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

<span class="kw">let </span><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:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <span class="p1">(<span class="default"><a href="relat_1.html#K6" title="RELAT_1:func.6">id</a> <span class="p2">(<span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">N</font> <a href="xboole_0.html#K4" title="XBOOLE_0:func.4">\</a> <span class="p3">(<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="c1">N</font></span>)</span></span>)</span></span>)</span> <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> 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="p1">(<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> &amp; <span class="p1">(<span class="default"><a href="relat_1.html#K6" title="RELAT_1:func.6">id</a> <span class="p2">(<span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">N</font> <a href="xboole_0.html#K4" title="XBOOLE_0:func.4">\</a> <span class="p3">(<span class="default"><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></span>)</span></span>)</span></span>)</span> <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> 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="p1">(<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><br/>

<a NAME="E1:42"/>
for <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">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="c1">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#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> holds <br/><span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">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> <span class="p1">(<span class="default"><a href="relat_1.html#K6" title="RELAT_1:func.6">id</a> <span class="p2">(<span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">N</font> <a href="xboole_0.html#K4" title="XBOOLE_0:func.4">\</a> <span class="p3">(<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="c1">N</font></span>)</span></span>)</span></span>)</span> <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>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="42_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c2">x</font>, <font color="Maroon" title="c3">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"> ( <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">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="c1">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#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> implies <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">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> <span class="p1">(<span class="default"><a href="relat_1.html#K6" title="RELAT_1:func.6">id</a> <span class="p2">(<span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">N</font> <a href="xboole_0.html#K4" title="XBOOLE_0:func.4">\</a> <span class="p3">(<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="c1">N</font></span>)</span></span>)</span></span>)</span> <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> )</span><br/>



<span class="kw">assume </span><a NAME="E1:42_1"/><span class="lab"><font color="Green" title="E14">A1</font></span>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">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="c1">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#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>
 ; <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="c2">x</font>,<font color="Maroon" title="c3">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> <span class="p1">(<span class="default"><a href="relat_1.html#K6" title="RELAT_1:func.6">id</a> <span class="p2">(<span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">N</font> <a href="xboole_0.html#K4" title="XBOOLE_0:func.4">\</a> <span class="p3">(<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="c1">N</font></span>)</span></span>)</span></span>)</span> <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></span><br/>

