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<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font> be   <a href="glib_000.html#NM2">_Graph</a>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be    <a href="glib_001.html#M3" target="_self">Walk</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>4</sub></font> be    <a href="glib_001.html#M3" target="_self">Walk</a> of <font color="Maroon">c<sub>2</sub></font>;<br/>







<b>assume </b><a NAME="E1:252"/><i><font color="Green">E161</font></i>: 
( <font color="Maroon">c<sub>1</sub></font> <a href="glib_000.html#R5">==</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> )
 ;<br/>

<a NAME="E2:252"/><b>then </b>
<font color="Maroon">c<sub>1</sub></font> is    <a href="glib_000.html#M2">Subgraph</a> of <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="glib_000.html#T90">GLIB_000:90</a></i>;<br/>
<b>hence </b><a NAME="E3:252"/>
( ( <font color="Maroon">c<sub>3</sub></font> is <a href="glib_001.html#V1" target="_self">closed</a> implies <font color="Maroon">c<sub>4</sub></font> is <a href="glib_001.html#V1" target="_self">closed</a> ) &amp; ( <font color="Maroon">c<sub>4</sub></font> is <a href="glib_001.html#V1" target="_self">closed</a> implies <font color="Maroon">c<sub>3</sub></font> is <a href="glib_001.html#V1" target="_self">closed</a> ) &amp; ( <font color="Maroon">c<sub>3</sub></font> is <a href="glib_001.html#V2" target="_self">directed</a> implies <font color="Maroon">c<sub>4</sub></font> is <a href="glib_001.html#V2" target="_self">directed</a> ) &amp; ( <font color="Maroon">c<sub>4</sub></font> is <a href="glib_001.html#V2" target="_self">directed</a> implies <font color="Maroon">c<sub>3</sub></font> is <a href="glib_001.html#V2" target="_self">directed</a> ) &amp; ( <font color="Maroon">c<sub>3</sub></font> is <a href="glib_001.html#V3" target="_self">trivial</a> implies <font color="Maroon">c<sub>4</sub></font> is <a href="glib_001.html#V3" target="_self">trivial</a> ) &amp; ( <font color="Maroon">c<sub>4</sub></font> is <a href="glib_001.html#V3" target="_self">trivial</a> implies <font color="Maroon">c<sub>3</sub></font> is <a href="glib_001.html#V3" target="_self">trivial</a> ) &amp; ( <font color="Maroon">c<sub>3</sub></font> is <a href="glib_001.html#V4" target="_self">Trail-like</a> implies <font color="Maroon">c<sub>4</sub></font> is <a href="glib_001.html#V4" target="_self">Trail-like</a> ) &amp; ( <font color="Maroon">c<sub>4</sub></font> is <a href="glib_001.html#V4" target="_self">Trail-like</a> implies <font color="Maroon">c<sub>3</sub></font> is <a href="glib_001.html#V4" target="_self">Trail-like</a> ) &amp; ( <font color="Maroon">c<sub>3</sub></font> is <a href="glib_001.html#V5" target="_self">Path-like</a> implies <font color="Maroon">c<sub>4</sub></font> is <a href="glib_001.html#V5" target="_self">Path-like</a> ) &amp; ( <font color="Maroon">c<sub>4</sub></font> is <a href="glib_001.html#V5" target="_self">Path-like</a> implies <font color="Maroon">c<sub>3</sub></font> is <a href="glib_001.html#V5" target="_self">Path-like</a> ) &amp; ( <font color="Maroon">c<sub>3</sub></font> is <a href="glib_001.html#V6" target="_self">vertex-distinct</a> implies <font color="Maroon">c<sub>4</sub></font> is <a href="glib_001.html#V6" target="_self">vertex-distinct</a> ) &amp; ( <font color="Maroon">c<sub>4</sub></font> is <a href="glib_001.html#V6" target="_self">vertex-distinct</a> implies <font color="Maroon">c<sub>3</sub></font> is <a href="glib_001.html#V6" target="_self">vertex-distinct</a> ) )
 <b>by </b><i><a class="txt" href="glib_001.html#E1:252"><i><font color="Green">E161</font></i></a>, <a class="ref" href="glib_001.html#T177" target="_self">Th177</a></i>;<br/>


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