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<span class="kw">let </span><font color="Maroon" title="c1">a</font>, <font color="Maroon" title="c2">b</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="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="ami_2.html#K5" title="AMI_2: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"><a href="scmpds_2.html#K14" title="SCMPDS_2:func.14">SubFrom</a> <font color="Maroon" title="c1">a</font>,<font color="Olive" title="b2">k1</font>,<font color="Maroon" title="c2">b</font>,<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="c3">l</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ami_2.html#K5" title="AMI_2: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">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"><a href="scmpds_2.html#K14" title="SCMPDS_2:func.14">SubFrom</a> <font color="Maroon" title="c1">a</font>,<font color="Olive" title="b1">k1</font>,<font color="Maroon" title="c2">b</font>,<font color="Olive" title="b2">k2</font></span>)</span>,<font color="Maroon" title="c3">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="c3">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="c4">k1</font>, <font color="Maroon" title="c5">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="Red">::  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"><a href="scmpds_2.html#K14" title="SCMPDS_2:func.14">SubFrom</a> <font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c4">k1</font>,<font color="Maroon" title="c2">b</font>,<font color="Maroon" title="c5">k2</font></span>)</span>,<font color="Maroon" title="c3">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="c3">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="c6">i</font> =  <a href="scmpds_2.html#K14" title="SCMPDS_2:func.14">SubFrom</a> <font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c4">k1</font>,<font color="Maroon" title="c2">b</font>,<font color="Maroon" title="c5">k2</font>;<br/>
<a NAME="E1:21"/>
for <font color="Olive" title="b1">s</font> being  <a href="ami_1.html#NM5" title="AMI_1:NM.5">State</a> of <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a>   st  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Olive" title="b1">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">l</font> &amp; <font color="Olive" title="b1">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> <font color="Maroon" title="c3">l</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K14" title="SCMPDS_2:func.14">SubFrom</a> <font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c4">k1</font>,<font color="Maroon" title="c2">b</font>,<font color="Maroon" title="c5">k2</font> holds <br/><span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K14" title="SCMPDS_2:func.14">SubFrom</a> <font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c4">k1</font>,<font color="Maroon" title="c2">b</font>,<font color="Maroon" title="c5">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="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</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="ami_1.html#K6" title="AMI_1:func.6">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#T62" title="SCMPDS_2:th.62">SCMPDS_2:62</a></span>;<br/>
<span class="kw">hence </span><a NAME="E2:21"/>
 <a href="amistd_1.html#K1" title="AMISTD_1:func.1">NIC</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K14" title="SCMPDS_2:func.14">SubFrom</a> <font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c4">k1</font>,<font color="Maroon" title="c2">b</font>,<font color="Maroon" title="c5">k2</font></span>)</span>,<font color="Maroon" title="c3">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="c3">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#T7" target="_self" title="SCMPDS_9:th.7">Th7</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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