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<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="E2:51_1_1"/><span class="lab"><font color="Green" title="E30">A1</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#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>
 <span class="kw">and </span><br/><a NAME="E3:51_1_1"/><span class="lab"><font color="Green" title="E31">A2</font></span>: 
( <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>  &amp; <font color="Maroon" title="c1">p</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="ref" href="zfmisc_1.html#D2" title="ZFMISC_1:def.2">ZFMISC_1:def 2</a></span>;<br/>
<a NAME="E4:51_1_1"/>
<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="#E2:51_1_1"><span class="lab"><font color="Green" title="E30">A1</font></span></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:51_1_1"/>
<span class="p1">(<span class="default"><a href="trees_1.html#K2" title="TREES_1:func.2">elementary_tree</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="trees_2.html#K9" title="TREES_2:func.9">--&gt;</a> <font color="Maroon" title="c1">p</font> is   <a href="modal_1.html#NM5" title="MODAL_1:NM.5">MP-wff</a>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:51_1_1"><span class="lab"><font color="Green" title="E31">A2</font></span></a>, <a class="ref" href="modal_1.html#T35" target="_self" title="MODAL_1:th.35">Th35</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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