</a> <span class="p1">(<span class="default"><a href="ordinal1.html#K1" title="ORDINAL1:func.1">succ</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">M</font>
 
<b>by </b><i><a class="ref" href="card_4.html#T30" target="_self" title="CARD_4:th.30">Th30</a></i>;<br/>
<b>then </b> <a href="card_1.html#K1" title="CARD_1:func.1">Card</a> <font color="Maroon" title="c2">M</font> = 
<span class="p1">(<span class="default"><a href="card_1.html#K1" title="CARD_1:func.1">Card</a> <span class="p2">(<span class="default"><a href="ordinal1.html#K1" title="ORDINAL1:func.1">succ</a> 1</span>)</span></span>)</span> <a href="card_2.html#K2" title="CARD_2:func.2">*`</a> <span class="p1">(<span class="default"><a href="card_1.html#K1" title="CARD_1:func.1">Card</a> <font color="Maroon" title="c2">M</font></span>)</span>
<b>by </b><i><a class="ref" href="card_2.html#T25" title="CARD_2:th.25">CARD_2:25</a></i>
<br/>.= 
 <a href="card_1.html#K1" title="CARD_1:func.1">Card</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ordinal1.html#K1" title="ORDINAL1:func.1">succ</a> 1</span>)</span> <a href="ordinal2.html#K11" title="ORDINAL2:func.11">*^</a> <font color="Maroon" title="c2">M</font></span>)</span>
<b>by </b><i><a class="ref" href="card_2.html#T25" title="CARD_2:th.25">CARD_2:25</a></i>
<br/>.= 
 <a href="card_1.html#K1" title="CARD_1:func.1">Card</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="ordinal2.html#K11" title="ORDINAL2:func.11">*^</a> <font color="Maroon" title="c2">M</font></span>)</span> <a href="ordinal2.html#K10" title="ORDINAL2:func.10">+^</a> <font color="Maroon" title="c2">M</font></span>)</span>
<b>by </b><i><a class="ref" href="ordinal2.html#T53" title="ORDINAL2:th.53">ORDINAL2:53</a></i>
<br/>.= 
 <a href="card_1.html#K1" title="CARD_1:func.1">Card</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">M</font> <a href="ordinal2.html#K10" title="ORDINAL2:func.10">+^</a> <font color="Maroon" title="c2">M</font></span>)</span>
<b>by </b><i><a class="ref" href="ordinal2.html#T56" title="ORDINAL2:th.56">ORDINAL2:56</a></i>
<br/>.= 
<font color="Maroon" title="c2">M</font> <a href="card_2.html#K1" title="CARD_2:func.1">+`</a> <font color="Maroon" title="c2">M</font>
<b>by </b><i><a class="ref" href="card_2.html#D1" title="CARD_2:def.1">CARD_2:def 1</a></i>
;<br/>
<b>hence </b><a NAME="E5:21"/>
<font color="Maroon" title="c2">M</font> <a href="card_2.html#K1" title="CARD_2:func.1">+`</a> <font color="Maroon" title="c2">M</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">M</font>
 <b>by </b><i><a class="ref" href="card_1.html#D5" title="CARD_1:def.5">CARD_1:def 5</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
