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

<b>let </b><font color="Maroon" title="c1">G1</font> be   <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">G2</font> being   <a href="glib_000.html#M2" title="GLIB_000:mode.2">Subgraph</a> of <font color="Maroon" title="c1">G1</font><br/> for <font color="Olive" title="b2">x</font>, <font color="Olive" title="b3">y</font>, <font color="Olive" title="b4">e</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b4">e</font> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Olive" title="b2">x</font>,<font color="Olive" title="b3">y</font>,<font color="Olive" title="b1">G2</font> holds <br/><font color="Maroon" title="c1">G1</font> <a href="glib_001.html#K2" title="GLIB_001:func.2">.walkOf</a> <font color="Olive" title="b2">x</font>,<font color="Olive" title="b4">e</font>,<font color="Olive" title="b3">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">G2</font> <a href="glib_001.html#K2" title="GLIB_001:func.2">.walkOf</a> <font color="Olive" title="b2">x</font>,<font color="Olive" title="b4">e</font>,<font color="Olive" title="b3">y</font></span><br/><b>let </b><font color="Maroon" title="c2">G2</font> be    <a href="glib_000.html#M2" title="GLIB_000:mode.2">Subgraph</a> of <font color="Maroon" title="c1">G1</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</font>, <font color="Olive" title="b3">e</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b3">e</font> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font>,<font color="Maroon" title="c2">G2</font> holds <br/><font color="Maroon" title="c1">G1</font> <a href="glib_001.html#K2" title="GLIB_001:func.2">.walkOf</a> <font color="Olive" title="b1">x</font>,<font color="Olive" title="b3">e</font>,<font color="Olive" title="b2">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">G2</font> <a href="glib_001.html#K2" title="GLIB_001:func.2">.walkOf</a> <font color="Olive" title="b1">x</font>,<font color="Olive" title="b3">e</font>,<font color="Olive" title="b2">y</font></span><br/><b>let </b><font color="Maroon" title="c3">x</font>, <font color="Maroon" title="c4">y</font>, <font color="Maroon" title="c5">e</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c5">e</font> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">y</font>,<font color="Maroon" title="c2">G2</font> implies <font color="Maroon" title="c1">G1</font> <a href="glib_001.html#K2" title="GLIB_001:func.2">.walkOf</a> <font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c5">e</font>,<font color="Maroon" title="c4">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">G2</font> <a href="glib_001.html#K2" title="GLIB_001:func.2">.walkOf</a> <font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c5">e</font>,<font color="Maroon" title="c4">y</font> )</span><br/>





<b>assume </b><a NAME="E1:244"/><i><font color="Green" title="E152">A1</font></i>: 
<font color="Maroon" title="c5">e</font> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">y</font>,<font color="Maroon" title="c2">G2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c1">G1</font> <a href="glib_001.html#K2" title="GLIB_001:func.2">.walkOf</a> <font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c5">e</font>,<font color="Maroon" title="c4">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">G2</font> <a href="glib_001.html#K2" title="GLIB_001:func.2">.walkOf</a> <font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c5">e</font>,<font color="Maroon" title="c4">y</font></span><br/>

<a NAME="E2:244"/><b>then </b><i><font color="Green" title="E153">A2</font></i>: 
<font color="Maroon" title="c2">G2</font> <a href="glib_001.html#K2" title="GLIB_001:func.2">.walkOf</a> <font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c5">e</font>,<font color="Maroon" title="c4">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">&lt;*</a><span class="default"><font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c5">e</font>,<font color="Maroon" title="c4">y</font></span><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">*&gt;</a></span>
 
<b>by </b><i><a class="ref" href="glib_001.html#D5" target="_self" title="GLIB_001:def.5">Def5</a></i>;<br/>
<a NAME="E3:244"/>
<font color="Maroon" title="c5">e</font> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">y</font>,<font color="Maroon" title="c1">G1</font>
 
<b>by </b><i><a class="txt" href="glib_001.html#E1:244"><i><font color="Green" title="E152">A1</font></i></a>, <a class="ref" href="glib_000.html#T75" title="GLIB_000:th.75">GLIB_000:75</a></i>;<br/>
<b>hence </b><a NAME="E4:244"/>
<font color="Maroon" title="c1">G1</font> <a href="glib_001.html#K2" title="GLIB_001:func.2">.walkOf</a> <font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c5">e</font>,<font color="Maroon" title="c4">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">G2</font> <a href="glib_001.html#K2" title="GLIB_001:func.2">.walkOf</a> <font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c5">e</font>,<font color="Maroon" title="c4">y</font>
 <b>by </b><i><a class="txt" href="glib_001.html#E2:244"><i><font color="Green" title="E153">A2</font></i></a>, <a class="ref" href="glib_001.html#D5" target="_self" title="GLIB_001:def.5">Def5</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
