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<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_7.html#V2" title="AMI_7:attr.2">with_non_trivial_ObjectKinds</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/>





<a NAME="E1:20"/>
for <font color="Olive" title="b1">o</font> being  <a href="ami_1.html#NM1" title="AMI_1:NM.1">Object</a> of <font color="Maroon" title="c2">A</font>  st <font color="Olive" title="b1">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ami_7.html#K3" title="AMI_7:func.3">Out_\_Inp</a> <font color="Maroon" title="c3">I</font> holds <br/><font color="Olive" title="b1">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>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c4">o</font> be   <a href="ami_1.html#NM1" title="AMI_1:NM.1">Object</a> of <font color="Maroon" title="c2">A</font>;<br/>

<b>assume </b><a NAME="E1:20_1"/><i><font color="Green" title="E12">A1</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#K3" title="AMI_7:func.3">Out_\_Inp</a> <font color="Maroon" title="c3">I</font> &amp; not <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> )
 ;<br/>

<b>consider </b><font color="Maroon" title="c5">s</font> being   <a href="ami_1.html#NM4" title="AMI_1:NM.4">State</a> of <font color="Maroon" title="c2">A</font>, <font color="Maroon" title="c6">a</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ami_1.html#K3" title="AMI_1:func.3">ObjectKind</a> <font color="Maroon" title="c4">o</font>;<br/>
<b>consider </b><font color="Maroon" title="c7">w</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E4:20_1"/><i><font color="Green" title="E13">A2</font></i>: 
( <font color="Maroon" title="c7">w</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ami_1.html#K3" title="AMI_1:func.3">ObjectKind</a> <font color="Maroon" title="c4">o</font> &amp; <font color="Maroon" title="c7">w</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">a</font> )
 <b>by </b><i><a class="ref" href="yellow15.html#T4" title="YELLOW15:th.4">YELLOW15:4</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c8">w</font> = <font color="Maroon" title="c7">w</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ami_1.html#K3" title="AMI_1:func.3">ObjectKind</a> <font color="Maroon" title="c4">o</font> <b>by </b><i><a class="txt" href="ami_7.html#E4:20_1"><i><font color="Green" title="E13">A2</font></i></a></i>;<br/>
<b>set </b><font color="Maroon" title="c9">t</font> = <font color="Maroon" title="c5">s</font> <a href="ami_7.html#K1" title="AMI_7:func.1">+*</a> <font color="Maroon" title="c4">o</font>,<font color="Maroon" title="c8">w</font>;<br/>
<a NAME="E6:20_1"/><i><font color="Green" title="E14">A3</font></i>: 
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c5">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="E7:20_1"/><i><font color="Green" title="E15">A4</font></i>: 
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">s</font> <a href="ami_7.html#K1" title="AMI_7:func.1">+*</a> <font color="Maroon" title="c4">o</font>,<font color="Maroon" title="c8">w</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/>
<i><font color="Green" title="E16">A5</font></i>: <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>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">s</font> <a href="ami_7.html#K1" title="AMI_7:func.1">+*</a> <font color="Maroon" title="c4">o</font>,<font color="Maroon" title="c8">w</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">o</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">s</font> <a href="ami_7.html#K1" title="AMI_7:func.1">+*</a> <font color="Maroon" title="c4">o</font>,<font color="Maroon" title="c8">w</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#E1:20_1"><i><font color="Green" title="E12">A1</font></i></a>, <a class="ref" href="ami_7.html#D3" target="_self" title="AMI_7:def.3">Def3</a></i>
<br/>.= 
<font color="Maroon" title="c8">w</font>
<b>by </b><i><a class="txt" href="ami_7.html#E6:20_1"><i><font color="Green" title="E14">A3</font></i></a>, <a class="ref" href="funct_7.html#T33" title="FUNCT_7:th.33">FUNCT_7:33</a></i>
;<br/>
<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>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c5">s</font> <a href="ami_7.html#K1" title="AMI_7:func.1">+*</a> <font color="Maroon" title="c4">o</font>,<font color="Maroon" title="c8">w</font></span>)</span> <a href="ami_7.html#K1" title="AMI_7:func.1">+*</a> <font color="Maroon" title="c4">o</font>,<font color="Maroon" title="c6">a</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">o</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">s</font> <a href="ami_7.html#K1" title="AMI_7:func.1">+*</a> <font color="Maroon" title="c4">o</font>,<font color="Maroon" title="c8">w</font></span>)</span> <a href="ami_7.html#K1" title="AMI_7:func.1">+*</a> <font color="Maroon" title="c4">o</font>,<font color="Maroon" title="c6">a</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#E1:20_1"><i><font color="Green" title="E12">A1</font></i></a>, <a class="ref" href="ami_7.html#D3" target="_self" title="AMI_7:def.3">Def3</a></i>
<br/>.= 
<font color="Maroon" title="c6">a</font>
<b>by </b><i><a class="txt" href="ami_7.html#E7:20_1"><i><font color="Green" title="E15">A4</font></i></a>, <a class="ref" href="funct_7.html#T33" title="FUNCT_7:th.33">FUNCT_7:33</a></i>
;<br/>
<b>hence </b><a NAME="E10:20_1"/>
contradiction
 <b>by </b><i><a class="txt" href="ami_7.html#E1:20_1"><i><font color="Green" title="E12">A1</font></i></a>, <a class="txt" href="ami_7.html#E4:20_1"><i><font color="Green" title="E13">A2</font></i></a>, <a class="txt" href="ami_7.html#E8:20_1"><i><font color="Green" title="E16">A5</font></i></a>, <a class="ref" href="ami_7.html#D4" target="_self" title="AMI_7:def.4">Def4</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E2:20"/>
 <a href="ami_7.html#K3" title="AMI_7:func.3">Out_\_Inp</a> <font color="Maroon" title="c3">I</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</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#T7" title="SUBSET_1:th.7">SUBSET_1:7</a></i>;<br/>


</div>
