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<b>let </b><font color="Maroon">c<sub>1</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>2</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#V4">halting</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">standard</a>  <a href="ami_1.html#L1">AMI-Struct</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be   <a href="amistd_1.html#NM1">pre-Macro</a> of <font color="Maroon">c<sub>2</sub></font>;<br/>





<b>assume </b><a NAME="E1:67"/><i><font color="Green">E38</font></i>: 
 <a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> 1
 ;<br/>

<b>then consider </b><font color="Maroon">c<sub>4</sub></font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E3:67"/><i><font color="Green">E39</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>4</sub></font></span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i><a class="ref" href="card_2.html#T60">CARD_2:60</a></i>;<br/>
<a NAME="E4:67"/>
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="txt" href="amistd_2.html#E3:67"><i><font color="Green">E39</font></i></a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<b>then consider </b><font color="Maroon">c<sub>5</sub></font>, <font color="Maroon">c<sub>6</sub></font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E6:67"/><i><font color="Green">E40</font></i>: 
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="ref" href="relat_1.html#D1">RELAT_1:def 1</a></i>;<br/>
<a NAME="E7:67"/><i><font color="Green">E41</font></i>: 
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>5</sub></font></span><a href="tarski.html#K1">}</a></span>
 
<b>by </b><i><a class="txt" href="amistd_2.html#E3:67"><i><font color="Green">E39</font></i></a>, <a class="txt" href="amistd_2.html#E6:67"><i><font color="Green">E40</font></i></a>, <a class="ref" href="relat_1.html#T23">RELAT_1:23</a></i>;<br/>
<a NAME="E8:67"/><i><font color="Green">E42</font></i>: 
 <a href="amistd_1.html#K5">il.</a> <font color="Maroon">c<sub>2</sub></font>,0 <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="ref" href="amistd_1.html#T49">AMISTD_1:49</a></i>;<br/>
<a NAME="E9:67"/><b>then </b><i><font color="Green">E43</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a>  <a href="amistd_1.html#K5">il.</a> <font color="Maroon">c<sub>2</sub></font>,0
 
<b>by </b><i><a class="txt" href="amistd_2.html#E7:67"><i><font color="Green">E41</font></i></a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="binarith.html#K5">-'</a> 1 = 
<span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1
<b>by </b><i><a class="ref" href="amistd_2.html#T4" target="_self">Th4</a></i>
<br/>.= 
0
<b>by </b><i><a class="txt" href="amistd_2.html#E1:67"><i><font color="Green">E38</font></i></a></i>
;<br/>
<a NAME="E11:67"/><b>then </b>
 <a href="amistd_1.html#K10">LastLoc</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="amistd_1.html#K5">il.</a> <font color="Maroon">c<sub>2</sub></font>,0
 
<b>by </b><i><a class="ref" href="amistd_1.html#T55">AMISTD_1:55</a></i>;<br/>
<a NAME="E12:67"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="amistd_1.html#K5">il.</a> <font color="Maroon">c<sub>2</sub></font>,0</span>)</span> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K5">halt</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="amistd_1.html#D22">AMISTD_1:def 22</a></i>;<br/>
<a NAME="E13:67"/><b>then </b>
 <a href="ami_1.html#K5">halt</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="txt" href="amistd_2.html#E8:67"><i><font color="Green">E42</font></i></a>, <a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/>
<a NAME="E14:67"/><b>then </b>
 <a href="ami_1.html#K5">halt</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>6</sub></font></span><a href="tarski.html#K1">}</a></span>
 
<b>by </b><i><a class="txt" href="amistd_2.html#E3:67"><i><font color="Green">E39</font></i></a>, <a class="txt" href="amistd_2.html#E6:67"><i><font color="Green">E40</font></i></a>, <a class="ref" href="relat_1.html#T23">RELAT_1:23</a></i>;<br/>
<b>then </b><font color="Maroon">c<sub>3</sub></font> = 
<span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2"><a href="domain_1.html#K1">[</a><span class="default"><span class="p3">(<span class="default"><a href="amistd_1.html#K5">il.</a> <font color="Maroon">c<sub>2</sub></font>,0</span>)</span>,<span class="p3">(<span class="default"><a href="ami_1.html#K5">halt</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="domain_1.html#K1">]</a></span></span><a href="domain_1.html#K6">}</a></span>
<b>by </b><i><a class="txt" href="amistd_2.html#E3:67"><i><font color="Green">E39</font></i></a>, <a class="txt" href="amistd_2.html#E6:67"><i><font color="Green">E40</font></i></a>, <a class="txt" href="amistd_2.html#E9:67"><i><font color="Green">E43</font></i></a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="amistd_1.html#K5">il.</a> <font color="Maroon">c<sub>2</sub></font>,0</span>)</span> <a href="ami_3.html#K14">.--&gt;</a> <span class="p1">(<span class="default"><a href="ami_1.html#K5">halt</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#T19">AMI_1:19</a></i>
;<br/>
<b>hence </b><a NAME="E16:67"/>
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="amistd_2.html#K6" target="_self">Stop</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/>


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