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<b>let </b><font color="Maroon">G</font> be   <a href="glib_000.html#NM2">_Graph</a>;<br/>

<b>assume </b><a NAME="E1:22"/><i><font color="Green">E28</font></i>: 
 <a href="glib_000.html#K7" target="_self">the_Edges_of</a> <font color="Maroon">G</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/>

<a NAME="E2:22"/><b>then </b>
for <font color="Olive">e</font> being   <a href="hidden.html#M1">set</a>   holds <br/>(  not <font color="Olive">e</font> <a href="hidden.html#R2">in</a>  <a href="glib_000.html#K7" target="_self">the_Edges_of</a> <font color="Maroon">G</font> or  not <span class="p1">(<span class="default"><a href="glib_000.html#K10" target="_self">the_Source_of</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">e</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="glib_000.html#K11" target="_self">the_Target_of</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">e</font> )
 
;<br/>
<a NAME="E3:22"/><b>then </b><i><font color="Green">E29</font></i>: 
<font color="Maroon">G</font> is <a href="glib_000.html#V3" target="_self">loopless</a>
 
<b>by </b><i/>;<br/>
<a NAME="E4:22"/>
for <font color="Olive">e1</font>, <font color="Olive">e2</font>, <font color="Olive">v1</font>, <font color="Olive">v2</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">e1</font> <a href="glib_000.html#R1" target="_self">Joins</a> <font color="Olive">v1</font>,<font color="Olive">v2</font>,<font color="Maroon">G</font> &amp; <font color="Olive">e2</font> <a href="glib_000.html#R1" target="_self">Joins</a> <font color="Olive">v1</font>,<font color="Olive">v2</font>,<font color="Maroon">G</font> holds <br/><font color="Olive">e1</font> <a href="hidden.html#R1">=</a> <font color="Olive">e2</font>
 
<b>by </b><i>, </i>;<br/>
<a NAME="E5:22"/><b>then </b>
<font color="Maroon">G</font> is <a href="glib_000.html#V5" target="_self">non-multi</a>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E6:22"/>
<font color="Maroon">G</font> is <a href="glib_000.html#V7" target="_self">simple</a>
 <b>by </b><i>, </i>;<br/>


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