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<span class="kw">let </span><font color="Maroon" title="c1">a</font>, <font color="Maroon" title="c2">b</font> be   <a href="card_5.html#NM1" title="CARD_5:NM.1">Aleph</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">a</font> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> <font color="Maroon" title="c2">b</font> implies  <a href="card_2.html#K3" title="CARD_2:func.3">exp</a> (<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_2.html#K3" title="CARD_2:func.3">exp</a> (2,<font color="Maroon" title="c2">b</font>) )</span><br/>



<a NAME="E1:41"/><span class="lab"><font color="Green" title="E31">A1</font></span>: 
 <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <span class="p1">(<span class="default"><a href="zfmisc_1.html#K1" title="ZFMISC_1:func.1">bool</a> <font color="Maroon" title="c1">a</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_2.html#K3" title="CARD_2:func.3">exp</a> (2,<span class="p1">(<span class="default"><a href="card_1.html#K1" title="CARD_1:func.1">card</a> <font color="Maroon" title="c1">a</font></span>)</span>)
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="card_2.html#T31" title="CARD_2:th.31">CARD_2:31</a></span>;<br/>
<a NAME="E2:41"/>
(  <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <font color="Maroon" title="c1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">a</font> &amp;  <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <font color="Maroon" title="c1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <span class="p1">(<span class="default"><a href="zfmisc_1.html#K1" title="ZFMISC_1:func.1">bool</a> <font color="Maroon" title="c1">a</font></span>)</span> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="card_1.html#T14" title="CARD_1:th.14">CARD_1:14</a>, <a class="ref" href="card_1.html#D2" title="CARD_1:def.2">CARD_1:def 2</a></span>;<br/>
<a NAME="E3:41"/><span class="kw">then </span><span class="lab"><font color="Green" title="E32">A2</font></span>: 
 <a href="card_2.html#K3" title="CARD_2:func.3">exp</a> (<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>) <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a>  <a href="card_2.html#K3" title="CARD_2:func.3">exp</a> (<span class="p1">(<span class="default"><a href="card_2.html#K3" title="CARD_2:func.3">exp</a> (2,<font color="Maroon" title="c1">a</font>)</span>)</span>,<font color="Maroon" title="c2">b</font>)
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:41"><span class="lab"><font color="Green" title="E31">A1</font></span></a>, <a class="ref" href="card_2.html#T92" title="CARD_2:th.92">CARD_2:92</a></span>;<br/>
<span class="kw">assume </span><a NAME="E4:41"/>
<font color="Maroon" title="c1">a</font> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> <font color="Maroon" title="c2">b</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="card_2.html#K3" title="CARD_2:func.3">exp</a> (<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_2.html#K3" title="CARD_2:func.3">exp</a> (2,<font color="Maroon" title="c2">b</font>)</span><br/>

<a NAME="E5:41"/><span class="kw">then </span><span class="lab"><font color="Green" title="E33">A3</font></span>: 
(  <a href="card_2.html#K3" title="CARD_2:func.3">exp</a> (<span class="p1">(<span class="default"><a href="card_2.html#K3" title="CARD_2:func.3">exp</a> (2,<font color="Maroon" title="c1">a</font>)</span>)</span>,<font color="Maroon" title="c2">b</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_2.html#K3" title="CARD_2:func.3">exp</a> (2,<span class="p1">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="card_2.html#K2" title="CARD_2:func.2">*`</a> <font color="Maroon" title="c2">b</font></span>)</span>) &amp; <font color="Maroon" title="c1">a</font> <a href="card_2.html#K2" title="CARD_2:func.2">*`</a> <font color="Maroon" title="c2">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">b</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="card_5.html#T18" target="_self" title="CARD_5:th.18">Th27</a>, <a class="ref" href="card_2.html#T30" title="CARD_2:th.30">CARD_2:30</a></span>;<br/>
<a NAME="E6:41"/>
2 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">a</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="card_5.html#E2"><span class="lab"><font color="Green" title="E2">Lm2</font></span></a>, <a class="ref" href="card_5.html#T16" target="_self" title="CARD_5:th.16">Th25</a></span>;<br/>
<a NAME="E7:41"/><span class="kw">then </span>
 <a href="card_2.html#K3" title="CARD_2:func.3">exp</a> (2,<font color="Maroon" title="c2">b</font>) <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a>  <a href="card_2.html#K3" title="CARD_2:func.3">exp</a> (<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>)
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="card_2.html#T92" title="CARD_2:th.92">CARD_2:92</a></span>;<br/>
<span class="kw">hence </span><a NAME="E8:41"/>
 <a href="card_2.html#K3" title="CARD_2:func.3">exp</a> (<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_2.html#K3" title="CARD_2:func.3">exp</a> (2,<font color="Maroon" title="c2">b</font>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:41"><span class="lab"><font color="Green" title="E32">A2</font></span></a>, <a class="txt" href="#E5:41"><span class="lab"><font color="Green" title="E33">A3</font></span></a>, <a class="ref" href="xboole_0.html#D10" title="XBOOLE_0:def.10">XBOOLE_0:def 10</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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