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

<b>let </b><font color="Maroon" title="c1">R</font> be  <a href="scmring1.html#V1" title="SCMRING1:attr.1">good</a> <a href="funcsdom.html#NM1" title="FUNCSDOM:NM.1">Ring</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">a</font> being   <a href="scmring2.html#M1" title="SCMRING2:mode.1">Data-Location</a> of <font color="Maroon" title="c1">R</font><br/> for <font color="Olive" title="b2">s1</font>, <font color="Olive" title="b3">s2</font> being  <a href="ami_1.html#NM5" title="AMI_1:NM.5">State</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c1">R</font></span>)</span>  st <font color="Olive" title="b2">s1</font>,<font color="Olive" title="b3">s2</font> <a href="funct_7.html#R1" title="FUNCT_7:pred.1">equal_outside</a>  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a>  holds <br/><font color="Olive" title="b2">s1</font> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Olive" title="b1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">s2</font> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Olive" title="b1">a</font></span><br/><b>let </b><font color="Maroon" title="c2">a</font> be    <a href="scmring2.html#M1" title="SCMRING2:mode.1">Data-Location</a> of <font color="Maroon" title="c1">R</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">s1</font>, <font color="Olive" title="b2">s2</font> being  <a href="ami_1.html#NM5" title="AMI_1:NM.5">State</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c1">R</font></span>)</span>  st <font color="Olive" title="b1">s1</font>,<font color="Olive" title="b2">s2</font> <a href="funct_7.html#R1" title="FUNCT_7:pred.1">equal_outside</a>  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a>  holds <br/><font color="Olive" title="b1">s1</font> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">s2</font> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c2">a</font></span><br/><b>let </b><font color="Maroon" title="c3">s1</font>, <font color="Maroon" title="c4">s2</font> be   <a href="ami_1.html#NM5" title="AMI_1:NM.5">State</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c1">R</font></span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c3">s1</font>,<font color="Maroon" title="c4">s2</font> <a href="funct_7.html#R1" title="FUNCT_7:pred.1">equal_outside</a>  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a>  implies <font color="Maroon" title="c3">s1</font> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">s2</font> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c2">a</font> )</span><br/>







<b>set </b><font color="Maroon" title="c5">IL</font> =  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a> ;<br/>
<b>assume </b><a NAME="E1:8"/><i><font color="Green" title="E7">A1</font></i>: 
<font color="Maroon" title="c3">s1</font>,<font color="Maroon" title="c4">s2</font> <a href="funct_7.html#R1" title="FUNCT_7:pred.1">equal_outside</a>  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c3">s1</font> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">s2</font> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c2">a</font></span><br/>

<a NAME="E2:8"/><i><font color="Green" title="E8">A2</font></i>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c3">s1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c1">R</font></span>)</span>
 
<b>by </b><i><a class="ref" href="ami_1.html#T79" title="AMI_1:th.79">AMI_1:79</a></i>;<br/>
<a NAME="E3:8"/><i><font color="Green" title="E9">A3</font></i>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c4">s2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c1">R</font></span>)</span>
 
<b>by </b><i><a class="ref" href="ami_1.html#T79" title="AMI_1:th.79">AMI_1:79</a></i>;<br/>
<a NAME="E4:8"/><i><font color="Green" title="E10">A4</font></i>: 
not <font color="Maroon" title="c2">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a> 
 
<b>by </b><i><a class="ref" href="scmring3.html#T2" target="_self" title="SCMRING3:th.2">Th2</a></i>;<br/>
<a NAME="E5:8"/><b>then </b>
<font color="Maroon" title="c2">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c3">s1</font></span>)</span> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a> 
 
<b>by </b><i><a class="txt" href="#E2:8"><i><font color="Green" title="E8">A2</font></i></a>, <a class="ref" href="xboole_0.html#D5" title="XBOOLE_0:def.5">XBOOLE_0:def 5</a></i>;<br/>
<a NAME="E6:8"/><b>then </b><i><font color="Green" title="E11">A5</font></i>: 
<font color="Maroon" title="c2">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c3">s1</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c3">s1</font></span>)</span> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a> </span>)</span>
 
<b>by </b><i><a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></i>;<br/>
<a NAME="E7:8"/>
<font color="Maroon" title="c2">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c4">s2</font></span>)</span> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a> 
 
<b>by </b><i><a class="txt" href="#E3:8"><i><font color="Green" title="E9">A3</font></i></a>, <a class="txt" href="#E4:8"><i><font color="Green" title="E10">A4</font></i></a>, <a class="ref" href="xboole_0.html#D5" title="XBOOLE_0:def.5">XBOOLE_0:def 5</a></i>;<br/>
<a NAME="E8:8"/><b>then </b><i><font color="Green" title="E12">A6</font></i>: 
<font color="Maroon" title="c2">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c4">s2</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c4">s2</font></span>)</span> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a> </span>)</span>
 
<b>by </b><i><a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></i>;<br/>
<b>thus </b><font color="Maroon" title="c3">s1</font> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c2">a</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">s1</font> <a href="card_3.html#K11" title="CARD_3:func.11">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c3">s1</font></span>)</span> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a> </span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c2">a</font>
<b>by </b><i><a class="txt" href="#E6:8"><i><font color="Green" title="E11">A5</font></i></a>, <a class="ref" href="funct_1.html#T71" title="FUNCT_1:th.71">FUNCT_1:71</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">s2</font> <a href="card_3.html#K11" title="CARD_3:func.11">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c4">s2</font></span>)</span> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a> </span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c2">a</font>
<b>by </b><i><a class="txt" href="#E1:8"><i><font color="Green" title="E7">A1</font></i></a>, <a class="ref" href="funct_7.html#D2" title="FUNCT_7:def.2">FUNCT_7:def 2</a></i>
<br/>.= 
<font color="Maroon" title="c4">s2</font> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c2">a</font>
<b>by </b><i><a class="txt" href="#E8:8"><i><font color="Green" title="E12">A6</font></i></a>, <a class="ref" href="funct_1.html#T71" title="FUNCT_1:th.71">FUNCT_1:71</a></i>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
