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

<b>let </b><font color="Maroon" title="c1">x</font>, <font color="Maroon" title="c2">y</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c3">N</font> be   <a href="e_siec.html#NM2" title="E_SIEC:NM.2">e_net</a>;<br/>





<a NAME="E1:25"/><i><font color="Green" title="E12">A1</font></i>: 
( <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="e_siec.html#U1" title="E_SIEC:sel.1">entrance</a> of <font color="Maroon" title="c3">N</font> &amp; <font color="Maroon" title="c1">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">y</font> implies ( <font color="Maroon" title="c1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="e_siec.html#K8" title="E_SIEC:func.8">e_Transitions</a> <font color="Maroon" title="c3">N</font> &amp; <font color="Maroon" title="c2">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="e_siec.html#K7" title="E_SIEC:func.7">e_Places</a> <font color="Maroon" title="c3">N</font> ) )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="25_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:25_1"/>
( <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="e_siec.html#U1" title="E_SIEC:sel.1">entrance</a> of <font color="Maroon" title="c3">N</font> &amp; <font color="Maroon" title="c1">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">y</font> )
 ;<br/>

<a NAME="E2:25_1"/><b>then </b>
( the <a href="e_siec.html#U1" title="E_SIEC:sel.1">entrance</a> of <font color="Maroon" title="c3">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="c3">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="c3">N</font> &amp; the <a href="e_siec.html#U1" title="E_SIEC:sel.1">entrance</a> of <font color="Maroon" title="c3">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="c3">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="c3">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>  &amp; <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="e_siec.html#U1" title="E_SIEC:sel.1">entrance</a> of <font color="Maroon" title="c3">N</font> &amp; <font color="Maroon" title="c1">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">y</font> )
 
<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="E3:25_1"/><b>then </b><i><font color="Green" title="E13">A2</font></i>: 
( the <a href="e_siec.html#U1" title="E_SIEC:sel.1">entrance</a> of <font color="Maroon" title="c3">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="c3">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="c3">N</font> &amp; the <a href="e_siec.html#U1" title="E_SIEC:sel.1">entrance</a> of <font color="Maroon" title="c3">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="c3">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#K1" title="RELAT_1:func.1">dom</a> the <a href="e_siec.html#U1" title="E_SIEC:sel.1">entrance</a> of <font color="Maroon" title="c3">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>  &amp; <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="e_siec.html#U1" title="E_SIEC:sel.1">entrance</a> of <font color="Maroon" title="c3">N</font> &amp; <font color="Maroon" title="c1">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">y</font> )
 
<b>by </b><i><a class="ref" href="e_siec.html#T16" target="_self" title="E_SIEC:th.16">Th16</a></i>;<br/>
<a NAME="E4:25_1"/>
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> the <a href="e_siec.html#U1" title="E_SIEC:sel.1">entrance</a> of <font color="Maroon" title="c3">N</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">N</font>
 
<b>by </b><i><a class="ref" href="e_siec.html#T19" target="_self" title="E_SIEC:th.19">Th19</a></i>;<br/>
<a NAME="E5:25_1"/><b>then </b>
( <font color="Maroon" title="c1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> the <a href="e_siec.html#U1" title="E_SIEC:sel.1">entrance</a> of <font color="Maroon" title="c3">N</font></span>)</span> <a href="xboole_0.html#K4" title="XBOOLE_0:func.4">\</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p2">(<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="c3">N</font></span>)</span></span>)</span> &amp; <span class="p1">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> the <a href="e_siec.html#U1" title="E_SIEC:sel.1">entrance</a> of <font color="Maroon" title="c3">N</font></span>)</span> <a href="xboole_0.html#K4" title="XBOOLE_0:func.4">\</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p2">(<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="c3">N</font></span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">N</font> <a href="xboole_0.html#K4" title="XBOOLE_0:func.4">\</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p2">(<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="c3">N</font></span>)</span></span>)</span> )
 
