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<b>let </b><font color="Maroon" title="c1">n</font> be  <a href="ordinal1.html#V7" title="ORDINAL1:attr.7">natural</a>  <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</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#V3" title="STRUCT_0:attr.3">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#V8" title="AMI_1:attr.8">definite</a> <a href="amistd_1.html#V4" title="AMISTD_1:attr.4">standard</a>  <a href="ami_1.html#L1" title="AMI_1:struct.1">AMI-Struct</a> of <font color="Maroon" title="c2">N</font>;<br/><b>let </b><font color="Maroon" title="c4">F</font> be   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instruction-Locations</a> of <font color="Maroon" title="c3">S</font>;<br/>







<b>assume </b><a NAME="E1:45"/><i><font color="Green" title="E23">A1</font></i>: 
<font color="Maroon" title="c4">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c3">S</font>,<font color="Maroon" title="c1">n</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 ;<br/>

<a NAME="E2:45"/><i><font color="Green" title="E24">A2</font></i>: 
 <a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c3">S</font>,<font color="Maroon" title="c1">n</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c3">S</font>,<font color="Maroon" title="c1">n</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<b>by </b><i><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/>
<a NAME="E3:45"/><i><font color="Green" title="E25">A3</font></i>: 
 <a href="amistd_1.html#K7" title="AMISTD_1:func.7">locnum</a> <span class="p1">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c3">S</font>,<font color="Maroon" title="c1">n</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">n</font>
 
<b>by </b><i><a class="ref" href="amistd_1.html#D13" title="AMISTD_1:def.13">AMISTD_1:def 13</a></i>;<br/>
<div><b>hereby </b> <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a>,<a class="ref" href="xboole_0.html#D10" title="XBOOLE_0:def.10">XBOOLE_0:def 10</a>
<div class="add"><b>let </b><font color="Maroon" title="c5">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>assume </b><a NAME="E1:45_1"/>
<font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="amistd_3.html#K3" title="AMISTD_3:func.3">LocNums</a> <font color="Maroon" title="c4">F</font>
 ;<br/><b>then consider </b><font color="Maroon" title="c6">l</font> being   <a href="ami_1.html#NM2" title="AMI_1:NM.2">Instruction-Location</a> of <font color="Maroon" title="c3">S</font><b> such that </b><br/><a NAME="E3:45_1"/><i><font color="Green" title="E26">A4</font></i>: 
<font color="Maroon" title="c5">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="amistd_1.html#K7" title="AMISTD_1:func.7">locnum</a> <font color="Maroon" title="c6">l</font>
 <b>and </b><br/><a NAME="E4:45_1"/><i><font color="Green" title="E27">A5</font></i>: 
<font color="Maroon" title="c6">l</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">F</font>
 ;<br/><a NAME="E5:45_1"/>
<font color="Maroon" title="c6">l</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c3">S</font>,<font color="Maroon" title="c1">n</font>
 <b>by </b><i><a class="txt" href="amistd_3.html#E1:45"><i><font color="Green" title="E23">A1</font></i></a>, <a class="txt" href="amistd_3.html#E4:45_1"><i><font color="Green" title="E27">A5</font></i></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/><a NAME="E6:45_1"/><b>then </b>
<font color="Maroon" title="c5">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">n</font>
 <b>by </b><i><a class="txt" href="amistd_3.html#E3:45_1"><i><font color="Green" title="E26">A4</font></i></a>, <a class="ref" href="amistd_1.html#D13" title="AMISTD_1:def.13">AMISTD_1:def 13</a></i>;<br/><b>hence </b><a NAME="E7:45_1"/>
<font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c1">n</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <b>by </b><i><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/></div>
<b>end;</b></div>

<b>let </b><font color="Maroon" title="c5">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E5:45"/>
<font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c1">n</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 ;<br/>

<a NAME="E6:45"/><b>then </b>
<font color="Maroon" title="c5">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">n</font>
 
<b>by </b><i><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/>
<b>hence </b><a NAME="E7:45"/>
<font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="amistd_3.html#K3" title="AMISTD_3:func.3">LocNums</a> <font color="Maroon" title="c4">F</font>
 <b>by </b><i><a class="txt" href="amistd_3.html#E1:45"><i><font color="Green" title="E23">A1</font></i></a>, <a class="txt" href="amistd_3.html#E2:45"><i><font color="Green" title="E24">A2</font></i></a>, <a class="txt" href="amistd_3.html#E3:45"><i><font color="Green" title="E25">A3</font></i></a></i>;<br/>


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