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<span class="kw">let </span><font color="Maroon" title="c1">N</font> be  non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <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:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">S</font> being 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">steady-programmed</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="c1">N</font><br/> for <font color="Olive" title="b2">L</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> <br/> for <font color="Olive" title="b3">J</font> being  <a href="ami_1.html#NM2" title="AMI_1:NM.2">Instruction</a> of <font color="Olive" title="b1">S</font>  st <font color="Olive" title="b1">S</font> is  <a href="ami_1.html#V9" title="AMI_1:attr.9">realistic</a>  &amp; <font color="Olive" title="b3">J</font> is  <a href="ami_1.html#V3" title="AMI_1:attr.3">halting</a>  holds <br/> <a href="amistd_3.html#K2" title="AMISTD_3:func.2">LocNums</a> <span class="p1">(<span class="default"><a href="amistd_1.html#K1" title="AMISTD_1:func.1">NIC</a> <font color="Olive" title="b3">J</font>,<font color="Olive" title="b2">L</font></span>)</span>,<font color="Olive" title="b1">S</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="seq_4.html#K1" title="SEQ_4:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="amistd_1.html#K7" title="AMISTD_1:func.7">locnum</a> <font color="Olive" title="b2">L</font>,<font color="Olive" title="b1">S</font></span>)</span></span><a href="seq_4.html#K1" title="SEQ_4:func.1">}</a></span></span><br/><span class="kw">let </span><font color="Maroon" title="c2">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">steady-programmed</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="c1">N</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">L</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> <br/> for <font color="Olive" title="b2">J</font> being  <a href="ami_1.html#NM2" title="AMI_1:NM.2">Instruction</a> of <font color="Maroon" title="c2">S</font>  st <font color="Maroon" title="c2">S</font> is  <a href="ami_1.html#V9" title="AMI_1:attr.9">realistic</a>  &amp; <font color="Olive" title="b2">J</font> is  <a href="ami_1.html#V3" title="AMI_1:attr.3">halting</a>  holds <br/> <a href="amistd_3.html#K2" title="AMISTD_3:func.2">LocNums</a> <span class="p1">(<span class="default"><a href="amistd_1.html#K1" title="AMISTD_1:func.1">NIC</a> <font color="Olive" title="b2">J</font>,<font color="Olive" title="b1">L</font></span>)</span>,<font color="Maroon" title="c2">S</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="seq_4.html#K1" title="SEQ_4:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="amistd_1.html#K7" title="AMISTD_1:func.7">locnum</a> <font color="Olive" title="b1">L</font>,<font color="Maroon" title="c2">S</font></span>)</span></span><a href="seq_4.html#K1" title="SEQ_4:func.1">}</a></span></span><br/><span class="kw">let </span><font color="Maroon" title="c3">L</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">J</font> being  <a href="ami_1.html#NM2" title="AMI_1:NM.2">Instruction</a> of <font color="Maroon" title="c2">S</font>  st <font color="Maroon" title="c2">S</font> is  <a href="ami_1.html#V9" title="AMI_1:attr.9">realistic</a>  &amp; <font color="Olive" title="b1">J</font> is  <a href="ami_1.html#V3" title="AMI_1:attr.3">halting</a>  holds <br/> <a href="amistd_3.html#K2" title="AMISTD_3:func.2">LocNums</a> <span class="p1">(<span class="default"><a href="amistd_1.html#K1" title="AMISTD_1:func.1">NIC</a> <font color="Olive" title="b1">J</font>,<font color="Maroon" title="c3">L</font></span>)</span>,<font color="Maroon" title="c2">S</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="seq_4.html#K1" title="SEQ_4:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="amistd_1.html#K7" title="AMISTD_1:func.7">locnum</a> <font color="Maroon" title="c3">L</font>,<font color="Maroon" title="c2">S</font></span>)</span></span><a