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

<b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> be    <a href="subset_1.html#M1">Element</a> of  <a href="finsub_1.html#K5">Fin</a> <a href="scmfsa_2.html#K2">Int-Locations</a> ;<br/>

<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:19_1_2_1"/>
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="enumset1.html#K3">{</a><span class="default">1,2,3,4,5</span><a href="enumset1.html#K3">}</a></span>
 ;<br/><b>given </b><font color="Maroon">c<sub>4</sub></font>, <font color="Maroon">c<sub>5</sub></font> being    <a href="scmfsa_2.html#M1">Int-Location</a> <b> such that </b><a NAME="E2:19_1_2_1"/><i><font color="Green">E14</font></i>: 
( ( <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="scmfsa_2.html#K8">:=</a> <font color="Maroon">c<sub>5</sub></font> or <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K9">AddTo</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> or <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K10">SubFrom</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> or <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K11">MultBy</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> or <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K12">Divide</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> ) &amp; <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span><a href="tarski.html#K2">}</a></span> )
 ;<br/><b>given </b><font color="Maroon">c<sub>6</sub></font>, <font color="Maroon">c<sub>7</sub></font> being    <a href="scmfsa_2.html#M1">Int-Location</a> <b> such that </b><a NAME="E3:19_1_2_1"/><i><font color="Green">E15</font></i>: 
( ( <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font> <a href="scmfsa_2.html#K8">:=</a> <font color="Maroon">c<sub>7</sub></font> or <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K9">AddTo</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font> or <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K10">SubFrom</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font> or <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K11">MultBy</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font> or <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K12">Divide</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font> ) &amp; <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span><a href="tarski.html#K2">}</a></span> )
 ;<br/><a NAME="E4:19_1_2_1"/><i><font color="Green">E16</font></i>: 
( ( <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K9">AddTo</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> or <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K9">AddTo</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font> ) implies  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> 2 )
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T43">SCMFSA_2:43</a></i>;<br/><a NAME="E5:19_1_2_1"/><i><font color="Green">E17</font></i>: 
( ( <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K10">SubFrom</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> or <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K10">SubFrom</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font> ) implies  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> 3 )
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T44">SCMFSA_2:44</a></i>;<br/><a NAME="E6:19_1_2_1"/><i><font color="Green">E18</font></i>: 
( ( <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K11">MultBy</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> or <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K11">MultBy</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font> ) implies  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> 4 )
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T45">SCMFSA_2:45</a></i>;<br/><a NAME="E7:19_1_2_1"/><i><font color="Green">E19</font></i>: 
( ( <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K12">Divide</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> or <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K12">Divide</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font> ) implies  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> 5 )
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T46">SCMFSA_2:46</a></i>;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="19_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="E1:19_1_2_1_1"/>
