<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon" title="c1">N</font> be  <a href="setfam_1.html#V1" title="SETFAM_1:attr.1">with_non-empty_elements</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c2">A</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> non <a href="ami_1.html#V2" title="AMI_1:attr.2">void</a> <a href="ami_1.html#V5" title="AMI_1:attr.5">IC-Ins-separated</a> <a href="ami_1.html#V7" title="AMI_1:attr.7">definite</a>  <a href="ami_1.html#L1" title="AMI_1:struct.1">AMI-Struct</a> of <font color="Maroon" title="c1">N</font>;<br/><b>let </b><font color="Maroon" title="c3">I</font> be   <a href="ami_1.html#NM3" title="AMI_1:NM.3">Instruction</a> of <font color="Maroon" title="c2">A</font>;<br/>





<b>thus </b><a NAME="E1:27"/>
( <font color="Maroon" title="c3">I</font> is <a href="ami_1.html#V3" title="AMI_1:attr.3">halting</a> implies  <a href="ami_7.html#K2" title="AMI_7:func.2">Output</a> <font color="Maroon" title="c3">I</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">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" title="E15">A1</font></i>: 
for <font color="Olive" title="b1">s</font> being  <a href="ami_1.html#NM4" title="AMI_1:NM.4">State</a> of <font color="Maroon" title="c2">A</font> holds   <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">I</font>,<font color="Olive" title="b1">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">s</font>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="ami_1.html#D8" title="AMI_1:def.8">AMI_1:def 8</a><br/>

<b>assume </b><a NAME="E2:27_1"/>
not  <a href="ami_7.html#K2" title="AMI_7:func.2">Output</a> <font color="Maroon" title="c3">I</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>
 ;<br/>

<b>then consider </b><font color="Maroon" title="c4">o</font> being   <a href="ami_1.html#NM1" title="AMI_1:NM.1">Object</a> of <font color="Maroon" title="c2">A</font><b> such that </b><br/><a NAME="E4:27_1"/><i><font color="Green" title="E16">A2</font></i>: 
<font color="Maroon" title="c4">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ami_7.html#K2" title="AMI_7:func.2">Output</a> <font color="Maroon" title="c3">I</font>
 <b>by </b><i><a class="ref" href="subset_1.html#T10" title="SUBSET_1:th.10">SUBSET_1:10</a></i>;<br/>
<a NAME="E5:27_1"/>
 ex <font color="Olive" title="b1">s</font> being  <a href="ami_1.html#NM4" title="AMI_1:NM.4">State</a> of <font color="Maroon" title="c2">A</font> st <font color="Olive" title="b1">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">I</font>,<font color="Olive" title="b1">s</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">o</font>
 
<b>by </b><i><a class="txt" href="ami_7.html#E4:27_1"><i><font color="Green" title="E16">A2</font></i></a>, <a class="ref" href="ami_7.html#D3" target="_self" title="AMI_7:def.3">Def3</a></i>;<br/>
<b>hence </b><a NAME="E6:27_1"/>
contradiction
 <b>by </b><i><a class="txt" href="ami_7.html#E1:27_1"><i><font color="Green" title="E15">A1</font></i></a></i>;<br/>


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

<b>assume </b><a NAME="E2:27"/><i><font color="Green" title="E15">A3</font></i>: 
 <a href="ami_7.html#K2" title="AMI_7:func.2">Output</a> <font color="Maroon" title="c3">I</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>
 ;<br/>

<b>let </b><font color="Maroon" title="c4">s</font> be   <a href="ami_1.html#NM4" title="AMI_1:NM.4">State</a> of <font color="Maroon" title="c2">A</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="ami_1.html#D8" title="AMI_1:def.8">AMI_1:def 8</a><br/>

<a NAME="E3:27"/><i><font color="Green" title="E16">A4</font></i>: 
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c4">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">A</font>
 
<b>by </b><i><a class="ref" href="ami_1.html#T79" title="AMI_1:th.79">AMI_1:79</a></i>;<br/>
<a NAME="E4:27"/><i><font color="Green" title="E17">A5</font></i>: 
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">I</font>,<font color="Maroon" title="c4">s</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">A</font>
 
<b>by </b><i><a class="ref" href="ami_1.html#T79" title="AMI_1:th.79">AMI_1:79</a></i>;<br/>
<b>assume </b><a NAME="E5:27"/>
 <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">I</font>,<font color="Maroon" title="c4">s</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">s</font>
 ;<br/>

<a NAME="E6:27"/><b>then </b>
 ex <font color="Olive" title="b1">x</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  st <br/>( <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">A</font> &amp; <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">I</font>,<font color="Maroon" title="c4">s</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">x</font> )
 
<b>by </b><i><a class="txt" href="ami_7.html#E3:27"><i><font color="Green" title="E16">A4</font></i></a>, <a class="txt" href="ami_7.html#E4:27"><i><font color="Green" title="E17">A5</font></i></a>, <a class="ref" href="funct_1.html#T9" title="FUNCT_1:th.9">FUNCT_1:9</a></i>;<br/>
<b>hence </b><a NAME="E7:27"/>
contradiction
 <b>by </b><i><a class="txt" href="ami_7.html#E2:27"><i><font color="Green" title="E15">A3</font></i></a>, <a class="ref" href="ami_7.html#D3" target="_self" title="AMI_7:def.3">Def3</a></i>;<br/>


</div>
