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

<span class="kw">let </span><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> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">N</font> being  <a href="e_siec.html#NM2" title="E_SIEC:NM.2">e_net</a>  st ( <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="Olive" title="b1">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="Olive" title="b1">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> holds <br/>( <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="Olive" title="b1">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="Olive" title="b1">N</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c3">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:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( ( <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> ) )</span><br/>





<a NAME="E1:31"/><span class="lab"><font color="Green" title="E12">A1</font></span>: 
( <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="31_1"><span class="kw">proof </span></a><div class="add">

<a NAME="E1:31_1"/>
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> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="e_siec.html#D3" target="_self" title="E_SIEC:def.3">Def3</a></span>;<br/>
<a NAME="E2:31_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E13">A2</font></span>: 
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#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="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> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="e_siec.html#T16" target="_self" title="E_SIEC:th.16">Th16</a></span>;<br/>
<a NAME="E3:31_1"/>
 <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="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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="e_siec.html#T19" target="_self" title="E_SIEC:th.19">Th19</a></span>;<br/>
<a NAME="E4:31_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E14">A3</font></span>: 
<span class="p1">(<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="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#NK2" title="RELAT_1:NK.2">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#NK2" title="RELAT_1:NK.2">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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_1.html#T33" title="XBOOLE_1:th.33">XBOOLE_1:33</a></span>;<br/>
<span class="kw">assume </span><a NAME="E5:31_1"/><span class="lab"><font color="Green" title="E15">A4</font></span>: 
( <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> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <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> )</span><br/>

<a NAME="E6:31_1"/><span class="lab"><font color="Green" title="E16">A5</font></span>: 
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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="e_siec.html#D2" target="_self" title="E_SIEC:def.2">Def2</a></span>;<br/>
<a NAME="E7:31_1"/><span class="kw">then </span>
<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#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="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#NK2" title="RELAT_1:NK.2">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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:31_1"><span class="lab"><font color="Green" title="E15">A4</font></span></a>, <a class="txt" href="#E2:31_1"><span class="lab"><font color="Green" title="E13">A2</font></span></a>, <a class="ref" href="sysrel.html#T49" title="SYSREL:th.49">SYSREL:49</a></span>;<br/>
<a NAME="E8:31_1"/><span class="kw">then </span>
<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#NK2" title="RELAT_1:NK.2">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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:31_1"><span class="lab"><font color="Green" title="E14">A3</font></span></a></span>;<br/>
<a NAME="E9:31_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E17">A6</font></span>: 
<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#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="c3">N</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="e_siec.html#T18" target="_self" title="E_SIEC:th.18">Th18</a></span>;<br/>
<a NAME="E10:31_1"/>
<font color="Maroon" title="c2">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</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="c3">N</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:31_1"><span class="lab"><font color="Green" title="E15">A4</font></span></a>, <a class="txt" href="#E6:31_1"><span class="lab"><font color="Green" title="E16">A5</font></span></a>, <a class="txt" href="#E2:31_1"><span class="lab"><font color="Green" title="E13">A2</font></span></a>, <a class="ref" href="sysrel.html#T49" title="SYSREL:th.49">SYSREL:49</a></span>;<br/>
<a NAME="E11:31_1"/><span class="kw">then </span>
<font color="Maroon" title="c2">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</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="c3">N</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="e_siec.html#T18" target="_self" title="E_SIEC:th.18">Th18</a></span>;<br/>
<span class="kw">hence </span><a NAME="E12:31_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> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:31_1"><span class="lab"><font color="Green" title="E17">A6</font></span></a>, <a class="ref" href="e_siec.html#T18" target="_self" title="E_SIEC:th.18">Th18</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<a NAME="E2:31"/>
( <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="31_2"><span class="kw">proof </span></a><div class="add">

<a NAME="E1:31_2"/>
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> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="e_siec.html#D3" target="_self" title="E_SIEC:def.3">Def3</a></span>;<br/>
<a NAME="E2:31_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E13">A7</font></span>: 
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#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="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> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="e_siec.html#T16" target="_self" title="E_SIEC:th.16">Th16</a></span>;<br/>
<a NAME="E3:31_2"/>
 <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="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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="e_siec.html#T19" target="_self" title="E_SIEC:th.19">Th19</a></span>;<br/>
<a NAME="E4:31_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E14">A8</font></span>: 
<span class="p1">(<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="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#NK2" title="RELAT_1:NK.2">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#NK2" title="RELAT_1:NK.2">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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_1.html#T33" title="XBOOLE_1:th.33">XBOOLE_1:33</a></span>;<br/>
<span class="kw">assume </span><a NAME="E5:31_2"/><span class="lab"><font color="Green" title="E15">A9</font></span>: 
( <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> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <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> )</span><br/>

<a NAME="E6:31_2"/><span class="lab"><font color="Green" title="E16">A10</font></span>: 
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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="e_siec.html#D2" target="_self" title="E_SIEC:def.2">Def2</a></span>;<br/>
<a NAME="E7:31_2"/><span class="kw">then </span>
<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#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="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#NK2" title="RELAT_1:NK.2">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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:31_2"><span class="lab"><font color="Green" title="E15">A9</font></span></a>, <a class="txt" href="#E2:31_2"><span class="lab"><font color="Green" title="E13">A7</font></span></a>, <a class="ref" href="sysrel.html#T49" title="SYSREL:th.49">SYSREL:49</a></span>;<br/>
<a NAME="E8:31_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E17">A11</font></span>: 
<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#NK2" title="RELAT_1:NK.2">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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:31_2"><span class="lab"><font color="Green" title="E14">A8</font></span></a></span>;<br/>
<a NAME="E9:31_2"/>
<font color="Maroon" title="c2">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</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="c3">N</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:31_2"><span class="lab"><font color="Green" title="E15">A9</font></span></a>, <a class="txt" href="#E6:31_2"><span class="lab"><font color="Green" title="E16">A10</font></span></a>, <a class="txt" href="#E2:31_2"><span class="lab"><font color="Green" title="E13">A7</font></span></a>, <a class="ref" href="sysrel.html#T49" title="SYSREL:th.49">SYSREL:49</a></span>;<br/>
<span class="kw">hence </span><a NAME="E10:31_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> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:31_2"><span class="lab"><font color="Green" title="E17">A11</font></span></a>, <a class="ref" href="e_siec.html#T18" target="_self" title="E_SIEC:th.18">Th18</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E3:31"/>
( ( <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> ) )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:31"><span class="lab"><font color="Green" title="E12">A1</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