( ( <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="scmfsa_2.html#K8">:=</a> <font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font> <a href="scmfsa_2.html#K8">:=</a> <font color="Maroon">c<sub>7</sub></font> ) or ( <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K9">AddTo</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K9">AddTo</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font> ) or ( <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K10">SubFrom</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K10">SubFrom</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font> ) or ( <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K11">MultBy</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K11">MultBy</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font> ) or ( <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K12">Divide</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K12">Divide</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font> ) )
 </span><b>by </b><i><a class="txt" href="sf_mastr.html#E2:19_1_2_1"><i><font color="Green">E14</font></i></a>, <a class="txt" href="sf_mastr.html#E3:19_1_2_1"><i><font color="Green">E15</font></i></a>, <a class="txt" href="sf_mastr.html#E4:19_1_2_1"><i><font color="Green">E16</font></i></a>, <a class="txt" href="sf_mastr.html#E5:19_1_2_1"><i><font color="Green">E17</font></i></a>, <a class="txt" href="sf_mastr.html#E6:19_1_2_1"><i><font color="Green">E18</font></i></a>, <a class="txt" href="sf_mastr.html#E7:19_1_2_1"><i><font color="Green">E19</font></i></a>, <a class="ref" href="scmfsa_2.html#T42">SCMFSA_2:42</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="19_1_2_1_1_1"><b>suppose </b></a><a NAME="E1:19_1_2_1_1_1"/>
( <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="scmfsa_2.html#K8">:=</a> <font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font> <a href="scmfsa_2.html#K8">:=</a> <font color="Maroon">c<sub>7</sub></font> )
 ;<br/><div class="add"><a NAME="E2:19_1_2_1_1_1"/><b>then </b>
( <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font> )
 <b>by </b><i><a class="ref" href="sf_mastr.html#T5" target="_self">Th5</a></i>;<br/><b>hence </b><a NAME="E3:19_1_2_1_1_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="sf_mastr.html#E2:19_1_2_1"><i><font color="Green">E14</font></i></a>, <a class="txt" href="sf_mastr.html#E3:19_1_2_1"><i><font color="Green">E15</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="19_1_2_1_1_2"><b>suppose </b></a><a NAME="E1:19_1_2_1_1_2"/>
( <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K9">AddTo</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K9">AddTo</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font> )
 ;<br/><div class="add"><a NAME="E2:19_1_2_1_1_2"/><b>then </b>
( <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font> )
 <b>by </b><i><a class="ref" href="sf_mastr.html#T6" target="_self">Th6</a></i>;<br/><b>hence </b><a NAME="E3:19_1_2_1_1_2"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="sf_mastr.html#E2:19_1_2_1"><i><font color="Green">E14</font></i></a>, <a class="txt" href="sf_mastr.html#E3:19_1_2_1"><i><font color="Green">E15</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="19_1_2_1_1_3"><b>suppose </b></a><a NAME="E1:19_1_2_1_1_3"/>
( <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K10">SubFrom</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K10">SubFrom</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font> )
 ;<br/><div class="add"><a NAME="E2:19_1_2_1_1_3"/><b>then </b>
( <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font> )
 <b>by </b><i><a class="ref" href="sf_mastr.html#T7" target="_self">Th7</a></i>;<br/><b>hence </b><a NAME="E3:19_1_2_1_1_3"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="sf_mastr.html#E2:19_1_2_1"><i><font color="Green">E14</font></i></a>, <a class="txt" href="sf_mastr.html#E3:19_1_2_1"><i><font color="Green">E15</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="19_1_2_1_1_4"><b>suppose </b></a><a NAME="E1:19_1_2_1_1_4"/>
( <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K11">MultBy</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K11">MultBy</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font> )
 ;<br/><div class="add"><a NAME="E2:19_1_2_1_1_4"/><b>then </b>
( <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font> )
 <b>by </b><i><a class="ref" href="sf_mastr.html#T8" target="_self">Th8</a></i>;<br/><b>hence </b><a NAME="E3:19_1_2_1_1_4"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="sf_mastr.html#E2:19_1_2_1"><i><font color="Green">E14</font></i></a>, <a class="txt" href="sf_mastr.html#E3:19_1_2_1"><i><font color="Green">E15</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="19_1_2_1_1_5"><b>suppose </b></a><a NAME="E1:19_1_2_1_1_5"/>
( <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K12">Divide</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K12">Divide</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font> )
 ;<br/><div class="add"><a NAME="E2:19_1_2_1_1_5"/><b>then </b>
( <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font> )