<a NAME="E2:42_1"/><span class="kw">then </span>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">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="c1">N</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_0.html#D5" title="XBOOLE_0:def.5">XBOOLE_0:def 5</a></span>;<br/>
<a NAME="E3:42_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E15">A2</font></span>: 
<font color="Maroon" title="c2">x</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> the <a href="e_siec.html#U2" title="E_SIEC:sel.2">escape</a> of <font color="Maroon" title="c1">N</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#D4" title="RELAT_1:def.4">RELAT_1:def 4</a></span>;<br/>
<a NAME="E4:42_1"/><span class="lab"><font color="Green" title="E16">A3</font></span>: 
not <font color="Maroon" title="c2">x</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="c1">N</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="42_1_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:42_1_1"/>
<font color="Maroon" title="c2">x</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="c1">N</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:42_1_1"/><span class="kw">then </span>
 ex <font color="Olive" title="b1">z</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  st <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b1">z</font>,<font color="Maroon" title="c2">x</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="c1">N</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#D5" title="RELAT_1:def.5">RELAT_1:def 5</a></span>;<br/>
<a NAME="E3:42_1_1"/><span class="kw">then </span>
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#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:42_1"><span class="lab"><font color="Green" title="E14">A1</font></span></a>, <a class="ref" href="relat_1.html#D8" title="RELAT_1:def.8">RELAT_1:def 8</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:42_1_1"/>
contradiction
 <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>; <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="E5:42_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="c1">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="c1">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="E6:42_1"/><span class="kw">then </span>
<font color="Maroon" title="c2">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="c1">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="c1">N</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:42_1"><span class="lab"><font color="Green" title="E15">A2</font></span></a>, <a class="txt" href="#E4:42_1"><span class="lab"><font color="Green" title="E16">A3</font></span></a>, <a class="ref" href="xboole_0.html#D5" title="XBOOLE_0:def.5">XBOOLE_0:def 5</a></span>;<br/>
<a NAME="E7:42_1"/><span class="kw">then </span>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c2">x</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K6" title="RELAT_1:func.6">id</a> <span class="p1">(<span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</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#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>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#D10" title="RELAT_1:def.10">RELAT_1:def 10</a></span>;<br/>
<span class="kw">hence </span><a NAME="E8:42_1"/>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">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> <span class="p1">(<span class="default"><a href="relat_1.html#K6" title="RELAT_1:func.6">id</a> <span class="p2">(<span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">N</font> <a href="xboole_0.html#K4" title="XBOOLE_0:func.4">\</a> <span class="p3">(<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="c1">N</font></span>)</span></span>)</span></span>)</span> <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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:42_1"><span class="lab"><font color="Green" title="E14">A1</font></span></a>, <a class="ref" href="relat_1.html#D8" title="RELAT_1:def.8">RELAT_1:def 8</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="E2:42"/><span class="kw">then </span><span class="lab"><font color="Green" title="E14">A4</font></span>: 
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="p1">(<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> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="relat_1.html#K6" title="RELAT_1:func.6">id</a> <span class="p2">(<span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">N</font> <a href="xboole_0.html#K4" title="XBOOLE_0:func.4">\</a> <span class="p3">(<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="c1">N</font></span>)</span></span>)</span></span>)</span> <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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#D3" title="RELAT_1:def.3">RELAT_1:def 3</a></span>;<br/>
<a NAME="E3:42"/>
for <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">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="c1">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#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> holds <br/><span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">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> <span class="p1">(<span class="default"><a href="relat_1.html#K6" title="RELAT_1:func.6">id</a> <span class="p2">(<span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">N</font> <a href="xboole_0.html#K4" title="XBOOLE_0:func.4">\</a> <span class="p3">(<span class="default"><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></span>)</span></span>)</span></span>)</span> <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>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="42_2"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c2">x</font>, <font color="Maroon" title="c3">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"> ( <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">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="c1">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#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> implies <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">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> <span class="p1">(<span class="default"><a href="relat_1.html#K6" title="RELAT_1:func.6">id</a> <span class="p2">(<span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">N</font> <a href="xboole_0.html#K4" title="XBOOLE_0:func.4">\</a> <span class="p3">(<span class="default"><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></span>)</span></span>)</span></span>)</span> <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> )</span><br/>



<span class="kw">assume </span><a NAME="E1:42_2"/><span class="lab"><font color="Green" title="E15">A5</font></span>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">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="c1">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#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>
 ; <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="c2">x</font>,<font color="Maroon" title="c3">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> <span class="p1">(<span class="default"><a href="relat_1.html#K6" title="RELAT_1:func.6">id</a> <span class="p2">(<span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">N</font> <a href="xboole_0.html#K4" title="XBOOLE_0:func.4">\</a> <span class="p3">(<span class="default"><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></span>)</span></span>)</span></span>)</span> <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></span><br/>

