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<b>let </b><font color="Maroon">p</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="cqc_lang.html#K7">CQC-WFF</a> ;<br/><b>let </b><font color="Maroon">i</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/>



<b>assume </b><a NAME="E1:42"/><i><font color="Green">E28</font></i>: 
 <a href="qc_lang3.html#K2">x.</a> <font color="Maroon">i</font> <a href="hidden.html#R2">in</a>  <a href="qc_lang1.html#K23">still_not-bound_in</a> <font color="Maroon">p</font>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="42_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:42_1"/><i><font color="Green">E29</font></i>: 
 <a href="cqc_sim1.html#K10" target="_self">min</a> <span class="p1">(<span class="default"><a href="cqc_sim1.html#K11" target="_self">NBI</a> <font color="Maroon">p</font></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">i</font>
 ;<br/><a NAME="E2:42_1"/>
 <a href="cqc_sim1.html#K10" target="_self">min</a> <span class="p1">(<span class="default"><a href="cqc_sim1.html#K11" target="_self">NBI</a> <font color="Maroon">p</font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="cqc_sim1.html#K11" target="_self">NBI</a> <font color="Maroon">p</font>
 <b>by </b><i/>;<br/><a NAME="E3:42_1"/><b>then </b>
 ex <font color="Olive">k</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  st <br/>( <font color="Olive">k</font> <a href="hidden.html#R1">=</a>  <a href="cqc_sim1.html#K10" target="_self">min</a> <span class="p1">(<span class="default"><a href="cqc_sim1.html#K11" target="_self">NBI</a> <font color="Maroon">p</font></span>)</span> &amp; ( for <font color="Olive">i</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>   st <font color="Olive">k</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">i</font> holds <br/> not  <a href="qc_lang3.html#K2">x.</a> <font color="Olive">i</font> <a href="hidden.html#R2">in</a>  <a href="qc_lang1.html#K23">still_not-bound_in</a> <font color="Maroon">p</font> ) )
 ;<br/><b>hence </b><a NAME="E4:42_1"/>
contradiction
 <b>by </b><i>, </i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:42"/>
<font color="Maroon">i</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="cqc_sim1.html#K12" target="_self">index</a> <font color="Maroon">p</font>
 ;<br/>


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