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

<b>let </b><font color="Maroon" title="c1">N</font> be   <a href="e_siec.html#NM2" title="E_SIEC:NM.2">e_net</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="relat_1.html#NK4" title="RELAT_1:NK.4">rng</a> the <a href="e_siec.html#U1" title="E_SIEC:sel.1">entrance</a> of <font color="Maroon" title="c1">N</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#NK4" title="RELAT_1:NK.4">rng</a> <span class="p1">(<span class="default"><a href="sysrel.html#K1" title="SYSREL:func.1">CL</a> the <a href="e_siec.html#U1" title="E_SIEC:sel.1">entrance</a> of <font color="Maroon" title="c1">N</font></span>)</span> &amp;  <a href="relat_1.html#NK4" title="RELAT_1:NK.4">rng</a> the <a href="e_siec.html#U1" title="E_SIEC:sel.1">entrance</a> of <font color="Maroon" title="c1">N</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="sysrel.html#K1" title="SYSREL:func.1">CL</a> the <a href="e_siec.html#U1" title="E_SIEC:sel.1">entrance</a> of <font color="Maroon" title="c1">N</font></span>)</span> &amp;  <a href="relat_1.html#NK4" title="RELAT_1:NK.4">rng</a> the <a href="e_siec.html#U2" title="E_SIEC:sel.2">escape</a> of <font color="Maroon" title="c1">N</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#NK4" title="RELAT_1:NK.4">rng</a> <span class="p1">(<span class="default"><a href="sysrel.html#K1" title="SYSREL:func.1">CL</a> the <a href="e_siec.html#U2" title="E_SIEC:sel.2">escape</a> of <font color="Maroon" title="c1">N</font></span>)</span> &amp;  <a href="relat_1.html#NK4" title="RELAT_1:NK.4">rng</a> the <a href="e_siec.html#U2" title="E_SIEC:sel.2">escape</a> of <font color="Maroon" title="c1">N</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="sysrel.html#K1" title="SYSREL:func.1">CL</a> the <a href="e_siec.html#U2" title="E_SIEC:sel.2">escape</a> of <font color="Maroon" title="c1">N</font></span>)</span> &amp;  <a href="relat_1.html#NK4" title="RELAT_1:NK.4">rng</a> the <a href="e_siec.html#U1" title="E_SIEC:sel.1">entrance</a> of <font color="Maroon" title="c1">N</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#NK4" title="RELAT_1:NK.4">rng</a> the <a href="e_siec.html#U2" title="E_SIEC:sel.2">escape</a> of <font color="Maroon" title="c1">N</font> )</span><br/>

<a NAME="E1:19"/><i><font color="Green" title="E9">A1</font></i>: 
(  <a href="relat_1.html#NK4" title="RELAT_1:NK.4">rng</a> the <a href="e_siec.html#U1" title="E_SIEC:sel.1">entrance</a> of <font color="Maroon" title="c1">N</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#NK4" title="RELAT_1:NK.4">rng</a> <span class="p1">(<span class="default"><a href="sysrel.html#K1" title="SYSREL:func.1">CL</a> the <a href="e_siec.html#U1" title="E_SIEC:sel.1">entrance</a> of <font color="Maroon" title="c1">N</font></span>)</span> &amp;  <a href="relat_1.html#NK4" title="RELAT_1:NK.4">rng</a> the <a href="e_siec.html#U1" title="E_SIEC:sel.1">entrance</a> of <font color="Maroon" title="c1">N</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="sysrel.html#K1" title="SYSREL:func.1">CL</a> the <a href="e_siec.html#U1" title="E_SIEC:sel.1">entrance</a> of <font color="Maroon" title="c1">N</font></span>)</span> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="19_1"><b>proof </b></a><div class="add">

<a NAME="E1:19_1"/>
( the <a href="e_siec.html#U1" title="E_SIEC:sel.1">entrance</a> of <font color="Maroon" title="c1">N</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">*</a> the <a href="e_siec.html#U1" title="E_SIEC:sel.1">entrance</a> of <font color="Maroon" title="c1">N</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="e_siec.html#U1" title="E_SIEC:sel.1">entrance</a> of <font color="Maroon" title="c1">N</font> &amp; the <a href="e_siec.html#U1" title="E_SIEC:sel.1">entrance</a> of <font color="Maroon" title="c1">N</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">*</a> <span class="p1">(<span class="default">the <a href="e_siec.html#U1" title="E_SIEC:sel.1">entrance</a> of <font color="Maroon" title="c1">N</font> <a href="xboole_0.html#K4" title="XBOOLE_0:func.4">\</a> <span class="p2">(<span class="default"><a href="relat_1.html#K6" title="RELAT_1:func.6">id</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">N</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  )
 
