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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_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>assume </b><a NAME="E1:29"/><i><font color="Green" title="E17">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="E2:29"/>
not  <a href="ami_7.html#K4" title="AMI_7:func.4">Out_U_Inp</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="E4:29"/><i><font color="Green" title="E18">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#K4" title="AMI_7:func.4">Out_U_Inp</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/>
<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><b> such that </b><br/><a NAME="E6:29"/><i><font color="Green" title="E19">A3</font></i>: 
 <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">I</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="c6">a</font></span>)</span> <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="Maroon" title="c5">s</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>
 <b>by </b><i><a class="txt" href="ami_7.html#E4:29"><i><font color="Green" title="E18">A2</font></i></a>, <a class="ref" href="ami_7.html#D5" target="_self" title="AMI_7:def.5">Def5</a></i>;<br/>
 <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">I</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="c6">a</font></span>)</span> = 
<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="c6">a</font>
<b>by </b><i><a class="txt" href="ami_7.html#E1:29"><i><font color="Green" title="E17">A1</font></i></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>,<font color="Maroon" title="c5">s</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>
<b>by </b><i><a class="txt" href="ami_7.html#E1:29"><i><font color="Green" title="E17">A1</font></i></a></i>
;<br/>
<b>hence </b><a NAME="E8:29"/>
contradiction
 <b>by </b><i><a class="txt" href="ami_7.html#E6:29"><i><font color="Green" title="E19">A3</font></i></a></i>;<br/>


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