<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon" title="c2">it1</font>, <font color="Maroon" title="c3">it2</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="finsub_1.html#K5" title="FINSUB_1:func.5">Fin</a> <a href="scmfsa_2.html#K3" title="SCMFSA_2:func.3">FinSeq-Locations</a> ;<br/>

<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:41_1_2_1"/>
(  <a href="ami_5.html#K1" title="AMI_5:func.1">InsCode</a> <font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 9 or  <a href="ami_5.html#K1" title="AMI_5:func.1">InsCode</a> <font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 10 )
 ;<br/><b>given </b><font color="Maroon" title="c4">a1</font>, <font color="Maroon" title="c5">b1</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a> , <font color="Maroon" title="c6">f1</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a> <b> such that </b><a NAME="E2:41_1_2_1"/><i><font color="Green" title="E31">A3</font></i>: 
( ( <font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">b1</font> <a href="scmfsa_2.html#K16" title="SCMFSA_2:func.16">:=</a> <font color="Maroon" title="c6">f1</font>,<font color="Maroon" title="c4">a1</font> or <font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">f1</font>,<font color="Maroon" title="c4">a1</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=</a> <font color="Maroon" title="c5">b1</font> ) &amp; <font color="Maroon" title="c2">it1</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"><font color="Maroon" title="c6">f1</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> )
 ;<br/><b>given </b><font color="Maroon" title="c7">a2</font>, <font color="Maroon" title="c8">b2</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a> , <font color="Maroon" title="c9">f2</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a> <b> such that </b><a NAME="E3:41_1_2_1"/><i><font color="Green" title="E32">A4</font></i>: 
( ( <font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">b2</font> <a href="scmfsa_2.html#K16" title="SCMFSA_2:func.16">:=</a> <font color="Maroon" title="c9">f2</font>,<font color="Maroon" title="c7">a2</font> or <font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">f2</font>,<font color="Maroon" title="c7">a2</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=</a> <font color="Maroon" title="c8">b2</font> ) &amp; <font color="Maroon" title="c3">it2</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"><font color="Maroon" title="c9">f2</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> )
 ;<br/><a NAME="E4:41_1_2_1"/><i><font color="Green" title="E33">A5</font></i>: 
( ( <font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">f1</font>,<font color="Maroon" title="c4">a1</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=</a> <font color="Maroon" title="c5">b1</font> or <font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">f2</font>,<font color="Maroon" title="c7">a2</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=</a> <font color="Maroon" title="c8">b2</font> ) implies  <a href="ami_5.html#K1" title="AMI_5:func.1">InsCode</a> <font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 10 )
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T51" title="SCMFSA_2:th.51">SCMFSA_2:51</a></i>;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="41_1_2_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:41_1_2_1_1"/>
( ( <font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">b1</font> <a href="scmfsa_2.html#K16" title="SCMFSA_2:func.16">:=</a> <font color="Maroon" title="c6">f1</font>,<font color="Maroon" title="c4">a1</font> &amp; <font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">b2</font> <a href="scmfsa_2.html#K16" title="SCMFSA_2:func.16">:=</a> <font color="Maroon" title="c9">f2</font>,<font color="Maroon" title="c7">a2</font> ) or ( <font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">f1</font>,<font color="Maroon" title="c4">a1</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=</a> <font color="Maroon" title="c5">b1</font> &amp; <font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">f2</font>,<font color="Maroon" title="c7">a2</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=</a> <font color="Maroon" title="c8">b2</font> ) )
 </span><b>by </b><i><a class="txt" href="sf_mastr.html#E2:41_1_2_1"><i><font color="Green" title="E31">A3</font></i></a>, <a class="txt" href="sf_mastr.html#E3:41_1_2_1"><i><font color="Green" title="E32">A4</font></i></a>, <a class="txt" href="sf_mastr.html#E4:41_1_2_1"><i><font color="Green" title="E33">A5</font></i></a>, <a class="ref" href="scmfsa_2.html#T50" title="SCMFSA_2:th.50">SCMFSA_2:50</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="41_1_2_1_1_1"><b>suppose </b></a><a NAME="E1:41_1_2_1_1_1"/>
