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<span class="kw">assume </span><a NAME="E1:29"/>
 not  <a href="modal_1.html#K4" title="MODAL_1:func.4">MP-conectives</a>  <a href="subset_1.html#R1" title="SUBSET_1:pred.1">misses</a>  <a href="modal_1.html#K3" title="MODAL_1:func.3">MP-variables</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c1">x</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <span class="kw"> such that </span><br/><a NAME="E3:29"/><span class="lab"><font color="Green" title="E22">A1</font></span>: 
<font color="Maroon" title="c1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="mcart_1.html#K12" title="MCART_1:func.12">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,1,2</span><a href="domain_1.html#K8" title="DOMAIN_1:func.8">}</a></span>,<a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a></span><a href="mcart_1.html#K12" title="MCART_1:func.12">:]</a></span>
 <span class="kw">and </span><br/><a NAME="E4:29"/><span class="lab"><font color="Green" title="E23">A2</font></span>: 
<font color="Maroon" title="c1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="mcart_1.html#K12" title="MCART_1:func.12">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default">3</span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a></span><a href="mcart_1.html#K12" title="MCART_1:func.12">:]</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_0.html#T3" title="XBOOLE_0:th.3">XBOOLE_0:3</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c2">x1</font>, <font color="Maroon" title="c3">x2</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <span class="kw"> such that </span><br/><a NAME="E6:29"/><span class="lab"><font color="Green" title="E24">A3</font></span>: 
<font color="Maroon" title="c2">x1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,1,2</span><a href="domain_1.html#K8" title="DOMAIN_1:func.8">}</a></span>
 <span class="kw">and </span><br/><a NAME="E7:29"/>
<font color="Maroon" title="c3">x2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> 
 <span class="kw">and </span><br/><a NAME="E8:29"/><span class="lab"><font color="Green" title="E25">A4</font></span>: 
<font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c3">x2</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:29"><span class="lab"><font color="Green" title="E22">A1</font></span></a>, <a class="ref" href="zfmisc_1.html#D2" title="ZFMISC_1:def.2">ZFMISC_1:def 2</a></span>;<br/>
<a NAME="E9:29"/>
<font color="Maroon" title="c2">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:29"><span class="lab"><font color="Green" title="E23">A2</font></span></a>, <a class="txt" href="#E8:29"><span class="lab"><font color="Green" title="E25">A4</font></span></a>, <a class="ref" href="zfmisc_1.html#T105" title="ZFMISC_1:th.105">ZFMISC_1:105</a></span>;<br/>
<span class="kw">hence </span><a NAME="E10:29"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:29"><span class="lab"><font color="Green" title="E24">A3</font></span></a>, <a class="ref" href="enumset1.html#D1" title="ENUMSET1:def.1">ENUMSET1: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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