<b>by </b><i><a class="txt" href="e_siec.html#E3:25_1"><i><font color="Green" title="E13">A2</font></i></a>, <a class="ref" href="sysrel.html#T49" title="SYSREL:th.49">SYSREL:49</a>, <a class="ref" href="xboole_1.html#T33" title="XBOOLE_1:th.33">XBOOLE_1:33</a></i>;<br/>
<a NAME="E6:25_1"/><b>then </b>
( <font color="Maroon" title="c1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">N</font> <a href="xboole_0.html#K4" title="XBOOLE_0:func.4">\</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p2">(<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="c3">N</font></span>)</span></span>)</span> &amp; <font color="Maroon" title="c2">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">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="c3">N</font></span>)</span> )
 
<b>by </b><i><a class="txt" href="e_siec.html#E3:25_1"><i><font color="Green" title="E13">A2</font></i></a>, <a class="ref" href="sysrel.html#T49" title="SYSREL:th.49">SYSREL:49</a></i>;<br/>
<b>hence </b><a NAME="E7:25_1"/>
( <font color="Maroon" title="c1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="e_siec.html#K8" title="E_SIEC:func.8">e_Transitions</a> <font color="Maroon" title="c3">N</font> &amp; <font color="Maroon" title="c2">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="e_siec.html#K7" title="E_SIEC:func.7">e_Places</a> <font color="Maroon" title="c3">N</font> )
 <b>by </b><i><a class="ref" href="e_siec.html#T18" target="_self" title="E_SIEC:th.18">Th18</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E2:25"/>
( <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="e_siec.html#U2" title="E_SIEC:sel.2">escape</a> of <font color="Maroon" title="c3">N</font> &amp; <font color="Maroon" title="c1">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">y</font> implies ( <font color="Maroon" title="c1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="e_siec.html#K8" title="E_SIEC:func.8">e_Transitions</a> <font color="Maroon" title="c3">N</font> &amp; <font color="Maroon" title="c2">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="e_siec.html#K7" title="E_SIEC:func.7">e_Places</a> <font color="Maroon" title="c3">N</font> ) )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="25_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:25_2"/>
( <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="e_siec.html#U2" title="E_SIEC:sel.2">escape</a> of <font color="Maroon" title="c3">N</font> &amp; <font color="Maroon" title="c1">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">y</font> )
 ;<br/>

<a NAME="E2:25_2"/><b>then </b>
( the <a href="e_siec.html#U2" title="E_SIEC:sel.2">escape</a> of <font color="Maroon" title="c3">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="c3">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="c3">N</font> &amp; the <a href="e_siec.html#U2" title="E_SIEC:sel.2">escape</a> of <font color="Maroon" title="c3">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="c3">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="c3">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>  &amp; <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="e_siec.html#U2" title="E_SIEC:sel.2">escape</a> of <font color="Maroon" title="c3">N</font> &amp; <font color="Maroon" title="c1">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">y</font> )
 
<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="E3:25_2"/><b>then </b><i><font color="Green" title="E13">A3</font></i>: 
( the <a href="e_siec.html#U2" title="E_SIEC:sel.2">escape</a> of <font color="Maroon" title="c3">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="c3">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="c3">N</font> &amp; the <a href="e_siec.html#U2" title="E_SIEC:sel.2">escape</a> of <font color="Maroon" title="c3">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="c3">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#K1" title="RELAT_1:func.1">dom</a> the <a href="e_siec.html#U2" title="E_SIEC:sel.2">escape</a> of <font color="Maroon" title="c3">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>  &amp; <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="e_siec.html#U2" title="E_SIEC:sel.2">escape</a> of <font color="Maroon" title="c3">N</font> &amp; <font color="Maroon" title="c1">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">y</font> )
 
<b>by </b><i><a class="ref" href="e_siec.html#T16" target="_self" title="E_SIEC:th.16">Th16</a></i>;<br/>
<a NAME="E4:25_2"/>
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> the <a href="e_siec.html#U2" title="E_SIEC:sel.2">escape</a> of <font color="Maroon" title="c3">N</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">N</font>
 