 <b>by </b><i><a class="ref" href="sf_mastr.html#T9" target="_self">Th9</a></i>;<br/><b>hence </b><a NAME="E3:19_1_2_1_1_5"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="sf_mastr.html#E2:19_1_2_1"><i><font color="Green">E14</font></i></a>, <a class="txt" href="sf_mastr.html#E3:19_1_2_1"><i><font color="Green">E15</font></i></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="E1:19_1_2_2"/>
(  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> 7 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> 8 )
 ;<br/><b>given </b><font color="Maroon">c<sub>4</sub></font> being    <a href="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">c<sub>5</sub></font> being   <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> <b> such that </b><a NAME="E2:19_1_2_2"/><i><font color="Green">E14</font></i>: 
( ( <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="scmfsa_2.html#K14">=0_goto</a> <font color="Maroon">c<sub>5</sub></font> or <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="scmfsa_2.html#K15">&gt;0_goto</a> <font color="Maroon">c<sub>5</sub></font> ) &amp; <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>4</sub></font></span><a href="tarski.html#K1">}</a></span> )
 ;<br/><b>given </b><font color="Maroon">c<sub>6</sub></font> being    <a href="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">c<sub>7</sub></font> being   <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> <b> such that </b><a NAME="E3:19_1_2_2"/><i><font color="Green">E15</font></i>: 
( ( <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font> <a href="scmfsa_2.html#K14">=0_goto</a> <font color="Maroon">c<sub>7</sub></font> or <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font> <a href="scmfsa_2.html#K15">&gt;0_goto</a> <font color="Maroon">c<sub>7</sub></font> ) &amp; <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>6</sub></font></span><a href="tarski.html#K1">}</a></span> )
 ;<br/><a NAME="E4:19_1_2_2"/><i><font color="Green">E16</font></i>: 
( ( <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="scmfsa_2.html#K15">&gt;0_goto</a> <font color="Maroon">c<sub>5</sub></font> or <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font> <a href="scmfsa_2.html#K15">&gt;0_goto</a> <font color="Maroon">c<sub>7</sub></font> ) implies  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> 8 )
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T49">SCMFSA_2:49</a></i>;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="19_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="E1:19_1_2_2_1"/>
( ( <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="scmfsa_2.html#K14">=0_goto</a> <font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font> <a href="scmfsa_2.html#K14">=0_goto</a> <font color="Maroon">c<sub>7</sub></font> ) or ( <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="scmfsa_2.html#K15">&gt;0_goto</a> <font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font> <a href="scmfsa_2.html#K15">&gt;0_goto</a> <font color="Maroon">c<sub>7</sub></font> ) )
 </span><b>by </b><i><a class="txt" href="sf_mastr.html#E2:19_1_2_2"><i><font color="Green">E14</font></i></a>, <a class="txt" href="sf_mastr.html#E3:19_1_2_2"><i><font color="Green">E15</font></i></a>, <a class="txt" href="sf_mastr.html#E4:19_1_2_2"><i><font color="Green">E16</font></i></a>, <a class="ref" href="scmfsa_2.html#T48">SCMFSA_2:48</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="19_1_2_2_1_1"><b>suppose </b></a><a NAME="E1:19_1_2_2_1_1"/>
( <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="scmfsa_2.html#K14">=0_goto</a> <font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font> <a href="scmfsa_2.html#K14">=0_goto</a> <font color="Maroon">c<sub>7</sub></font> )
 ;<br/><div class="add"><b>hence </b><a NAME="E2:19_1_2_2_1_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="sf_mastr.html#E2:19_1_2_2"><i><font color="Green">E14</font></i></a>, <a class="txt" href="sf_mastr.html#E3:19_1_2_2"><i><font color="Green">E15</font></i></a>, <a class="ref" href="sf_mastr.html#T11" target="_self">Th11</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="19_1_2_2_1_2"><b>suppose </b></a><a NAME="E1:19_1_2_2_1_2"/>
( <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="scmfsa_2.html#K15">&gt;0_goto</a> <font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font> <a href="scmfsa_2.html#K15">&gt;0_goto</a> <font color="Maroon">c<sub>7</sub></font> )
 ;<br/><div class="add"><b>hence </b><a NAME="E2:19_1_2_2_1_2"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="sf_mastr.html#E2:19_1_2_2"><i><font color="Green">E14</font></i></a>, <a class="txt" href="sf_mastr.html#E3:19_1_2_2"><i><font color="Green">E15</font></i></a>, <a class="ref" href="sf_mastr.html#T12" target="_self">Th12</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="E1:19_1_2_3"/>
