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<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> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">l</font> being   <a href="ami_1.html#M3" title="AMI_1:mode.3">Instruction-Location</a> of  <a href="amistd_1.html#K4" title="AMISTD_1:func.4">STC</a> <font color="Maroon" title="c2">N</font><br/> for <font color="Olive" title="b2">i</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instructions</a> of <span class="p1">(<span class="default"><a href="amistd_1.html#K4" title="AMISTD_1:func.4">STC</a> <font color="Maroon" title="c2">N</font></span>)</span>  st  <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <font color="Olive" title="b2">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 holds <br/> <a href="amistd_1.html#K1" title="AMISTD_1:func.1">NIC</a> <font color="Olive" title="b2">i</font>,<font color="Olive" title="b1">l</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2">(<span class="default"><a href="amistd_1.html#K9" title="AMISTD_1:func.9">NextLoc</a> <font color="Olive" title="b1">l</font></span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span><br/><b>let </b><font color="Maroon" title="c3">l</font> be    <a href="ami_1.html#M3" title="AMI_1:mode.3">Instruction-Location</a> of  <a href="amistd_1.html#K4" title="AMISTD_1:func.4">STC</a> <font color="Maroon" title="c2">N</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">i</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instructions</a> of <span class="p1">(<span class="default"><a href="amistd_1.html#K4" title="AMISTD_1:func.4">STC</a> <font color="Maroon" title="c2">N</font></span>)</span>  st  <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <font color="Olive" title="b1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 holds <br/> <a href="amistd_1.html#K1" title="AMISTD_1:func.1">NIC</a> <font color="Olive" title="b1">i</font>,<font color="Maroon" title="c3">l</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2">(<span class="default"><a href="amistd_1.html#K9" title="AMISTD_1:func.9">NextLoc</a> <font color="Maroon" title="c3">l</font></span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span><br/><b>let </b><font color="Maroon" title="c4">i</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instructions</a> of <span class="p1">(<span class="default"><a href="amistd_1.html#K4" title="AMISTD_1:func.4">STC</a> <font color="Maroon" title="c2">N</font></span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 implies  <a href="amistd_1.html#K1" title="AMISTD_1:func.1">NIC</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">l</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2">(<span class="default"><a href="amistd_1.html#K9" title="AMISTD_1:func.9">NextLoc</a> <font color="Maroon" title="c3">l</font></span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> )</span><br/>





<b>assume </b><a NAME="E1:62"/><i><font color="Green" title="E31">A1</font></i>: 
 <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="amistd_1.html#K1" title="AMISTD_1:func.1">NIC</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">l</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2">(<span class="default"><a href="amistd_1.html#K9" title="AMISTD_1:func.9">NextLoc</a> <font color="Maroon" title="c3">l</font></span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span><br/>

<b>set </b><font color="Maroon" title="c5">M</font> =  <a href="amistd_1.html#K4" title="AMISTD_1:func.4">STC</a> <font color="Maroon" title="c2">N</font>;<br/>
<b>consider </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><br/><a NAME="E3:62"/><i><font color="Green" title="E32">A2</font></i>: 
<font color="Maroon" title="c3">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> <span class="p1">(<span class="default"><a href="amistd_1.html#K4" title="AMISTD_1:func.4">STC</a> <font color="Maroon" title="c2">N</font></span>)</span>,<font color="Maroon" title="c6">k</font>
 <b>by </b><i><a class="ref" href="amistd_1.html#T26" target="_self" title="AMISTD_1:th.26">Th26</a></i>;<br/>
<a NAME="E4:62"/>
<font color="Maroon" title="c6">k</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="c3">l</font>
 
<b>by </b><i><a class="txt" href="amistd_1.html#E3:62"><i><font color="Green" title="E32">A2</font></i></a>, <a class="ref" href="amistd_1.html#D13" target="_self" title="AMISTD_1:def.13">Def13</a></i>;<br/>
<a NAME="E5:62"/><b>then </b>
 <a href="amistd_1.html#K9" title="AMISTD_1:func.9">NextLoc</a> <font color="Maroon" title="c3">l</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1
 
<b>by </b><i><a class="ref" href="amistd_1.html#T37" target="_self" title="AMISTD_1:th.37">Th37</a></i>;<br/>
<b>hence </b><a NAME="E6:62"/>
 <a href="amistd_1.html#K1" title="AMISTD_1:func.1">NIC</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">l</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2">(<span class="default"><a href="amistd_1.html#K9" title="AMISTD_1:func.9">NextLoc</a> <font color="Maroon" title="c3">l</font></span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>
 <b>by </b><i><a class="txt" href="amistd_1.html#E1:62"><i><font color="Green" title="E31">A1</font></i></a>, <a class="txt" href="amistd_1.html#E3:62"><i><font color="Green" title="E32">A2</font></i></a>, <a class="txt" href="amistd_1.html#E39"><i><font color="Green" title="E18">Lm5</font></i></a>, <a class="ref" href="amistd_1.html#T37" target="_self" title="AMISTD_1:th.37">Th37</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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