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<span class="kw">let </span><font color="Maroon" title="c1">K</font>, <font color="Maroon" title="c2">L</font>, <font color="Maroon" title="c3">M</font>, <font color="Maroon" title="c4">N</font> be   <a href="card_1.html#NM1" title="CARD_1:NM.1">Cardinal</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( (  not <!--HUMANRECFAILED-->( <font color="Maroon" title="c1">K</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">L</font> &amp; <font color="Maroon" title="c3">M</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">N</font> ) &amp;  not <!--HUMANRECFAILED-->( <font color="Maroon" title="c1">K</font> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> <font color="Maroon" title="c2">L</font> &amp; <font color="Maroon" title="c3">M</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">N</font> ) &amp;  not <!--HUMANRECFAILED-->( <font color="Maroon" title="c1">K</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">L</font> &amp; <font color="Maroon" title="c3">M</font> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> <font color="Maroon" title="c4">N</font> ) &amp;  not <!--HUMANRECFAILED-->( <font color="Maroon" title="c1">K</font> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> <font color="Maroon" title="c2">L</font> &amp; <font color="Maroon" title="c3">M</font> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> <font color="Maroon" title="c4">N</font> ) ) or <font color="Maroon" title="c1">K</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  or  <a href="card_2.html#K3" title="CARD_2:func.3">exp</a> (<font color="Maroon" title="c1">K</font>,<font color="Maroon" title="c3">M</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="c2">L</font>,<font color="Maroon" title="c4">N</font>) )</span><br/>







<span class="kw">assume </span><a NAME="E1:95"/><span class="lab"><font color="Green" title="E62">A1</font></span>: 
( ( <font color="Maroon" title="c1">K</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">L</font> &amp; <font color="Maroon" title="c3">M</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">N</font> ) or ( <font color="Maroon" title="c1">K</font> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> <font color="Maroon" title="c2">L</font> &amp; <font color="Maroon" title="c3">M</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">N</font> ) or ( <font color="Maroon" title="c1">K</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">L</font> &amp; <font color="Maroon" title="c3">M</font> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> <font color="Maroon" title="c4">N</font> ) or ( <font color="Maroon" title="c1">K</font> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> <font color="Maroon" title="c2">L</font> &amp; <font color="Maroon" title="c3">M</font> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> <font color="Maroon" title="c4">N</font> ) )
 ; <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">K</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  or  <a href="card_2.html#K3" title="CARD_2:func.3">exp</a> (<font color="Maroon" title="c1">K</font>,<font color="Maroon" title="c3">M</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="c2">L</font>,<font color="Maroon" title="c4">N</font>) )</span><br/>

<a NAME="E2:95"/><span class="lab"><font color="Green" title="E63">A2</font></span>: 
<font color="Maroon" title="c1">K</font> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> <font color="Maroon" title="c2">L</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:95"><span class="lab"><font color="Green" title="E62">A1</font></span></a>, <a class="ref" href="card_1.html#T3" title="CARD_1:th.3">CARD_1:3</a></span>;<br/>
<a NAME="E3:95"/><span class="lab"><font color="Green" title="E64">A3</font></span>: 
<font color="Maroon" title="c3">M</font> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> <font color="Maroon" title="c4">N</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:95"><span class="lab"><font color="Green" title="E62">A1</font></span></a>, <a class="ref" href="card_1.html#T3" title="CARD_1:th.3">CARD_1:3</a></span>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="95_1"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:95_1"/>
<font color="Maroon" title="c2">L</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</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">K</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  or  <a href="card_2.html#K3" title="CARD_2:func.3">exp</a> (<font color="Maroon" title="c1">K</font>,<font color="Maroon" title="c3">M</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="c2">L</font>,<font color="Maroon" title="c4">N</font>) )</span><br/><a NAME="E2:95_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E65">A4</font></span>: 
 <a href="funct_2.html#K1" title="FUNCT_2:func.1">Funcs</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c4">N</font> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <font color="Maroon" title="c3">M</font></span>)</span>,<font color="Maroon" title="c2">L</font>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#T8" title="FUNCT_2:th.8">FUNCT_2:8</a></span>;<br/><a NAME="E3:95_1"/>
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a>  <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <span class="p1">(<span class="default"><a href="funct_2.html#K1" title="FUNCT_2:func.1">Funcs</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c4">N</font> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <font color="Maroon" title="c3">M</font></span>)</span>,<font color="Maroon" title="c2">L</font>)</span>)</span>
 ;<br/><a NAME="E4:95_1"/><span class="kw">then </span>
