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<b>let </b><font color="Maroon">c<sub>2</sub></font> be    <a href="glib_000.html#M2">Subgraph</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_1_1"><b>now </b></a><div class="add"><b>given </b><font color="Maroon">c<sub>3</sub></font> being    <a href="glib_001.html#M3">Walk</a> of <font color="Maroon">c<sub>2</sub></font><b> such that </b><a NAME="E1:15_1_1_1"/><i><font color="Green">E6</font></i>: 
<font color="Maroon">c<sub>3</sub></font> is <a href="glib_001.html#V8">Cycle-like</a>
 ;<br/><a NAME="E2:15_1_1_1"/><i><font color="Green">E7</font></i>: 
( <font color="Maroon">c<sub>3</sub></font> is <a href="glib_001.html#V1">closed</a> &amp; not <font color="Maroon">c<sub>3</sub></font> is <a href="glib_001.html#V3">trivial</a> &amp; <font color="Maroon">c<sub>3</sub></font> is <a href="glib_001.html#V5">Path-like</a> )
 <b>by </b><i><a class="txt" href="glib_002.html#E1:15_1_1_1"><i><font color="Green">E6</font></i></a>, <a class="ref" href="glib_001.html#D31">GLIB_001:def 31</a></i>;<br/><b>reconsider </b><font color="Maroon">c<sub>4</sub></font> = <font color="Maroon">c<sub>3</sub></font> as    <a href="glib_001.html#M3">Walk</a> of <font color="Maroon">c<sub>1</sub></font> <b>by </b><i><a class="ref" href="glib_001.html#T168">GLIB_001:168</a></i>;<br/><a NAME="E4:15_1_1_1"/>
( <font color="Maroon">c<sub>4</sub></font> is <a href="glib_001.html#V1">closed</a> &amp; not <font color="Maroon">c<sub>4</sub></font> is <a href="glib_001.html#V3">trivial</a> &amp; <font color="Maroon">c<sub>4</sub></font> is <a href="glib_001.html#V5">Path-like</a> )
 <b>by </b><i><a class="txt" href="glib_002.html#E2:15_1_1_1"><i><font color="Green">E7</font></i></a>, <a class="ref" href="glib_001.html#T177">GLIB_001:177</a></i>;<br/><a NAME="E5:15_1_1_1"/><b>then </b>
<font color="Maroon">c<sub>4</sub></font> is <a href="glib_001.html#V8">Cycle-like</a>
 <b>by </b><i><a class="ref" href="glib_001.html#D31">GLIB_001:def 31</a></i>;<br/><b>hence </b><a NAME="E6:15_1_1_1"/>
contradiction
 <b>by </b><i><a class="ref" href="glib_002.html#D2" target="_self">Def2</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:15_1_1"/>
<font color="Maroon">c<sub>2</sub></font> is <a href="glib_002.html#V2" target="_self">acyclic</a>
 <b>by </b><i><a class="ref" href="glib_002.html#D2" target="_self">Def2</a></i>;<br/>


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