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<b>let </b><font color="Maroon" title="c2">K</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>;<br/>





<b>assume </b><a NAME="E1:69"/><i><font color="Green" title="E50">A1</font></i>: 
( <font color="Maroon" title="c2">K</font> <a href="card_2.html#K1" title="CARD_2:func.1">+`</a> <font color="Maroon" title="c3">M</font> <a href="card_1.html#NR2" title="CARD_1:NR.2">&lt;`</a> <font color="Maroon" title="c2">K</font> <a href="card_2.html#K1" title="CARD_2:func.1">+`</a> <font color="Maroon" title="c4">N</font> &amp; not <font color="Maroon" title="c3">M</font> <a href="card_1.html#NR2" title="CARD_1:NR.2">&lt;`</a> <font color="Maroon" title="c4">N</font> )
 ;<br/>

<a NAME="E2:69"/><b>then </b>
( <font color="Maroon" title="c4">N</font> <a href="card_1.html#NR1" title="CARD_1:NR.1">&lt;=`</a> <font color="Maroon" title="c3">M</font> &amp; <font color="Maroon" title="c2">K</font> <a href="card_1.html#NR1" title="CARD_1:NR.1">&lt;=`</a> <font color="Maroon" title="c2">K</font> )
 
<b>by </b><i><a class="ref" href="card_1.html#T14" title="CARD_1:th.14">CARD_1:14</a></i>;<br/>
<a NAME="E3:69"/><b>then </b>
<font color="Maroon" title="c2">K</font> <a href="card_2.html#K1" title="CARD_2:func.1">+`</a> <font color="Maroon" title="c4">N</font> <a href="card_1.html#NR1" title="CARD_1:NR.1">&lt;=`</a> <font color="Maroon" title="c2">K</font> <a href="card_2.html#K1" title="CARD_2:func.1">+`</a> <font color="Maroon" title="c3">M</font>
 
<b>by </b><i><a class="ref" href="card_4.html#T41" target="_self" title="CARD_4:th.41">Th41</a></i>;<br/>
<b>hence </b><a NAME="E4:69"/>
contradiction
 <b>by </b><i><a class="txt" href="card_4.html#E1:69"><i><font color="Green" title="E50">A1</font></i></a>, <a class="ref" href="card_1.html#T14" title="CARD_1:th.14">CARD_1:14</a></i>;<br/>


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