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <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="funct_2.html#K1" title="FUNCT_2:func.1">Funcs</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c4">N</font> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <font color="Maroon" title="c3">M</font></span>)</span>,<font color="Maroon" title="c2">L</font>)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:95_1"><span class="lab"><font color="Green" title="E65">A4</font></span></a>, <a class="ref" href="card_1.html#T3" title="CARD_1:th.3">CARD_1:3</a></span>;<br/><a NAME="E5:95_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E66">A5</font></span>: 
 <a href="card_1.html#K2" title="CARD_1:func.2">nextcard</a> <span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a>  <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <span class="p1">(<span class="default"><a href="funct_2.html#K1" title="FUNCT_2:func.1">Funcs</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c4">N</font> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <font color="Maroon" title="c3">M</font></span>)</span>,<font color="Maroon" title="c2">L</font>)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="card_1.html#D3" title="CARD_1:def.3">CARD_1:def 3</a></span>;<br/><a NAME="E6:95_1"/>
<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 ;<br/><a NAME="E7:95_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E67">A6</font></span>: 
1 <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a>  <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <span class="p1">(<span class="default"><a href="funct_2.html#K1" title="FUNCT_2:func.1">Funcs</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c4">N</font> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <font color="Maroon" title="c3">M</font></span>)</span>,<font color="Maroon" title="c2">L</font>)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:95_1"><span class="lab"><font color="Green" title="E66">A5</font></span></a>, <a class="txt" href="card_2.html#E78"><span class="lab"><font color="Green" title="E46">Lm3</font></span></a>, <a class="ref" href="nat_1.html#T42" title="NAT_1:th.42">NAT_1:42</a></span>;<br/><a NAME="E8:95_1"/><span class="lab"><font color="Green" title="E68">A7</font></span>: 
<font color="Maroon" title="c3">M</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <font color="Maroon" title="c4">N</font> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <font color="Maroon" title="c3">M</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_1.html#T79" title="XBOOLE_1:th.79">XBOOLE_1:79</a></span>;<br/><a NAME="E9:95_1"/><span class="lab"><font color="Green" title="E69">A8</font></span>: 
 <a href="card_2.html#K3" title="CARD_2:func.3">exp</a> (<font color="Maroon" title="c1">K</font>,<font color="Maroon" title="c3">M</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <span class="p1">(<span class="default"><a href="funct_2.html#K1" title="FUNCT_2:func.1">Funcs</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c1">K</font>)</span>)</span>
 ;<br/><a NAME="E10:95_1"/><span class="lab"><font color="Green" title="E70">A9</font></span>: 
 <a href="card_2.html#K3" title="CARD_2:func.3">exp</a> (<font color="Maroon" title="c2">L</font>,<font color="Maroon" title="c4">N</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <span class="p1">(<span class="default"><a href="funct_2.html#K1" title="FUNCT_2:func.1">Funcs</a> (<font color="Maroon" title="c4">N</font>,<font color="Maroon" title="c2">L</font>)</span>)</span>
 ;<br/><a NAME="E11:95_1"/><span class="lab"><font color="Green" title="E71">A10</font></span>: 
<font color="Maroon" title="c4">N</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">M</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">N</font> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <font color="Maroon" title="c3">M</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:95"><span class="lab"><font color="Green" title="E64">A3</font></span></a>, <a class="ref" href="xboole_1.html#T45" title="XBOOLE_1:th.45">XBOOLE_1:45</a></span>;<br/><a NAME="E12:95_1"/>
 <a href="funct_2.html#K1" title="FUNCT_2:func.1">Funcs</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c1">K</font>) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="funct_2.html#K1" title="FUNCT_2:func.1">Funcs</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c2">L</font>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:95"><span class="lab"><font color="Green" title="E63">A2</font></span></a>, <a class="ref" href="funct_5.html#T56" title="FUNCT_5:th.56">FUNCT_5:56</a></span>;<br/><a NAME="E13:95_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E72">A11</font></span>: 
 <a href="card_2.html#K3" title="CARD_2:func.3">exp</a> (<font color="Maroon" title="c1">K</font>,<font color="Maroon" title="c3">M</font>) <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a>  <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <span class="p1">(<span class="default"><a href="funct_2.html#K1" title="FUNCT_2:func.1">Funcs</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c2">L</font>)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:95_1"><span class="lab"><font color="Green" title="E69">A8</font></span></a>, <a class="ref" href="card_1.html#T11" title="CARD_1:th.11">CARD_1:11</a></span>;<br/><a NAME="E14:95_1"/><span class="lab"><font color="Green" title="E73">A12</font></span>: 
 <a href="card_2.html#K3" title="CARD_2:func.3">exp</a> (<font color="Maroon" title="c2">L</font>,<font color="Maroon" title="c4">N</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="funct_2.html#K1" title="FUNCT_2:func.1">Funcs</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c2">L</font>)</span>)</span>,<span class="p2">(<span class="default"><a href="funct_2.html#K1" title="FUNCT_2:func.1">Funcs</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c4">N</font> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <font color="Maroon" title="c3">M</font></span>)</span>,<font color="Maroon" title="c2">L</font>)</span>)</span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:95_1"><span class="lab"><font color="Green" title="E68">A7</font></span></a>, <a class="txt" href="#E10:95_1"><span class="lab"><font color="Green" title="E70">A9</font></span></a>, <a class="txt" href="#E11:95_1"><span class="lab"><font color="Green" title="E71">A10</font></span></a>, <a class="ref" href="funct_5.html#T62" title="FUNCT_5:th.62">FUNCT_5:62</a></span>;<br/><a NAME="E15:95_1"/><span class="lab"><font color="Green" title="E74">A13</font></span>: 
