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<b>let </b><font color="Maroon">G1</font> be   <a href="glib_000.html#NM2">_Graph</a>;<br/><b>let </b><font color="Maroon">G2</font> be   <a href="glib_000.html#NM2">_Graph</a>;<br/><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/>





<b>assume </b><a NAME="E1:83"/><i><font color="Green">E41</font></i>: 
( <font color="Maroon">G1</font> <a href="glib_000.html#R5">==</a> <font color="Maroon">G2</font> &amp; <font color="Maroon">G1</font> <a href="glib_002.html#R1" target="_self">is_DTree_rooted_at</a> <font color="Maroon">x</font> )
 ;<br/>

<a NAME="E2:83"/><b>then </b><i><font color="Green">E42</font></i>: 
( <font color="Maroon">G1</font> is <a href="glib_002.html#V3" target="_self">Tree-like</a> &amp; ( for <font color="Olive">y</font> being  <a href="glib_000.html#NM10">Vertex</a> of <font color="Maroon">G1</font>  ex <font color="Olive">W</font> being  <a href="glib_001.html#NM6">DWalk</a> of <font color="Maroon">G1</font> st <font color="Olive">W</font> <a href="glib_001.html#R1">is_Walk_from</a> <font color="Maroon">x</font>,<font color="Olive">y</font> ) )
 
<b>by </b><i/>;<br/>
<a NAME="E3:83"/><i><font color="Green">E43</font></i>: 
<font color="Maroon">G2</font> is <a href="glib_002.html#V3" target="_self">Tree-like</a>
 
<b>by </b><i>, , </i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="83_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">y</font> be   <a href="glib_000.html#NM10">Vertex</a> of <font color="Maroon">G2</font>;<br/><b>reconsider </b><font color="Maroon">y'</font> = <font color="Maroon">y</font> as   <a href="glib_000.html#NM10">Vertex</a> of <font color="Maroon">G1</font> <b>by </b><i>, <a class="ref" href="glib_000.html#D36">GLIB_000:def 36</a></i>;<br/><b>consider </b><font color="Maroon">W</font> being   <a href="glib_001.html#NM6">DWalk</a> of <font color="Maroon">G1</font><b> such that </b><br/><a NAME="E3:83_1"/><i><font color="Green">E44</font></i>: 
<font color="Maroon">W</font> <a href="glib_001.html#R1">is_Walk_from</a> <font color="Maroon">x</font>,<font color="Maroon">y'</font>
 <b>by </b><i>, </i>;<br/><b>reconsider </b><font color="Maroon">W'</font> = <font color="Maroon">W</font> as   <a href="glib_001.html#NM6">DWalk</a> of <font color="Maroon">G2</font> <b>by </b><i>, <a class="ref" href="glib_001.html#T180">GLIB_001:180</a>, <a class="ref" href="glib_001.html#T182">GLIB_001:182</a></i>;<br/><b>take </b><font color="Maroon">W'</font> = <font color="Maroon">W'</font>;<br/><b>thus </b><a NAME="E5:83_1"/>
<font color="Maroon">W'</font> <a href="glib_001.html#R1">is_Walk_from</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>
 <b>by </b><i><a class="ref" href="glib_002.html#D3" target="_self">Def3</a>, <a class="ref" href="glib_001.html#T20">GLIB_001:20</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E5:83"/>
<font color="Maroon">G2</font> <a href="glib_002.html#R1" target="_self">is_DTree_rooted_at</a> <font color="Maroon">x</font>
 <b>by </b><i><a class="ref" href="glib_002.html#D2" target="_self">Def2</a>, </i>;<br/>


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