<a NAME="E2:42_2"/><span class="kw">then </span>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">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="c1">N</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_0.html#D5" title="XBOOLE_0:def.5">XBOOLE_0:def 5</a></span>;<br/>
<a NAME="E3:42_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E16">A6</font></span>: 
<font color="Maroon" title="c2">x</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> the <a href="e_siec.html#U1" title="E_SIEC:sel.1">entrance</a> of <font color="Maroon" title="c1">N</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#D4" title="RELAT_1:def.4">RELAT_1:def 4</a></span>;<br/>
<a NAME="E4:42_2"/><span class="lab"><font color="Green" title="E17">A7</font></span>: 
not <font color="Maroon" title="c2">x</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#U1" title="E_SIEC:sel.1">entrance</a> of <font color="Maroon" title="c1">N</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="42_2_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:42_2_1"/>
<font color="Maroon" title="c2">x</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#U1" title="E_SIEC:sel.1">entrance</a> of <font color="Maroon" title="c1">N</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:42_2_1"/><span class="kw">then </span>
 ex <font color="Olive" title="b1">z</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  st <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b1">z</font>,<font color="Maroon" title="c2">x</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="c1">N</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#D5" title="RELAT_1:def.5">RELAT_1:def 5</a></span>;<br/>
<a NAME="E3:42_2_1"/><span class="kw">then </span>
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#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:42_2"><span class="lab"><font color="Green" title="E15">A5</font></span></a>, <a class="ref" href="relat_1.html#D8" title="RELAT_1:def.8">RELAT_1:def 8</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:42_2_1"/>
contradiction
 <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>; <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="E5:42_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="c1">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="c1">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="E6:42_2"/><span class="kw">then </span>
<font color="Maroon" title="c2">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="c1">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#U1" title="E_SIEC:sel.1">entrance</a> of <font color="Maroon" title="c1">N</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:42_2"><span class="lab"><font color="Green" title="E16">A6</font></span></a>, <a class="txt" href="#E4:42_2"><span class="lab"><font color="Green" title="E17">A7</font></span></a>, <a class="ref" href="xboole_0.html#D5" title="XBOOLE_0:def.5">XBOOLE_0:def 5</a></span>;<br/>
<a NAME="E7:42_2"/><span class="kw">then </span>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c2">x</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K6" title="RELAT_1:func.6">id</a> <span class="p1">(<span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</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#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></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#D10" title="RELAT_1:def.10">RELAT_1:def 10</a></span>;<br/>
<span class="kw">hence </span><a NAME="E8:42_2"/>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">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> <span class="p1">(<span class="default"><a href="relat_1.html#K6" title="RELAT_1:func.6">id</a> <span class="p2">(<span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">N</font> <a href="xboole_0.html#K4" title="XBOOLE_0:func.4">\</a> <span class="p3">(<span class="default"><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></span>)</span></span>)</span></span>)</span> <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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:42_2"><span class="lab"><font color="Green" title="E15">A5</font></span></a>, <a class="ref" href="relat_1.html#D8" title="RELAT_1:def.8">RELAT_1:def 8</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="E4:42"/><span class="kw">then </span><span class="lab"><font color="Green" title="E15">A8</font></span>: 
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="p1">(<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> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="relat_1.html#K6" title="RELAT_1:func.6">id</a> <span class="p2">(<span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">N</font> <a href="xboole_0.html#K4" title="XBOOLE_0:func.4">\</a> <span class="p3">(<span class="default"><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></span>)</span></span>)</span></span>)</span> <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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#D3" title="RELAT_1:def.3">RELAT_1:def 3</a></span>;<br/>
<a NAME="E5:42"/>
( <span class="p1">(<span class="default"><a href="relat_1.html#K6" title="RELAT_1:func.6">id</a> <span class="p2">(<span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">N</font> <a href="xboole_0.html#K4" title="XBOOLE_0:func.4">\</a> <span class="p3">(<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="c1">N</font></span>)</span></span>)</span></span>)</span> <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="tarski.html#R1" title="TARSKI:pred.1">c=</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="xboole_0.html#K4" title="XBOOLE_0:func.4">\</a> <span class="p1">(<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> &amp; <span class="p1">(<span class="default"><a href="relat_1.html#K6" title="RELAT_1:func.6">id</a> <span class="p2">(<span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">N</font> <a href="xboole_0.html#K4" title="XBOOLE_0:func.4">\</a> <span class="p3">(<span class="default"><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></span>)</span></span>)</span></span>)</span> <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="tarski.html#R1" title="TARSKI:pred.1">c=</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="xboole_0.html#K4" title="XBOOLE_0:func.4">\</a> <span class="p1">(<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 class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#T76" title="RELAT_1:th.76">RELAT_1:76</a></span>;<br/>
<span class="kw">hence </span><a NAME="E6:42"/>
( <span class="p1">(<span class="default"><a href="relat_1.html#K6" title="RELAT_1:func.6">id</a> <span class="p2">(<span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">N</font> <a href="xboole_0.html#K4" title="XBOOLE_0:func.4">\</a> <span class="p3">(<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="c1">N</font></span>)</span></span>)</span></span>)</span> <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> 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="p1">(<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> &amp; <span class="p1">(<span class="default"><a href="relat_1.html#K6" title="RELAT_1:func.6">id</a> <span class="p2">(<span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">N</font> <a href="xboole_0.html#K4" title="XBOOLE_0:func.4">\</a> <span class="p3">(<span class="default"><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></span>)</span></span>)</span></span>)</span> <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> 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="p1">(<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 class="kw">by</span> <span class="lab"><a class="txt" href="#E2:42"><span class="lab"><font color="Green" title="E14">A4</font></span></a>, <a class="txt" href="#E4:42"><span class="lab"><font color="Green" title="E15">A8</font></span></a>, <a class="ref" href="xboole_0.html#D10" title="XBOOLE_0:def.10">XBOOLE_0:def 10</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/>


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