 <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="funct_2.html#K1" title="FUNCT_2:func.1">Funcs</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c2">L</font>)</span>)</span>,<span class="p2">(<span class="default"><a href="funct_2.html#K1" title="FUNCT_2:func.1">Funcs</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c4">N</font> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <font color="Maroon" title="c3">M</font></span>)</span>,<font color="Maroon" title="c2">L</font>)</span>)</span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K1" title="CARD_1:func.1">card</a> <span class="p3">(<span class="default"><a href="funct_2.html#K1" title="FUNCT_2:func.1">Funcs</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c2">L</font>)</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="card_1.html#K1" title="CARD_1:func.1">card</a> <span class="p3">(<span class="default"><a href="funct_2.html#K1" title="FUNCT_2:func.1">Funcs</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c4">N</font> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <font color="Maroon" title="c3">M</font></span>)</span>,<font color="Maroon" title="c2">L</font>)</span>)</span></span>)</span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="card_2.html#T7" target="_self" title="CARD_2:th.7">Th14</a></span>;<br/><a NAME="E16:95_1"/>
<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="funct_2.html#K1" title="FUNCT_2:func.1">Funcs</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c2">L</font>)</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> <span class="p2">(<span class="default"><a href="funct_2.html#K1" title="FUNCT_2:func.1">Funcs</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c4">N</font> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <font color="Maroon" title="c3">M</font></span>)</span>,<font color="Maroon" title="c2">L</font>)</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K1" title="CARD_1:func.1">card</a> <span class="p3">(<span class="default"><a href="funct_2.html#K1" title="FUNCT_2:func.1">Funcs</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c2">L</font>)</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="card_1.html#K1" title="CARD_1:func.1">card</a> <span class="p3">(<span class="default"><a href="funct_2.html#K1" title="FUNCT_2:func.1">Funcs</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c4">N</font> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <font color="Maroon" title="c3">M</font></span>)</span>,<font color="Maroon" title="c2">L</font>)</span>)</span></span>)</span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="card_3.html#D2" title="CARD_3:def.2">CARD_3:def 2</a></span>;<br/><a NAME="E17:95_1"/><span class="kw">then </span>
1 <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> <span class="p2">(<span class="default"><a href="funct_2.html#K1" title="FUNCT_2:func.1">Funcs</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c2">L</font>)</span>)</span></span>)</span> <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="c2">L</font>,<font color="Maroon" title="c4">N</font>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:95_1"><span class="lab"><font color="Green" title="E67">A6</font></span></a>, <a class="txt" href="#E14:95_1"><span class="lab"><font color="Green" title="E73">A12</font></span></a>, <a class="txt" href="#E15:95_1"><span class="lab"><font color="Green" title="E74">A13</font></span></a>, <a class="ref" href="card_2.html#T90" target="_self" title="CARD_2:th.90">Th136</a></span>;<br/><a NAME="E18:95_1"/><span class="kw">then </span>
 <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <span class="p1">(<span class="default"><a href="funct_2.html#K1" title="FUNCT_2:func.1">Funcs</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c2">L</font>)</span>)</span> <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="c2">L</font>,<font color="Maroon" title="c4">N</font>)
 <span class="kw">by</span> <span class="lab"><a class="ref" href="card_2.html#T21" target="_self" title="CARD_2:th.21">Th33</a></span>;<br/><span class="kw">hence </span><a NAME="E19:95_1"/>
( <font color="Maroon" title="c1">K</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  or  <a href="card_2.html#K3" title="CARD_2:func.3">exp</a> (<font color="Maroon" title="c1">K</font>,<font color="Maroon" title="c3">M</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="c2">L</font>,<font color="Maroon" title="c4">N</font>) )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:95_1"><span class="lab"><font color="Green" title="E72">A11</font></span></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</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/></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E5:95"/>
( <font color="Maroon" title="c1">K</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  or  <a href="card_2.html#K3" title="CARD_2:func.3">exp</a> (<font color="Maroon" title="c1">K</font>,<font color="Maroon" title="c3">M</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="c2">L</font>,<font color="Maroon" title="c4">N</font>) )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:95"><span class="lab"><font color="Green" title="E62">A1</font></span></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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