(  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> 9 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> 10 )
 ;<br/><b>given </b><font color="Maroon">c<sub>4</sub></font>, <font color="Maroon">c<sub>5</sub></font> being    <a href="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">c<sub>6</sub></font> being    <a href="scmfsa_2.html#M2">FinSeq-Location</a> <b> such that </b><a NAME="E2:19_1_2_3"/><i><font color="Green">E14</font></i>: 
( ( <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K16">:=</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font> or <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="scmfsa_2.html#K17">:=</a> <font color="Maroon">c<sub>5</sub></font> ) &amp; <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span><a href="tarski.html#K2">}</a></span> )
 ;<br/><b>given </b><font color="Maroon">c<sub>7</sub></font>, <font color="Maroon">c<sub>8</sub></font> being    <a href="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">c<sub>9</sub></font> being    <a href="scmfsa_2.html#M2">FinSeq-Location</a> <b> such that </b><a NAME="E3:19_1_2_3"/><i><font color="Green">E15</font></i>: 
( ( <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>8</sub></font> <a href="scmfsa_2.html#K16">:=</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>7</sub></font> or <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="scmfsa_2.html#K17">:=</a> <font color="Maroon">c<sub>8</sub></font> ) &amp; <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font></span><a href="tarski.html#K2">}</a></span> )
 ;<br/><a NAME="E4:19_1_2_3"/><i><font color="Green">E16</font></i>: 
( ( <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="scmfsa_2.html#K17">:=</a> <font color="Maroon">c<sub>5</sub></font> or <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="scmfsa_2.html#K17">:=</a> <font color="Maroon">c<sub>8</sub></font> ) implies  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> 10 )
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T51">SCMFSA_2:51</a></i>;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="19_1_2_3_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:19_1_2_3_1"/>
( ( <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K16">:=</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font> &amp; <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>8</sub></font> <a href="scmfsa_2.html#K16">:=</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>7</sub></font> ) or ( <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="scmfsa_2.html#K17">:=</a> <font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="scmfsa_2.html#K17">:=</a> <font color="Maroon">c<sub>8</sub></font> ) )
 </span><b>by </b><i><a class="txt" href="sf_mastr.html#E2:19_1_2_3"><i><font color="Green">E14</font></i></a>, <a class="txt" href="sf_mastr.html#E3:19_1_2_3"><i><font color="Green">E15</font></i></a>, <a class="txt" href="sf_mastr.html#E4:19_1_2_3"><i><font color="Green">E16</font></i></a>, <a class="ref" href="scmfsa_2.html#T50">SCMFSA_2:50</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="19_1_2_3_1_1"><b>suppose </b></a><a NAME="E1:19_1_2_3_1_1"/>
( <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K16">:=</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font> &amp; <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>8</sub></font> <a href="scmfsa_2.html#K16">:=</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>7</sub></font> )
 ;<br/><div class="add"><a NAME="E2:19_1_2_3_1_1"/><b>then </b>
( <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>8</sub></font> )
 <b>by </b><i><a class="ref" href="sf_mastr.html#T13" target="_self">Th13</a></i>;<br/><b>hence </b><a NAME="E3:19_1_2_3_1_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="sf_mastr.html#E2:19_1_2_3"><i><font color="Green">E14</font></i></a>, <a class="txt" href="sf_mastr.html#E3:19_1_2_3"><i><font color="Green">E15</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="19_1_2_3_1_2"><b>suppose </b></a><a NAME="E1:19_1_2_3_1_2"/>
( <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="scmfsa_2.html#K17">:=</a> <font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="scmfsa_2.html#K17">:=</a> <font color="Maroon">c<sub>8</sub></font> )
 ;<br/><div class="add"><a NAME="E2:19_1_2_3_1_2"/><b>then </b>
( <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>8</sub></font> )
 <b>by </b><i><a class="ref" href="sf_mastr.html#T14" target="_self">Th14</a></i>;<br/><b>hence </b><a NAME="E3:19_1_2_3_1_2"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="sf_mastr.html#E2:19_1_2_3"><i><font color="Green">E14</font></i></a>, <a class="txt" href="sf_mastr.html#E3:19_1_2_3"><i><font color="Green">E15</font></i></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="E1:19_1_2_4"/>
