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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="glib_000.html#NM11">GraphSeq</a>;<br/>

<b>assume </b><a NAME="E1:57_4_1"/><i><font color="Green">E40</font></i>: 
<font color="Maroon">c<sub>1</sub></font> is <a href="glib_002.html#V8" target="_self">Tree-like</a>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="57_4_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>reconsider </b><font color="Maroon">c<sub>3</sub></font> = <font color="Maroon">c<sub>1</sub></font> <a href="glib_000.html#K42">.-&gt;</a> <font color="Maroon">c<sub>2</sub></font> as  <a href="glib_002.html#V3" target="_self">Tree-like</a> <a href="glib_000.html#NM2">_Graph</a> <b>by </b><i><a class="txt" href="glib_002.html#E1:57_4_1"><i><font color="Green">E40</font></i></a>, <a class="ref" href="glib_002.html#D14" target="_self">Def14</a></i>;<br/><a NAME="E2:57_4_1_1"/>
( <font color="Maroon">c<sub>3</sub></font> is <a href="glib_002.html#V2" target="_self">acyclic</a> &amp; <font color="Maroon">c<sub>3</sub></font> is <a href="glib_002.html#V1" target="_self">connected</a> )
 ;<br/><b>hence </b><a NAME="E3:57_4_1_1"/>
( <font color="Maroon">c<sub>1</sub></font> <a href="glib_000.html#K42">.-&gt;</a> <font color="Maroon">c<sub>2</sub></font> is <a href="glib_002.html#V2" target="_self">acyclic</a> &amp; <font color="Maroon">c<sub>1</sub></font> <a href="glib_000.html#K42">.-&gt;</a> <font color="Maroon">c<sub>2</sub></font> is <a href="glib_002.html#V1" target="_self">connected</a> )
 ;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:57_4_1"/>
( <font color="Maroon">c<sub>1</sub></font> is <a href="glib_002.html#V7" target="_self">acyclic</a> &amp; <font color="Maroon">c<sub>1</sub></font> is <a href="glib_002.html#V6" target="_self">connected</a> )
 <b>by </b><i><a class="ref" href="glib_002.html#D13" target="_self">Def13</a>, <a class="ref" href="glib_002.html#D12" target="_self">Def12</a></i>;<br/>


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