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<span class="kw">given </span><font color="Maroon" title="c3">y</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <span class="kw"> such that </span><a NAME="E2:85"/><span class="lab"><font color="Green" title="E68">A1</font></span>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><a href="arytm_3.html#K11" title="ARYTM_3:func.11">{}</a> ,<font color="Maroon" title="c3">y</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="arytm_3.html#K5" title="ARYTM_3:func.5">RAT+</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<span class="kw">consider </span><font color="Maroon" title="c4">i</font>, <font color="Maroon" title="c5">j</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ordinal1.html#K5" title="ORDINAL1:func.5">omega</a> <span class="kw"> such that </span><br/><a NAME="E4:85"/><span class="lab"><font color="Green" title="E69">A2</font></span>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><a href="arytm_3.html#K11" title="ARYTM_3:func.11">{}</a> ,<font color="Maroon" title="c3">y</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <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="c4">i</font>,<font color="Maroon" title="c5">j</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 <span class="kw">and </span><br/><a NAME="E5:85"/><span class="lab"><font color="Green" title="E70">A3</font></span>: 
<font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c5">j</font> <a href="arytm_3.html#R1" title="ARYTM_3:pred.1">are_relative_prime</a> 
 <span class="kw">and </span><br/><a NAME="E6:85"/>
<font color="Maroon" title="c5">j</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="arytm_3.html#K11" title="ARYTM_3:func.11">{}</a> 
 <span class="kw">and </span><br/><a NAME="E7:85"/><span class="lab"><font color="Green" title="E71">A4</font></span>: 
<font color="Maroon" title="c5">j</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 1
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:85"><span class="lab"><font color="Green" title="E68">A1</font></span></a>, <a class="ref" href="arytm_3.html#T35" target="_self" title="ARYTM_3:th.35">Th35</a>, <a class="ref" href="arytm_3.html#T38" target="_self" title="ARYTM_3:th.38">Th38</a></span>;<br/>
<a NAME="E8:85"/>
<font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="arytm_3.html#K11" title="ARYTM_3:func.11">{}</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:85"><span class="lab"><font color="Green" title="E69">A2</font></span></a>, <a class="ref" href="zfmisc_1.html#T33" title="ZFMISC_1:th.33">ZFMISC_1:33</a></span>;<br/>
<span class="kw">hence </span><a NAME="E9:85"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:85"><span class="lab"><font color="Green" title="E70">A3</font></span></a>, <a class="txt" href="#E7:85"><span class="lab"><font color="Green" title="E71">A4</font></span></a>, <a class="ref" href="arytm_3.html#T7" target="_self" title="ARYTM_3:th.7">Th7</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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