href="seq_4.html#K1" title="SEQ_4:func.1">}</a></span></span><br/><span class="kw">let </span><font color="Maroon" title="c4">J</font> be   <a href="ami_1.html#NM2" title="AMI_1:NM.2">Instruction</a> of <font color="Maroon" title="c2">S</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">S</font> is  <a href="ami_1.html#V9" title="AMI_1:attr.9">realistic</a>  &amp; <font color="Maroon" title="c4">J</font> is  <a href="ami_1.html#V3" title="AMI_1:attr.3">halting</a>  implies  <a href="amistd_3.html#K2" title="AMISTD_3:func.2">LocNums</a> <span class="p1">(<span class="default"><a href="amistd_1.html#K1" title="AMISTD_1:func.1">NIC</a> <font color="Maroon" title="c4">J</font>,<font color="Maroon" title="c3">L</font></span>)</span>,<font color="Maroon" title="c2">S</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="seq_4.html#K1" title="SEQ_4:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="amistd_1.html#K7" title="AMISTD_1:func.7">locnum</a> <font color="Maroon" title="c3">L</font>,<font color="Maroon" title="c2">S</font></span>)</span></span><a href="seq_4.html#K1" title="SEQ_4:func.1">}</a></span> )</span><br/>







<span class="kw">assume </span><a NAME="E1:33"/>
( <font color="Maroon" title="c2">S</font> is  <a href="ami_1.html#V9" title="AMI_1:attr.9">realistic</a>  &amp; <font color="Maroon" title="c4">J</font> is  <a href="ami_1.html#V3" title="AMI_1:attr.3">halting</a>  )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="amistd_3.html#K2" title="AMISTD_3:func.2">LocNums</a> <span class="p1">(<span class="default"><a href="amistd_1.html#K1" title="AMISTD_1:func.1">NIC</a> <font color="Maroon" title="c4">J</font>,<font color="Maroon" title="c3">L</font></span>)</span>,<font color="Maroon" title="c2">S</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="seq_4.html#K1" title="SEQ_4:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="amistd_1.html#K7" title="AMISTD_1:func.7">locnum</a> <font color="Maroon" title="c3">L</font>,<font color="Maroon" title="c2">S</font></span>)</span></span><a href="seq_4.html#K1" title="SEQ_4:func.1">}</a></span></span><br/>

<span class="kw">then </span> <a href="amistd_1.html#K1" title="AMISTD_1:func.1">NIC</a> <font color="Maroon" title="c4">J</font>,<font color="Maroon" title="c3">L</font> = 
<span class="p1"><a href="seq_4.html#K1" title="SEQ_4:func.1">{</a><span class="default"><font color="Maroon" title="c3">L</font></span><a href="seq_4.html#K1" title="SEQ_4:func.1">}</a></span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="amistd_1.html#T15" title="AMISTD_1:th.15">AMISTD_1:15</a></span>
<br/>.= 
<span class="p1"><a href="seq_4.html#K1" title="SEQ_4: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="c2">S</font>,<span class="p3">(<span class="default"><a href="amistd_1.html#K7" title="AMISTD_1:func.7">locnum</a> <font color="Maroon" title="c3">L</font>,<font color="Maroon" title="c2">S</font></span>)</span></span>)</span></span><a href="seq_4.html#K1" title="SEQ_4:func.1">}</a></span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="amistd_1.html#D13" title="AMISTD_1:def.13">AMISTD_1:def 13</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E3:33"/>
 <a href="amistd_3.html#K2" title="AMISTD_3:func.2">LocNums</a> <span class="p1">(<span class="default"><a href="amistd_1.html#K1" title="AMISTD_1:func.1">NIC</a> <font color="Maroon" title="c4">J</font>,<font color="Maroon" title="c3">L</font></span>)</span>,<font color="Maroon" title="c2">S</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="seq_4.html#K1" title="SEQ_4:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="amistd_1.html#K7" title="AMISTD_1:func.7">locnum</a> <font color="Maroon" title="c3">L</font>,<font color="Maroon" title="c2">S</font></span>)</span></span><a href="seq_4.html#K1" title="SEQ_4:func.1">}</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="amistd_3.html#T26" target="_self" title="AMISTD_3:th.26">Th26</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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