( <font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">b1</font> <a href="scmfsa_2.html#K16" title="SCMFSA_2:func.16">:=</a> <font color="Maroon" title="c6">f1</font>,<font color="Maroon" title="c4">a1</font> &amp; <font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">b2</font> <a href="scmfsa_2.html#K16" title="SCMFSA_2:func.16">:=</a> <font color="Maroon" title="c9">f2</font>,<font color="Maroon" title="c7">a2</font> )
 ;<br/><div class="add"><b>hence </b><a NAME="E2:41_1_2_1_1_1"/>
<font color="Maroon" title="c2">it1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">it2</font>
 <b>by </b><i><a class="txt" href="sf_mastr.html#E2:41_1_2_1"><i><font color="Green" title="E31">A3</font></i></a>, <a class="txt" href="sf_mastr.html#E3:41_1_2_1"><i><font color="Green" title="E32">A4</font></i></a>, <a class="ref" href="sf_mastr.html#T13" target="_self" title="SF_MASTR:th.13">Th13</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="41_1_2_1_1_2"><b>suppose </b></a><a NAME="E1:41_1_2_1_1_2"/>
( <font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">f1</font>,<font color="Maroon" title="c4">a1</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=</a> <font color="Maroon" title="c5">b1</font> &amp; <font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">f2</font>,<font color="Maroon" title="c7">a2</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=</a> <font color="Maroon" title="c8">b2</font> )
 ;<br/><div class="add"><b>hence </b><a NAME="E2:41_1_2_1_1_2"/>
<font color="Maroon" title="c2">it1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">it2</font>
 <b>by </b><i><a class="txt" href="sf_mastr.html#E2:41_1_2_1"><i><font color="Green" title="E31">A3</font></i></a>, <a class="txt" href="sf_mastr.html#E3:41_1_2_1"><i><font color="Green" title="E32">A4</font></i></a>, <a class="ref" href="sf_mastr.html#T14" target="_self" title="SF_MASTR:th.14">Th14</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div>
<b>end;</b></div>

<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:41_1_2_2"/>
(  <a href="ami_5.html#K1" title="AMI_5:func.1">InsCode</a> <font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 11 or  <a href="ami_5.html#K1" title="AMI_5:func.1">InsCode</a> <font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 12 )
 ;<br/><b>given </b><font color="Maroon" title="c4">a1</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a> , <font color="Maroon" title="c5">f1</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a> <b> such that </b><a NAME="E2:41_1_2_2"/><i><font color="Green" title="E31">A6</font></i>: 
( ( <font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">a1</font> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">:=len</a> <font color="Maroon" title="c5">f1</font> or <font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">f1</font> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">:=&lt;0,...,0&gt;</a> <font color="Maroon" title="c4">a1</font> ) &amp; <font color="Maroon" title="c2">it1</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"><font color="Maroon" title="c5">f1</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> )
 ;<br/><b>given </b><font color="Maroon" title="c6">a2</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a> , <font color="Maroon" title="c7">f2</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a> <b> such that </b><a NAME="E3:41_1_2_2"/><i><font color="Green" title="E32">A7</font></i>: 
( ( <font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">a2</font> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">:=len</a> <font color="Maroon" title="c7">f2</font> or <font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">f2</font> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">:=&lt;0,...,0&gt;</a> <font color="Maroon" title="c6">a2</font> ) &amp; <font color="Maroon" title="c3">it2</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"><font color="Maroon" title="c7">f2</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> )
 ;<br/><a NAME="E4:41_1_2_2"/><i><font color="Green" title="E33">A8</font></i>: 