<b>by </b><i><a class="ref" href="e_siec.html#D2" target="_self" title="E_SIEC:def.2">Def2</a>, <a class="ref" href="e_siec.html#D3" target="_self" title="E_SIEC:def.3">Def3</a></i>;<br/>
<a NAME="E2:19_1"/><b>then </b>
( the <a href="e_siec.html#U1" title="E_SIEC:sel.1">entrance</a> of <font color="Maroon" title="c1">N</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">*</a> the <a href="e_siec.html#U1" title="E_SIEC:sel.1">entrance</a> of <font color="Maroon" title="c1">N</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="e_siec.html#U1" title="E_SIEC:sel.1">entrance</a> of <font color="Maroon" title="c1">N</font> &amp; the <a href="e_siec.html#U1" title="E_SIEC:sel.1">entrance</a> of <font color="Maroon" title="c1">N</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">*</a> <span class="p1">(<span class="default">the <a href="e_siec.html#U1" title="E_SIEC:sel.1">entrance</a> of <font color="Maroon" title="c1">N</font> <a href="xboole_0.html#K4" title="XBOOLE_0:func.4">\</a> <span class="p2">(<span class="default"><a href="relat_1.html#K6" title="RELAT_1:func.6">id</a> <span class="p3">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> the <a href="e_siec.html#U1" title="E_SIEC:sel.1">entrance</a> of <font color="Maroon" title="c1">N</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  )
 
<b>by </b><i><a class="ref" href="e_siec.html#T16" target="_self" title="E_SIEC:th.16">Th16</a></i>;<br/>
<b>hence </b><a NAME="E3:19_1"/>
(  <a href="relat_1.html#NK4" title="RELAT_1:NK.4">rng</a> the <a href="e_siec.html#U1" title="E_SIEC:sel.1">entrance</a> of <font color="Maroon" title="c1">N</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#NK4" title="RELAT_1:NK.4">rng</a> <span class="p1">(<span class="default"><a href="sysrel.html#K1" title="SYSREL:func.1">CL</a> the <a href="e_siec.html#U1" title="E_SIEC:sel.1">entrance</a> of <font color="Maroon" title="c1">N</font></span>)</span> &amp;  <a href="relat_1.html#NK4" title="RELAT_1:NK.4">rng</a> the <a href="e_siec.html#U1" title="E_SIEC:sel.1">entrance</a> of <font color="Maroon" title="c1">N</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="sysrel.html#K1" title="SYSREL:func.1">CL</a> the <a href="e_siec.html#U1" title="E_SIEC:sel.1">entrance</a> of <font color="Maroon" title="c1">N</font></span>)</span> )
 <b>by </b><i><a class="ref" href="sysrel.html#T50" title="SYSREL:th.50">SYSREL:50</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><b>end;</b></div>
<a NAME="E2:19"/>
(  <a href="relat_1.html#NK4" title="RELAT_1:NK.4">rng</a> the <a href="e_siec.html#U2" title="E_SIEC:sel.2">escape</a> of <font color="Maroon" title="c1">N</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#NK4" title="RELAT_1:NK.4">rng</a> <span class="p1">(<span class="default"><a href="sysrel.html#K1" title="SYSREL:func.1">CL</a> the <a href="e_siec.html#U2" title="E_SIEC:sel.2">escape</a> of <font color="Maroon" title="c1">N</font></span>)</span> &amp;  <a href="relat_1.html#NK4" title="RELAT_1:NK.4">rng</a> the <a href="e_siec.html#U2" title="E_SIEC:sel.2">escape</a> of <font color="Maroon" title="c1">N</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="sysrel.html#K1" title="SYSREL:func.1">CL</a> the <a href="e_siec.html#U2" title="E_SIEC:sel.2">escape</a> of <font color="Maroon" title="c1">N</font></span>)</span> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="19_2"><b>proof </b></a><div class="add">

<a NAME="E1:19_2"/>
( the <a href="e_siec.html#U2" title="E_SIEC:sel.2">escape</a> of <font color="Maroon" title="c1">N</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">*</a> the <a href="e_siec.html#U2" title="E_SIEC:sel.2">escape</a> of <font color="Maroon" title="c1">N</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="e_siec.html#U2" title="E_SIEC:sel.2">escape</a> of <font color="Maroon" title="c1">N</font> &amp; the <a href="e_siec.html#U2" title="E_SIEC:sel.2">escape</a> of <font color="Maroon" title="c1">N</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">*</a> <span class="p1">(<span class="default">the <a href="e_siec.html#U2" title="E_SIEC:sel.2">escape</a> of <font color="Maroon" title="c1">N</font> <a href="xboole_0.html#K4" title="XBOOLE_0:func.4">\</a> <span class="p2">(<span class="default"><a href="relat_1.html#K6" title="RELAT_1:func.6">id</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">N</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  )
 
