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<b>let </b><font color="Maroon">N</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">A</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="ami_1.html#L1">AMI-Struct</a> of <font color="Maroon">N</font>;<br/><b>let </b><font color="Maroon">I</font> be   <a href="ami_1.html#NM3">Instruction</a> of <font color="Maroon">A</font>;<br/>





<b>thus </b><a NAME="E1:27"/>
( <font color="Maroon">I</font> is <a href="ami_1.html#V3">halting</a> implies  <a href="ami_7.html#K2" target="_self">Output</a> <font color="Maroon">I</font> is <a href="xboole_0.html#V1">empty</a> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="27_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:27_1"/><i><font color="Green">E44</font></i>: 
for <font color="Olive">s</font> being  <a href="ami_1.html#NM4">State</a> of <font color="Maroon">A</font> holds   <a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<font color="Olive">s</font> <a href="hidden.html#R1">=</a> <font color="Olive">s</font>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="ami_1.html#D8">AMI_1:def 8</a><br/>

<b>assume </b><a NAME="E2:27_1"/>
not  <a href="ami_7.html#K2" target="_self">Output</a> <font color="Maroon">I</font> is <a href="xboole_0.html#V1">empty</a>
 ;<br/>

<b>then consider </b><font color="Maroon">o</font> being   <a href="ami_1.html#NM1">Object</a> of <font color="Maroon">A</font><b> such that </b><br/><a NAME="E4:27_1"/><i><font color="Green">E47</font></i>: 
<font color="Maroon">o</font> <a href="hidden.html#R2">in</a>  <a href="ami_7.html#K2" target="_self">Output</a> <font color="Maroon">I</font>
 <b>by </b><i><a class="ref" href="subset_1.html#T10">SUBSET_1:10</a></i>;<br/>
<a NAME="E5:27_1"/>
 ex <font color="Olive">s</font> being  <a href="ami_1.html#NM4">State</a> of <font color="Maroon">A</font> st <font color="Olive">s</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">o</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<font color="Olive">s</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">o</font>
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E6:27_1"/>
contradiction
 <b>by </b><i/>;<br/>


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

<b>assume </b><a NAME="E2:27"/><i><font color="Green">E51</font></i>: 
 <a href="ami_7.html#K2" target="_self">Output</a> <font color="Maroon">I</font> is <a href="xboole_0.html#V1">empty</a>
 ;<br/>

<b>let </b><font color="Maroon">s</font> be   <a href="ami_1.html#NM4">State</a> of <font color="Maroon">A</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="ami_1.html#D8">AMI_1:def 8</a><br/>

<a NAME="E3:27"/><i><font color="Green">E52</font></i>: 
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">s</font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">A</font>
 
<b>by </b><i><a class="ref" href="ami_3.html#T36">AMI_3:36</a></i>;<br/>
<a NAME="E4:27"/><i><font color="Green">E53</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<font color="Maroon">s</font></span>)</span> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">A</font>
 
<b>by </b><i><a class="ref" href="ami_3.html#T36">AMI_3:36</a></i>;<br/>
<b>assume </b><a NAME="E5:27"/>
 <a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<font color="Maroon">s</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">s</font>
 ;<br/>

<a NAME="E6:27"/><b>then </b>
 ex <font color="Olive">x</font> being   <a href="hidden.html#M1">set</a>  st <br/>( <font color="Olive">x</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">A</font> &amp; <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<font color="Maroon">s</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">x</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">s</font> <a href="funct_1.html#K1">.</a> <font color="Olive">x</font> )
 
<b>by </b><i>, , <a class="ref" href="funct_1.html#T9">FUNCT_1:9</a></i>;<br/>
<b>hence </b><a NAME="E7:27"/>
contradiction
 <b>by </b><i>, </i>;<br/>


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