( ( <font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">f1</font> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">:=&lt;0,...,0&gt;</a> <font color="Maroon" title="c4">a1</font> or <font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">f2</font> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">:=&lt;0,...,0&gt;</a> <font color="Maroon" title="c6">a2</font> ) implies  <a href="ami_5.html#K1" title="AMI_5:func.1">InsCode</a> <font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 12 )
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T53" title="SCMFSA_2:th.53">SCMFSA_2:53</a></i>;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="41_1_2_2_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:41_1_2_2_1"/>
( ( <font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">a1</font> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">:=len</a> <font color="Maroon" title="c5">f1</font> &amp; <font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">a2</font> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">:=len</a> <font color="Maroon" title="c7">f2</font> ) or ( <font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">f1</font> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">:=&lt;0,...,0&gt;</a> <font color="Maroon" title="c4">a1</font> &amp; <font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">f2</font> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">:=&lt;0,...,0&gt;</a> <font color="Maroon" title="c6">a2</font> ) )
 </span><b>by </b><i><a class="txt" href="sf_mastr.html#E2:41_1_2_2"><i><font color="Green" title="E31">A6</font></i></a>, <a class="txt" href="sf_mastr.html#E3:41_1_2_2"><i><font color="Green" title="E32">A7</font></i></a>, <a class="txt" href="sf_mastr.html#E4:41_1_2_2"><i><font color="Green" title="E33">A8</font></i></a>, <a class="ref" href="scmfsa_2.html#T52" title="SCMFSA_2:th.52">SCMFSA_2:52</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="41_1_2_2_1_1"><b>suppose </b></a><a NAME="E1:41_1_2_2_1_1"/>
( <font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">a1</font> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">:=len</a> <font color="Maroon" title="c5">f1</font> &amp; <font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">a2</font> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">:=len</a> <font color="Maroon" title="c7">f2</font> )
 ;<br/><div class="add"><b>hence </b><a NAME="E2:41_1_2_2_1_1"/>
<font color="Maroon" title="c2">it1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">it2</font>
 <b>by </b><i><a class="txt" href="sf_mastr.html#E2:41_1_2_2"><i><font color="Green" title="E31">A6</font></i></a>, <a class="txt" href="sf_mastr.html#E3:41_1_2_2"><i><font color="Green" title="E32">A7</font></i></a>, <a class="ref" href="sf_mastr.html#T15" target="_self" title="SF_MASTR:th.15">Th15</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="41_1_2_2_1_2"><b>suppose </b></a><a NAME="E1:41_1_2_2_1_2"/>
( <font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">f1</font> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">:=&lt;0,...,0&gt;</a> <font color="Maroon" title="c4">a1</font> &amp; <font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">f2</font> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">:=&lt;0,...,0&gt;</a> <font color="Maroon" title="c6">a2</font> )
 ;<br/><div class="add"><b>hence </b><a NAME="E2:41_1_2_2_1_2"/>
<font color="Maroon" title="c2">it1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">it2</font>
 <b>by </b><i><a class="txt" href="sf_mastr.html#E2:41_1_2_2"><i><font color="Green" title="E31">A6</font></i></a>, <a class="txt" href="sf_mastr.html#E3:41_1_2_2"><i><font color="Green" title="E32">A7</font></i></a>, <a class="ref" href="sf_mastr.html#T16" target="_self" title="SF_MASTR:th.16">Th16</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div>
<b>end;</b></div>

<b>thus </b><a NAME="E3:41_1_2"/>
(  <a href="ami_5.html#K1" title="AMI_5:func.1">InsCode</a> <font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 9 or  <a href="ami_5.html#K1" title="AMI_5:func.1">InsCode</a> <font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 10 or  <a href="ami_5.html#K1" title="AMI_5:func.1">InsCode</a> <font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 11 or  <a href="ami_5.html#K1" title="AMI_5:func.1">InsCode</a> <font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 12 or  not <font color="Maroon" title="c2">it1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  or  not <font color="Maroon" title="c3">it2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  or <font color="Maroon" title="c2">it1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">it2</font> )
 ;<br/>


</div>
