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<span class="kw">let </span><font color="Maroon" title="c1">a</font> be    <a href="scmpds_2.html#M1" title="SCMPDS_2:mode.1">Int_position</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">l</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> <br/>  for <font color="Olive" title="b2">k1</font>, <font color="Olive" title="b3">k2</font> being   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a> holds   <a href="amistd_1.html#K1" title="AMISTD_1:func.1">NIC</a> (<span class="p1">(<span class="default">(<font color="Maroon" title="c1">a</font>,<font color="Olive" title="b2">k1</font>) <a href="scmpds_2.html#K11" title="SCMPDS_2:func.11">:=</a> <font color="Olive" title="b3">k2</font></span>)</span>,<font color="Olive" title="b1">l</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="ordinal1.html#K1" title="ORDINAL1:func.1">succ</a> <font color="Olive" title="b1">l</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span><br/><span class="kw">let </span><font color="Maroon" title="c2">l</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">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="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">k1</font>, <font color="Olive" title="b2">k2</font> being   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a> holds   <a href="amistd_1.html#K1" title="AMISTD_1:func.1">NIC</a> (<span class="p1">(<span class="default">(<font color="Maroon" title="c1">a</font>,<font color="Olive" title="b1">k1</font>) <a href="scmpds_2.html#K11" title="SCMPDS_2:func.11">:=</a> <font color="Olive" title="b2">k2</font></span>)</span>,<font color="Maroon" title="c2">l</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="ordinal1.html#K1" title="ORDINAL1:func.1">succ</a> <font color="Maroon" title="c2">l</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span><br/><span class="kw">let </span><font color="Maroon" title="c3">k1</font>, <font color="Maroon" title="c4">k2</font> be   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="amistd_1.html#K1" title="AMISTD_1:func.1">NIC</a> (<span class="p1">(<span class="default">(<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c3">k1</font>) <a href="scmpds_2.html#K11" title="SCMPDS_2:func.11">:=</a> <font color="Maroon" title="c4">k2</font></span>)</span>,<font color="Maroon" title="c2">l</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="ordinal1.html#K1" title="ORDINAL1:func.1">succ</a> <font color="Maroon" title="c2">l</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span><br/>







<span class="kw">set </span><font color="Maroon" title="c5">i</font> = (<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c3">k1</font>) <a href="scmpds_2.html#K11" title="SCMPDS_2:func.11">:=</a> <font color="Maroon" title="c4">k2</font>;<br/>
<a NAME="E1:11"/>
 for <font color="Olive" title="b1">s</font> being   <a href="memstr_0.html#NM2" title="MEMSTR_0:NM.2">State</a> of <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a>  st  <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <font color="Olive" title="b1">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">l</font> holds <br/><span class="p1">(<span class="default"><a href="extpro_1.html#K2" title="EXTPRO_1:func.2">Exec</a> (<span class="p2">(<span class="default">(<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c3">k1</font>) <a href="scmpds_2.html#K11" title="SCMPDS_2:func.11">:=</a> <font color="Maroon" title="c4">k2</font></span>)</span>,<font color="Olive" title="b1">s</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="memstr_0.html#NK2" title="MEMSTR_0:NK.2">IC</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ordinal1.html#K1" title="ORDINAL1:func.1">succ</a> <span class="p1">(<span class="default"><a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <font color="Olive" title="b1">s</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmpds_2.html#T46" title="SCMPDS_2:th.46">SCMPDS_2:46</a></span>;<br/>
<span class="kw">hence </span><a NAME="E2:11"/>
 <a href="amistd_1.html#K1" title="AMISTD_1:func.1">NIC</a> (<span class="p1">(<span class="default">(<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c3">k1</font>) <a href="scmpds_2.html#K11" title="SCMPDS_2:func.11">:=</a> <font color="Maroon" title="c4">k2</font></span>)</span>,<font color="Maroon" title="c2">l</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="ordinal1.html#K1" title="ORDINAL1:func.1">succ</a> <font color="Maroon" title="c2">l</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmpds_9.html#T1" target="_self" title="SCMPDS_9:th.1">Th7</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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