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<b>let </b><font color="Maroon" title="c1">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c2">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="c3">S</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="ami_1.html#V2" title="AMI_1:attr.2">stored-program</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#V14" title="AMI_1:attr.14">standard-ins</a> <a href="amistd_1.html#V4" title="AMISTD_1:attr.4">standard</a> <a href="amistd_2.html#V6" title="AMISTD_2:attr.6">regular</a>  <a href="ami_1.html#L1" title="AMI_1:struct.1">AMI-Struct</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ,<font color="Maroon" title="c2">N</font>;<br/><b>let </b><font color="Maroon" title="c4">I</font>, <font color="Maroon" title="c5">J</font> be   <a href="ami_1.html#NM4" title="AMI_1:NM.4">Instruction</a> of <font color="Maroon" title="c3">S</font>;<br/>







<b>given </b><font color="Maroon" title="c6">k</font> being  <a href="ordinal1.html#V7" title="ORDINAL1:attr.7">natural</a>  <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a> <b> such that </b><a NAME="E2:71"/><i><font color="Green" title="E35">A1</font></i>: 
 <a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c6">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c5">J</font>,<font color="Maroon" title="c6">k</font>
 ;<br/>

<b>assume </b><a NAME="E3:71"/><i><font color="Green" title="E36">A2</font></i>: 
<span class="p1">(<span class="default"><a href="card_3.html#K10" title="CARD_3:func.10">product"</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressParts</a> <span class="p3">(<span class="default"><a href="ami_1.html#K20" title="AMI_1:func.20">InsCode</a> <font color="Maroon" title="c4">I</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> 
 ;<br/>

<b>assume </b><a NAME="E4:71"/>
<span class="p1">(<span class="default"><a href="card_3.html#K10" title="CARD_3:func.10">product"</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressParts</a> <span class="p3">(<span class="default"><a href="ami_1.html#K20" title="AMI_1:func.20">InsCode</a> <font color="Maroon" title="c5">J</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> 
 ;<br/>

<a NAME="E5:71"/><b>then </b>
<span class="p1">(<span class="default"><a href="card_3.html#K10" title="CARD_3:func.10">product"</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressParts</a> <span class="p3">(<span class="default"><a href="ami_1.html#K20" title="AMI_1:func.20">InsCode</a> <span class="p4">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c5">J</font>,<font color="Maroon" title="c6">k</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> 
 
<b>by </b><i><a class="ref" href="amistd_2.html#T31" target="_self" title="AMISTD_2:th.31">Th31</a></i>;<br/>
<b>hence </b><a NAME="E6:71"/>
contradiction
 <b>by </b><i><a class="txt" href="amistd_2.html#E2:71"><i><font color="Green" title="E35">A1</font></i></a>, <a class="txt" href="amistd_2.html#E3:71"><i><font color="Green" title="E36">A2</font></i></a>, <a class="ref" href="amistd_2.html#T31" target="_self" title="AMISTD_2:th.31">Th31</a></i>;<br/>


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