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<span class="kw">let </span><font color="Maroon" title="c1">N</font>, <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:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">N</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  implies ( <font color="Maroon" title="c2">M</font> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> <font color="Maroon" title="c2">M</font> <a href="card_2.html#K2" title="CARD_2:func.2">*`</a> <font color="Maroon" title="c1">N</font> &amp; <font color="Maroon" title="c2">M</font> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> <font color="Maroon" title="c1">N</font> <a href="card_2.html#K2" title="CARD_2:func.2">*`</a> <font color="Maroon" title="c2">M</font> ) )</span><br/>



<span class="kw">assume </span><a NAME="E1:169"/><span class="lab"><font color="Green" title="E81">A1</font></span>: 
<font color="Maroon" title="c1">N</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</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="c2">M</font> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> <font color="Maroon" title="c2">M</font> <a href="card_2.html#K2" title="CARD_2:func.2">*`</a> <font color="Maroon" title="c1">N</font> &amp; <font color="Maroon" title="c2">M</font> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> <font color="Maroon" title="c1">N</font> <a href="card_2.html#K2" title="CARD_2:func.2">*`</a> <font color="Maroon" title="c2">M</font> )</span><br/>

<a NAME="E2:169"/><span class="lab"><font color="Green" title="E82">A2</font></span>: 
 <a href="card_1.html#K1" title="CARD_1:func.1">card</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 class="kw">by</span> <span class="lab"><a class="ref" href="card_1.html#D5" title="CARD_1:def.5">CARD_1:def 5</a></span>;<br/>
<a NAME="E3:169"/>
 <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <font color="Maroon" title="c1">N</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">N</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="card_1.html#D5" title="CARD_1:def.5">CARD_1:def 5</a></span>;<br/>
<a NAME="E4:169"/><span class="kw">then </span><span class="lab"><font color="Green" title="E83">A3</font></span>: 
<font color="Maroon" title="c2">M</font> <a href="card_2.html#K2" title="CARD_2:func.2">*`</a> <font color="Maroon" title="c1">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"><font color="Maroon" title="c2">M</font> <a href="ordinal2.html#K11" title="ORDINAL2:func.11">*^</a> <font color="Maroon" title="c1">N</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:169"><span class="lab"><font color="Green" title="E82">A2</font></span></a>, <a class="ref" href="card_2.html#T25" title="CARD_2:th.25">CARD_2:25</a></span>;<br/>
<a NAME="E5:169"/>
<font color="Maroon" title="c2">M</font> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> <font color="Maroon" title="c2">M</font> <a href="ordinal2.html#K11" title="ORDINAL2:func.11">*^</a> <font color="Maroon" title="c1">N</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:169"><span class="lab"><font color="Green" title="E81">A1</font></span></a>, <a class="ref" href="ordinal3.html#T39" title="ORDINAL3:th.39">ORDINAL3:39</a></span>;<br/>
<span class="kw">hence </span><a NAME="E6:169"/>
( <font color="Maroon" title="c2">M</font> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> <font color="Maroon" title="c2">M</font> <a href="card_2.html#K2" title="CARD_2:func.2">*`</a> <font color="Maroon" title="c1">N</font> &amp; <font color="Maroon" title="c2">M</font> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> <font color="Maroon" title="c1">N</font> <a href="card_2.html#K2" title="CARD_2:func.2">*`</a> <font color="Maroon" title="c2">M</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:169"><span class="lab"><font color="Green" title="E82">A2</font></span></a>, <a class="txt" href="#E4:169"><span class="lab"><font color="Green" title="E83">A3</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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