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<div class="add">

<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>set </b><font color="Maroon">c<sub>2</sub></font> =  <a href="ami_1.html#K1" target="_self">Trivial-AMI</a> <font color="Maroon">c<sub>1</sub></font>;<br/>
<a NAME="E1:16"/><i><font color="Green">E6</font></i>: 
<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2"><a href="tarski.html#K4">[</a><span class="default">0,<a href="xboole_0.html#K1">{}</a> </span><a href="tarski.html#K4">]</a></span></span><a href="tarski.html#K1">}</a></span> <a href="hidden.html#R1">=</a> the <a href="ami_1.html#U4" target="_self">Instructions</a> of <span class="p1">(<span class="default"><a href="ami_1.html#K1" target="_self">Trivial-AMI</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="ami_1.html#D2" target="_self">Def2</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">c<sub>3</sub></font> = <span class="p1"><a href="tarski.html#K4">[</a><span class="default">0,<a href="xboole_0.html#K1">{}</a> </span><a href="tarski.html#K4">]</a></span> as   <a href="ami_1.html#NM3">Instruction</a> of <span class="p1">(<span class="default"><a href="ami_1.html#K1" target="_self">Trivial-AMI</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<b>take </b>
<font color="Maroon">c<sub>3</sub></font>
; <i><font color="Red">:: according to </font></i><a class="ref" href="ami_1.html#D9" target="_self">AMI_1:def 9</a><br/>

<b>thus </b><a NAME="E3:16"/>
<font color="Maroon">c<sub>3</sub></font> is <a href="ami_1.html#V3" target="_self">halting</a>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>4</sub></font> be   <a href="ami_1.html#NM4">State</a> of <span class="p1">(<span class="default"><a href="ami_1.html#K1" target="_self">Trivial-AMI</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>; <i><font color="Red">:: according to </font></i><a class="ref" href="ami_1.html#D8" target="_self">AMI_1:def 8</a><br/>

<i><font color="Green">E7</font></i>:  <a href="card_3.html#K4">product</a> the <a href="ami_1.html#U5" target="_self">Object-Kind</a> of <span class="p1">(<span class="default"><a href="ami_1.html#K1" target="_self">Trivial-AMI</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> = 
 <a href="card_3.html#K4">product</a> <span class="p1">(<span class="default">0,1 <a href="funct_4.html#K4">--&gt;</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default">1</span><a href="domain_1.html#K6">}</a></span>,<span class="p2"><a href="tarski.html#K1">{</a><span class="default"><span class="p3"><a href="tarski.html#K4">[</a><span class="default">0,<a href="xboole_0.html#K1">{}</a> </span><a href="tarski.html#K4">]</a></span></span><a href="tarski.html#K1">}</a></span></span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#D2" target="_self">Def2</a></i>
<br/>.= 
<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default">0,1 <a href="funct_4.html#K4">--&gt;</a> 1,<span class="p3"><a href="tarski.html#K4">[</a><span class="default">0,<a href="xboole_0.html#K1">{}</a> </span><a href="tarski.html#K4">]</a></span></span>)</span></span><a href="tarski.html#K1">}</a></span>
<b>by </b><i><a class="ref" href="card_3.html#T63">CARD_3:63</a></i>
;<br/>
<b>hence </b> <a href="ami_1.html#K4" target="_self">Exec</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font> = 
0,1 <a href="funct_4.html#K4">--&gt;</a> 1,<span class="p1"><a href="tarski.html#K4">[</a><span class="default">0,<a href="xboole_0.html#K1">{}</a> </span><a href="tarski.html#K4">]</a></span>
<b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>
<br/>.= 
<font color="Maroon">c<sub>4</sub></font>
<b>by </b><i><a class="txt" href="ami_1.html#E1:16_1"><i><font color="Green">E7</font></i></a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>
;<br/><br/>


</div><b>end;</b></div>

<b>let </b><font color="Maroon">c<sub>4</sub></font> be   <a href="ami_1.html#NM3">Instruction</a> of <span class="p1">(<span class="default"><a href="ami_1.html#K1" target="_self">Trivial-AMI</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>;<br/>

<b>assume </b><a NAME="E4:16"/>
<font color="Maroon">c<sub>4</sub></font> is <a href="ami_1.html#V3" target="_self">halting</a>
 ;<br/>

<b>thus </b><a NAME="E5:16"/>
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="txt" href="ami_1.html#E1:16"><i><font color="Green">E6</font></i></a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>


</div>
