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<span class="kw">let </span><font color="Maroon" title="c1">M</font>, <font color="Maroon" title="c2">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"> ( <font color="Maroon" title="c1">M</font> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> <font color="Maroon" title="c1">M</font> <a href="card_2.html#K1" title="CARD_2:func.1">+`</a> <font color="Maroon" title="c2">N</font> &amp; <font color="Maroon" title="c2">N</font> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> <font color="Maroon" title="c1">M</font> <a href="card_2.html#K1" title="CARD_2:func.1">+`</a> <font color="Maroon" title="c2">N</font> )</span><br/>



<a NAME="E1:97"/><span class="lab"><font color="Green" title="E63">A1</font></span>: 
<font color="Maroon" title="c1">M</font> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> <font color="Maroon" title="c1">M</font> <a href="ordinal2.html#K10" title="ORDINAL2:func.10">+^</a> <font color="Maroon" title="c2">N</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="ordinal3.html#T24" title="ORDINAL3:th.24">ORDINAL3:24</a></span>;<br/>
<a NAME="E2:97"/><span class="lab"><font color="Green" title="E64">A2</font></span>: 
<font color="Maroon" title="c2">N</font> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> <font color="Maroon" title="c1">M</font> <a href="ordinal2.html#K10" title="ORDINAL2:func.10">+^</a> <font color="Maroon" title="c2">N</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="ordinal3.html#T24" title="ORDINAL3:th.24">ORDINAL3:24</a></span>;<br/>
<a NAME="E3:97"/><span class="lab"><font color="Green" title="E65">A3</font></span>: 
 <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <font color="Maroon" title="c2">N</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">N</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="card_1.html#D2" title="CARD_1:def.2">CARD_1:def 2</a></span>;<br/>
<a NAME="E4:97"/>
 <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <font color="Maroon" title="c1">M</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">M</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="card_1.html#D2" title="CARD_1:def.2">CARD_1:def 2</a></span>;<br/>
<a NAME="E5:97"/><span class="kw">then </span><span class="lab"><font color="Green" title="E66">A4</font></span>: 
<font color="Maroon" title="c1">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"><font color="Maroon" title="c1">M</font> <a href="ordinal2.html#K10" title="ORDINAL2:func.10">+^</a> <font color="Maroon" title="c2">N</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:97"><span class="lab"><font color="Green" title="E63">A1</font></span></a>, <a class="ref" href="card_1.html#T11" title="CARD_1:th.11">CARD_1:11</a></span>;<br/>
<a NAME="E6:97"/>
<font color="Maroon" title="c2">N</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"><font color="Maroon" title="c1">M</font> <a href="ordinal2.html#K10" title="ORDINAL2:func.10">+^</a> <font color="Maroon" title="c2">N</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:97"><span class="lab"><font color="Green" title="E64">A2</font></span></a>, <a class="txt" href="#E3:97"><span class="lab"><font color="Green" title="E65">A3</font></span></a>, <a class="ref" href="card_1.html#T11" title="CARD_1:th.11">CARD_1:11</a></span>;<br/>
<span class="kw">hence </span><a NAME="E7:97"/>
( <font color="Maroon" title="c1">M</font> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> <font color="Maroon" title="c1">M</font> <a href="card_2.html#K1" title="CARD_2:func.1">+`</a> <font color="Maroon" title="c2">N</font> &amp; <font color="Maroon" title="c2">N</font> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> <font color="Maroon" title="c1">M</font> <a href="card_2.html#K1" title="CARD_2:func.1">+`</a> <font color="Maroon" title="c2">N</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:97"><span class="lab"><font color="Green" title="E66">A4</font></span></a>, <a class="ref" href="card_3.html#D1" title="CARD_3:def.1">CARD_3:def 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/>


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