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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="Red">::  thesis: </font></span></a><span class="hide"> ( ( ( <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> ) ) implies ( <font color="Maroon" title="c1">K</font> <a href="card_2.html#K2" title="CARD_2:func.2">*`</a> <font color="Maroon" title="c3">M</font> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> <font color="Maroon" title="c2">L</font> <a href="card_2.html#K2" title="CARD_2:func.2">*`</a> <font color="Maroon" title="c4">N</font> &amp; <font color="Maroon" title="c3">M</font> <a href="card_2.html#K2" title="CARD_2:func.2">*`</a> <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> <a href="card_2.html#K2" title="CARD_2:func.2">*`</a> <font color="Maroon" title="c4">N</font> ) )</span><br/>







<span class="kw">assume </span><a NAME="E1:165"/><span class="lab"><font color="Green" title="E79">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="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">K</font> <a href="card_2.html#K2" title="CARD_2:func.2">*`</a> <font color="Maroon" title="c3">M</font> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> <font color="Maroon" title="c2">L</font> <a href="card_2.html#K2" title="CARD_2:func.2">*`</a> <font color="Maroon" title="c4">N</font> &amp; <font color="Maroon" title="c3">M</font> <a href="card_2.html#K2" title="CARD_2:func.2">*`</a> <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> <a href="card_2.html#K2" title="CARD_2:func.2">*`</a> <font color="Maroon" title="c4">N</font> )</span><br/>

<a NAME="E2:165"/><span class="lab"><font color="Green" title="E80">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="#E1:165"><span class="lab"><font color="Green" title="E79">A1</font></span></a>, <a class="ref" href="card_1.html#T13" title="CARD_1:th.13">CARD_1:13</a></span>;<br/>
<a NAME="E3:165"/><span class="lab"><font color="Green" title="E81">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="#E1:165"><span class="lab"><font color="Green" title="E79">A1</font></span></a>, <a class="ref" href="card_1.html#T13" title="CARD_1:th.13">CARD_1:13</a></span>;<br/>
<a NAME="E4:165"/><span class="lab"><font color="Green" title="E82">A4</font></span>: 
<font color="Maroon" title="c1">K</font> <a href="card_2.html#K2" title="CARD_2:func.2">*`</a> <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"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Maroon" title="c1">K</font>,<font color="Maroon" title="c3">M</font></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#D2" title="CARD_2:def.2">CARD_2:def 2</a></span>;<br/>
<a NAME="E5:165"/><span class="lab"><font color="Green" title="E83">A5</font></span>: 
<font color="Maroon" title="c2">L</font> <a href="card_2.html#K2" title="CARD_2:func.2">*`</a> <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"><font color="Maroon" title="c2">L</font>,<font color="Maroon" title="c4">N</font></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#D2" title="CARD_2:def.2">CARD_2:def 2</a></span>;<br/>
<a NAME="E6:165"/><span class="lab"><font color="Green" title="E84">A6</font></span>: 
<span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Maroon" title="c1">K</font>,<font color="Maroon" title="c3">M</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Maroon" title="c2">L</font>,<font color="Maroon" title="c4">N</font></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="#E2:165"><span class="lab"><font color="Green" title="E80">A2</font></span></a>, <a class="txt" href="#E3:165"><span class="lab"><font color="Green" title="E81">A3</font></span></a>, <a class="ref" href="zfmisc_1.html#T119" title="ZFMISC_1:th.119">ZFMISC_1:119</a></span>;<br/>
<span class="kw">hence </span><a NAME="E7:165"/>
<font color="Maroon" title="c1">K</font> <a href="card_2.html#K2" title="CARD_2:func.2">*`</a> <font color="Maroon" title="c3">M</font> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> <font color="Maroon" title="c2">L</font> <a href="card_2.html#K2" title="CARD_2:func.2">*`</a> <font color="Maroon" title="c4">N</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:165"><span class="lab"><font color="Green" title="E82">A4</font></span></a>, <a class="txt" href="#E5:165"><span class="lab"><font color="Green" title="E83">A5</font></span></a>, <a class="ref" href="card_1.html#T27" title="CARD_1:th.27">CARD_1:27</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c3">M</font> <a href="card_2.html#K2" title="CARD_2:func.2">*`</a> <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> <a href="card_2.html#K2" title="CARD_2:func.2">*`</a> <font color="Maroon" title="c4">N</font></span><br/>

<span class="kw">thus </span><a NAME="E8:165"/>
<font color="Maroon" title="c3">M</font> <a href="card_2.html#K2" title="CARD_2:func.2">*`</a> <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> <a href="card_2.html#K2" title="CARD_2:func.2">*`</a> <font color="Maroon" title="c4">N</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:165"><span class="lab"><font color="Green" title="E82">A4</font></span></a>, <a class="txt" href="#E5:165"><span class="lab"><font color="Green" title="E83">A5</font></span></a>, <a class="txt" href="#E6:165"><span class="lab"><font color="Green" title="E84">A6</font></span></a>, <a class="ref" href="card_1.html#T27" title="CARD_1:th.27">CARD_1:27</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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