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<b>let </b><font color="Maroon">c<sub>2</sub></font> be  <a href="setfam_1.html#V1">with_non-empty_elements</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be  non <a href="struct_0.html#V3">empty</a> non <a href="ami_1.html#V2">void</a> <a href="ami_1.html#V5">IC-Ins-separated</a> <a href="ami_1.html#V8">definite</a> <a href="amistd_1.html#V4" target="_self">standard</a>  <a href="ami_1.html#L1">AMI-Struct</a> of <font color="Maroon">c<sub>2</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>4</sub></font> be    <a href="subset_1.html#M2">Element</a> of the <a href="ami_1.html#U4">Instructions</a> of <font color="Maroon">c<sub>3</sub></font>;<br/>





<b>set </b><font color="Maroon">c<sub>5</sub></font> = <span class="p1">(<span class="default"><a href="amistd_1.html#K5" target="_self">il.</a> <font color="Maroon">c<sub>3</sub></font>,0</span>)</span> <a href="ami_3.html#K14">.--&gt;</a> <font color="Maroon">c<sub>4</sub></font>;<br/>
<a NAME="E1:80"/><i><font color="Green">E42</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="amistd_1.html#K5" target="_self">il.</a> <font color="Maroon">c<sub>3</sub></font>,0</span>)</span> <a href="ami_3.html#K14">.--&gt;</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2">(<span class="default"><a href="amistd_1.html#K5" target="_self">il.</a> <font color="Maroon">c<sub>3</sub></font>,0</span>)</span></span><a href="domain_1.html#K6">}</a></span>
 
<b>by </b><i><a class="ref" href="cqc_lang.html#T5">CQC_LANG:5</a></i>;<br/>
<b>let </b><font color="Maroon">c<sub>6</sub></font> be   <a href="ami_1.html#NM2">Instruction-Location</a> of <font color="Maroon">c<sub>3</sub></font>; <i><font color="Red">:: according to </font></i><a class="ref" href="amistd_1.html#D20" target="_self">AMISTD_1:def 20</a><br/>

<b>assume </b><a NAME="E2:80"/><i><font color="Green">E43</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="amistd_1.html#K5" target="_self">il.</a> <font color="Maroon">c<sub>3</sub></font>,0</span>)</span> <a href="ami_3.html#K14">.--&gt;</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
 ;<br/>

<a NAME="E3:80"/><i><font color="Green">E44</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a>  <a href="amistd_1.html#K5" target="_self">il.</a> <font color="Maroon">c<sub>3</sub></font>,0
 
<b>by </b><i><a class="txt" href="amistd_1.html#E1:80"><i><font color="Green">E42</font></i></a>, <a class="txt" href="amistd_1.html#E2:80"><i><font color="Green">E43</font></i></a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<b>let </b><font color="Maroon">c<sub>7</sub></font> be   <a href="ami_1.html#NM2">Instruction-Location</a> of <font color="Maroon">c<sub>3</sub></font>;<br/>

<b>assume </b><a NAME="E4:80"/><i><font color="Green">E45</font></i>: 
<font color="Maroon">c<sub>7</sub></font> <a href="amistd_1.html#R1" target="_self">&lt;=</a> <font color="Maroon">c<sub>6</sub></font>
 ;<br/>

<b>consider </b><font color="Maroon">c<sub>8</sub></font> being  <a href="ordinal1.html#V7">natural</a>  <a href="ordinal1.html#NM1" target="_self">number</a> <b> such that </b><br/><a NAME="E6:80"/><i><font color="Green">E46</font></i>: 
<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a>  <a href="amistd_1.html#K5" target="_self">il.</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>8</sub></font>
 <b>by </b><i><a class="ref" href="amistd_1.html#T26" target="_self">Th26</a></i>;<br/>
<a NAME="E7:80"/>
( 0 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>8</sub></font> &amp; <font color="Maroon">c<sub>8</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> 0 )
 
<b>by </b><i><a class="txt" href="amistd_1.html#E3:80"><i><font color="Green">E44</font></i></a>, <a class="txt" href="amistd_1.html#E4:80"><i><font color="Green">E45</font></i></a>, <a class="txt" href="amistd_1.html#E6:80"><i><font color="Green">E46</font></i></a>, <a class="ref" href="amistd_1.html#T28" target="_self">Th28</a>, <a class="ref" href="nat_1.html#T18">NAT_1:18</a></i>;<br/>
<b>hence </b><a NAME="E8:80"/>
<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="amistd_1.html#K5" target="_self">il.</a> <font color="Maroon">c<sub>3</sub></font>,0</span>)</span> <a href="ami_3.html#K14">.--&gt;</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="amistd_1.html#E2:80"><i><font color="Green">E43</font></i></a>, <a class="txt" href="amistd_1.html#E3:80"><i><font color="Green">E44</font></i></a>, <a class="txt" href="amistd_1.html#E6:80"><i><font color="Green">E46</font></i></a>, <a class="ref" href="xxreal_0.html#T1">XXREAL_0:1</a></i>;<br/>


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