(  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> 11 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> 12 )
 ;<br/><b>given </b><font color="Maroon">c<sub>4</sub></font> being    <a href="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">c<sub>5</sub></font> being    <a href="scmfsa_2.html#M2">FinSeq-Location</a> <b> such that </b><a NAME="E2:19_1_2_4"/><i><font color="Green">E14</font></i>: 
( ( <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="scmfsa_2.html#K18">:=len</a> <font color="Maroon">c<sub>5</sub></font> or <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>4</sub></font> ) &amp; <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>4</sub></font></span><a href="tarski.html#K1">}</a></span> )
 ;<br/><b>given </b><font color="Maroon">c<sub>6</sub></font> being    <a href="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">c<sub>7</sub></font> being    <a href="scmfsa_2.html#M2">FinSeq-Location</a> <b> such that </b><a NAME="E3:19_1_2_4"/><i><font color="Green">E15</font></i>: 
( ( <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font> <a href="scmfsa_2.html#K18">:=len</a> <font color="Maroon">c<sub>7</sub></font> or <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>6</sub></font> ) &amp; <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>6</sub></font></span><a href="tarski.html#K1">}</a></span> )
 ;<br/><a NAME="E4:19_1_2_4"/><i><font color="Green">E16</font></i>: 
( ( <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>4</sub></font> or <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>6</sub></font> ) implies  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> 12 )
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T53">SCMFSA_2:53</a></i>;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="19_1_2_4_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:19_1_2_4_1"/>
( ( <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="scmfsa_2.html#K18">:=len</a> <font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font> <a href="scmfsa_2.html#K18">:=len</a> <font color="Maroon">c<sub>7</sub></font> ) or ( <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>4</sub></font> &amp; <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>6</sub></font> ) )
 </span><b>by </b><i><a class="txt" href="sf_mastr.html#E2:19_1_2_4"><i><font color="Green">E14</font></i></a>, <a class="txt" href="sf_mastr.html#E3:19_1_2_4"><i><font color="Green">E15</font></i></a>, <a class="txt" href="sf_mastr.html#E4:19_1_2_4"><i><font color="Green">E16</font></i></a>, <a class="ref" href="scmfsa_2.html#T52">SCMFSA_2:52</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="19_1_2_4_1_1"><b>suppose </b></a><a NAME="E1:19_1_2_4_1_1"/>
( <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="scmfsa_2.html#K18">:=len</a> <font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font> <a href="scmfsa_2.html#K18">:=len</a> <font color="Maroon">c<sub>7</sub></font> )
 ;<br/><div class="add"><b>hence </b><a NAME="E2:19_1_2_4_1_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="sf_mastr.html#E2:19_1_2_4"><i><font color="Green">E14</font></i></a>, <a class="txt" href="sf_mastr.html#E3:19_1_2_4"><i><font color="Green">E15</font></i></a>, <a class="ref" href="sf_mastr.html#T15" target="_self">Th15</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="19_1_2_4_1_2"><b>suppose </b></a><a NAME="E1:19_1_2_4_1_2"/>
( <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>4</sub></font> &amp; <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>6</sub></font> )
 ;<br/><div class="add"><b>hence </b><a NAME="E2:19_1_2_4_1_2"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="sf_mastr.html#E2:19_1_2_4"><i><font color="Green">E14</font></i></a>, <a class="txt" href="sf_mastr.html#E3:19_1_2_4"><i><font color="Green">E15</font></i></a>, <a class="ref" href="sf_mastr.html#T16" target="_self">Th16</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div>
<b>end;</b></div>

<b>thus </b><a NAME="E5:19_1_2"/>
(  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="enumset1.html#K3">{</a><span class="default">1,2,3,4,5</span><a href="enumset1.html#K3">}</a></span> or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> 7 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> 8 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> 9 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> 10 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> 11 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> 12 or  not <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  or  not <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  or <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> )
 ;<br/>


</div>
