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<span class="kw">let </span><font color="Maroon" title="c1">K</font>, <font color="Maroon" title="c2">M</font>, <font color="Maroon" title="c3">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">K</font> <a href="card_2.html#K2" title="CARD_2:func.2">*`</a> <font color="Maroon" title="c2">M</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">K</font> <a href="card_2.html#K2" title="CARD_2:func.2">*`</a> <font color="Maroon" title="c3">N</font> implies <font color="Maroon" title="c2">M</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">N</font> )</span><br/>





<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:102"/><span class="lab"><font color="Green" title="E64">A1</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="c2">M</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">K</font> <a href="card_2.html#K2" title="CARD_2:func.2">*`</a> <font color="Maroon" title="c3">N</font>
 <span class="kw">and </span><br/><a NAME="E2:102"/><span class="lab"><font color="Green" title="E65">A2</font></span>: 
 not <font color="Maroon" title="c2">M</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">N</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E3:102"/>
<font color="Maroon" title="c3">N</font> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> <font color="Maroon" title="c2">M</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:102"><span class="lab"><font color="Green" title="E65">A2</font></span></a>, <a class="ref" href="card_1.html#T4" title="CARD_1:th.4">CARD_1:4</a></span>;<br/>
<a NAME="E4:102"/><span class="kw">then </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">N</font> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> <font color="Maroon" title="c1">K</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="ref" href="card_2.html#T90" target="_self" title="CARD_2:th.90">Th136</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:102"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:102"><span class="lab"><font color="Green" title="E64">A1</font></span></a>, <a class="ref" href="card_1.html#T4" title="CARD_1:th.4">CARD_1:4</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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