<b>by </b><i><a class="ref" href="e_siec.html#D2" target="_self" title="E_SIEC:def.2">Def2</a>, <a class="ref" href="e_siec.html#D3" target="_self" title="E_SIEC:def.3">Def3</a></i>;<br/>
<a NAME="E2:19_2"/><b>then </b>
( the <a href="e_siec.html#U2" title="E_SIEC:sel.2">escape</a> of <font color="Maroon" title="c1">N</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">*</a> the <a href="e_siec.html#U2" title="E_SIEC:sel.2">escape</a> of <font color="Maroon" title="c1">N</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="e_siec.html#U2" title="E_SIEC:sel.2">escape</a> of <font color="Maroon" title="c1">N</font> &amp; the <a href="e_siec.html#U2" title="E_SIEC:sel.2">escape</a> of <font color="Maroon" title="c1">N</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">*</a> <span class="p1">(<span class="default">the <a href="e_siec.html#U2" title="E_SIEC:sel.2">escape</a> of <font color="Maroon" title="c1">N</font> <a href="xboole_0.html#K4" title="XBOOLE_0:func.4">\</a> <span class="p2">(<span class="default"><a href="relat_1.html#K6" title="RELAT_1:func.6">id</a> <span class="p3">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> the <a href="e_siec.html#U2" title="E_SIEC:sel.2">escape</a> of <font color="Maroon" title="c1">N</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  )
 
<b>by </b><i><a class="ref" href="e_siec.html#T16" target="_self" title="E_SIEC:th.16">Th16</a></i>;<br/>
<b>hence </b><a NAME="E3:19_2"/>
(  <a href="relat_1.html#NK4" title="RELAT_1:NK.4">rng</a> the <a href="e_siec.html#U2" title="E_SIEC:sel.2">escape</a> of <font color="Maroon" title="c1">N</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#NK4" title="RELAT_1:NK.4">rng</a> <span class="p1">(<span class="default"><a href="sysrel.html#K1" title="SYSREL:func.1">CL</a> the <a href="e_siec.html#U2" title="E_SIEC:sel.2">escape</a> of <font color="Maroon" title="c1">N</font></span>)</span> &amp;  <a href="relat_1.html#NK4" title="RELAT_1:NK.4">rng</a> the <a href="e_siec.html#U2" title="E_SIEC:sel.2">escape</a> of <font color="Maroon" title="c1">N</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="sysrel.html#K1" title="SYSREL:func.1">CL</a> the <a href="e_siec.html#U2" title="E_SIEC:sel.2">escape</a> of <font color="Maroon" title="c1">N</font></span>)</span> )
 <b>by </b><i><a class="ref" href="sysrel.html#T50" title="SYSREL:th.50">SYSREL:50</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><b>end;</b></div>
<b>hence </b><a NAME="E3:19"/>
(  <a href="relat_1.html#NK4" title="RELAT_1:NK.4">rng</a> the <a href="e_siec.html#U1" title="E_SIEC:sel.1">entrance</a> of <font color="Maroon" title="c1">N</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#NK4" title="RELAT_1:NK.4">rng</a> <span class="p1">(<span class="default"><a href="sysrel.html#K1" title="SYSREL:func.1">CL</a> the <a href="e_siec.html#U1" title="E_SIEC:sel.1">entrance</a> of <font color="Maroon" title="c1">N</font></span>)</span> &amp;  <a href="relat_1.html#NK4" title="RELAT_1:NK.4">rng</a> the <a href="e_siec.html#U1" title="E_SIEC:sel.1">entrance</a> of <font color="Maroon" title="c1">N</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="sysrel.html#K1" title="SYSREL:func.1">CL</a> the <a href="e_siec.html#U1" title="E_SIEC:sel.1">entrance</a> of <font color="Maroon" title="c1">N</font></span>)</span> &amp;  <a href="relat_1.html#NK4" title="RELAT_1:NK.4">rng</a> the <a href="e_siec.html#U2" title="E_SIEC:sel.2">escape</a> of <font color="Maroon" title="c1">N</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#NK4" title="RELAT_1:NK.4">rng</a> <span class="p1">(<span class="default"><a href="sysrel.html#K1" title="SYSREL:func.1">CL</a> the <a href="e_siec.html#U2" title="E_SIEC:sel.2">escape</a> of <font color="Maroon" title="c1">N</font></span>)</span> &amp;  <a href="relat_1.html#NK4" title="RELAT_1:NK.4">rng</a> the <a href="e_siec.html#U2" title="E_SIEC:sel.2">escape</a> of <font color="Maroon" title="c1">N</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="sysrel.html#K1" title="SYSREL:func.1">CL</a> the <a href="e_siec.html#U2" title="E_SIEC:sel.2">escape</a> of <font color="Maroon" title="c1">N</font></span>)</span> &amp;  <a href="relat_1.html#NK4" title="RELAT_1:NK.4">rng</a> the <a href="e_siec.html#U1" title="E_SIEC:sel.1">entrance</a> of <font color="Maroon" title="c1">N</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#NK4" title="RELAT_1:NK.4">rng</a> the <a href="e_siec.html#U2" title="E_SIEC:sel.2">escape</a> of <font color="Maroon" title="c1">N</font> )
 <b>by </b><i><a class="txt" href="#E1:19"><i><font color="Green" title="E9">A1</font></i></a>, <a class="ref" href="e_siec.html#T17" target="_self" title="E_SIEC:th.17">Th17</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>
