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<span class="kw">let </span><font color="Maroon" title="c1">G</font> be   <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">G</font> is  <a href="glib_012.html#V1" title="GLIB_012:attr.1">loopfull</a>  implies  not <font color="Maroon" title="c1">G</font> is  <a href="glib_000.html#V3" title="GLIB_000:attr.3">loopless</a>  )</span><br/>

<span class="kw">assume </span><a NAME="E1:4_1_1"/>
<font color="Maroon" title="c1">G</font> is  <a href="glib_012.html#V1" title="GLIB_012:attr.1">loopfull</a> 
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  not <font color="Maroon" title="c1">G</font> is  <a href="glib_000.html#V3" title="GLIB_000:attr.3">loopless</a> </span><br/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c2">e</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> <span class="kw"> such that </span><br/><a NAME="E3:4_1_1"/><span class="lab"><font color="Green" title="E3">A1</font></span>: 
<font color="Maroon" title="c2">e</font> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a>  the   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c1">G</font>, the   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c1">G</font>
 ;<br/>
<span class="kw">thus </span><a NAME="E4:4_1_1"/>
 not <font color="Maroon" title="c1">G</font> is  <a href="glib_000.html#V3" title="GLIB_000:attr.3">loopless</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:4_1_1"><span class="lab"><font color="Green" title="E3">A1</font></span></a>, <a class="ref" href="glib_000.html#T18" onmouseover="rs('glib_000/T18')" onmouseout="rh()">GLIB_000:18</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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