<b>by </b><i><a class="ref" href="e_siec.html#T19" target="_self" title="E_SIEC:th.19">Th19</a></i>;<br/>
<a NAME="E5:25_2"/><b>then </b>
( <font color="Maroon" title="c1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> the <a href="e_siec.html#U2" title="E_SIEC:sel.2">escape</a> of <font color="Maroon" title="c3">N</font></span>)</span> <a href="xboole_0.html#K4" title="XBOOLE_0:func.4">\</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p2">(<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="c3">N</font></span>)</span></span>)</span> &amp; <span class="p1">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> the <a href="e_siec.html#U2" title="E_SIEC:sel.2">escape</a> of <font color="Maroon" title="c3">N</font></span>)</span> <a href="xboole_0.html#K4" title="XBOOLE_0:func.4">\</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p2">(<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="c3">N</font></span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">N</font> <a href="xboole_0.html#K4" title="XBOOLE_0:func.4">\</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p2">(<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="c3">N</font></span>)</span></span>)</span> )
 
<b>by </b><i><a class="txt" href="e_siec.html#E3:25_2"><i><font color="Green" title="E13">A3</font></i></a>, <a class="ref" href="sysrel.html#T49" title="SYSREL:th.49">SYSREL:49</a>, <a class="ref" href="xboole_1.html#T33" title="XBOOLE_1:th.33">XBOOLE_1:33</a></i>;<br/>
<a NAME="E6:25_2"/><b>then </b>
( <font color="Maroon" title="c1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">N</font> <a href="xboole_0.html#K4" title="XBOOLE_0:func.4">\</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p2">(<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="c3">N</font></span>)</span></span>)</span> &amp; <font color="Maroon" title="c2">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">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="c3">N</font></span>)</span> )
 
<b>by </b><i><a class="txt" href="e_siec.html#E3:25_2"><i><font color="Green" title="E13">A3</font></i></a>, <a class="ref" href="sysrel.html#T49" title="SYSREL:th.49">SYSREL:49</a></i>;<br/>
<a NAME="E7:25_2"/><b>then </b>
( <font color="Maroon" title="c1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">N</font> <a href="xboole_0.html#K4" title="XBOOLE_0:func.4">\</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> the <a href="e_siec.html#U2" title="E_SIEC:sel.2">escape</a> of <font color="Maroon" title="c3">N</font></span>)</span> &amp; <font color="Maroon" title="c2">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> the <a href="e_siec.html#U2" title="E_SIEC:sel.2">escape</a> of <font color="Maroon" title="c3">N</font> )
 
<b>by </b><i><a class="ref" href="e_siec.html#T18" target="_self" title="E_SIEC:th.18">Th18</a></i>;<br/>
<b>hence </b><a NAME="E8:25_2"/>
( <font color="Maroon" title="c1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="e_siec.html#K8" title="E_SIEC:func.8">e_Transitions</a> <font color="Maroon" title="c3">N</font> &amp; <font color="Maroon" title="c2">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="e_siec.html#K7" title="E_SIEC:func.7">e_Places</a> <font color="Maroon" title="c3">N</font> )
 <b>by </b><i><a class="ref" href="e_siec.html#T18" target="_self" title="E_SIEC:th.18">Th18</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E3:25"/>
( ( <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="e_siec.html#U1" title="E_SIEC:sel.1">entrance</a> of <font color="Maroon" title="c3">N</font> or <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="e_siec.html#U2" title="E_SIEC:sel.2">escape</a> of <font color="Maroon" title="c3">N</font> ) &amp; <font color="Maroon" title="c1">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">y</font> implies ( <font color="Maroon" title="c1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="e_siec.html#K8" title="E_SIEC:func.8">e_Transitions</a> <font color="Maroon" title="c3">N</font> &amp; <font color="Maroon" title="c2">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="e_siec.html#K7" title="E_SIEC:func.7">e_Places</a> <font color="Maroon" title="c3">N</font> ) )
 <b>by </b><i><a class="txt" href="e_siec.html#E1:25"><i><font color="Green" title="E12">A1</font></i></a></i>;<br/>


</div>
