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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="Red">::  thesis: </font></span></a><span class="hide"> ( not <font color="Maroon" title="c1">M</font> is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>  &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> or <font color="Maroon" title="c2">N</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">M</font> ) implies ( <font color="Maroon" title="c1">M</font> <a href="card_2.html#K2" title="CARD_2:func.2">*`</a> <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> &amp; <font color="Maroon" title="c2">N</font> <a href="card_2.html#K2" title="CARD_2:func.2">*`</a> <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> ) )</span><br/>



<span class="kw">assume </span><a NAME="E1:81"/>
( not <font color="Maroon" title="c1">M</font> is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>  &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> or <font color="Maroon" title="c2">N</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">M</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">M</font> <a href="card_2.html#K2" title="CARD_2:func.2">*`</a> <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> &amp; <font color="Maroon" title="c2">N</font> <a href="card_2.html#K2" title="CARD_2:func.2">*`</a> <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> )</span><br/>

<a NAME="E2:81"/><span class="kw">then </span>
( <font color="Maroon" title="c1">M</font> <a href="card_2.html#K2" title="CARD_2:func.2">*`</a> <font color="Maroon" title="c2">N</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">M</font> or  not  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">N</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="card_4.html#T78" target="_self" title="CARD_4:th.78">Th78</a></span>;<br/>
<a NAME="E3:81"/><span class="kw">then </span>
( <font color="Maroon" title="c1">M</font> <a href="card_2.html#K2" title="CARD_2:func.2">*`</a> <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> or ( <font color="Maroon" title="c2">N</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp; <font color="Maroon" title="c1">M</font> <a href="card_2.html#K2" title="CARD_2:func.2">*`</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp;  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> <font color="Maroon" title="c1">M</font> ) )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="card_2.html#T32" title="CARD_2:th.32">CARD_2:32</a>, <a class="ref" href="ordinal3.html#T10" title="ORDINAL3:th.10">ORDINAL3:10</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:81"/>
( <font color="Maroon" title="c1">M</font> <a href="card_2.html#K2" title="CARD_2:func.2">*`</a> <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> &amp; <font color="Maroon" title="c2">N</font> <a href="card_2.html#K2" title="CARD_2:func.2">*`</a> <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 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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