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<span class="kw">let </span><font color="Maroon" title="c1">C</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">C</font> is 3 <a href="glib_013.html#V3" title="GLIB_013:attr.3">-vertex</a>  &amp; <font color="Maroon" title="c1">C</font> is  <a href="glib_000.html#V7" title="GLIB_000:attr.7">simple</a>  &amp; <font color="Maroon" title="c1">C</font> is  <a href="chord.html#V2" title="CHORD:attr.2">complete</a>  implies <font color="Maroon" title="c1">C</font> is  <a href="glpacy00.html#V4" title="GLPACY00:attr.4">Cycle-like</a>  )</span><br/>

<span class="kw">assume </span><a NAME="E1:112_1_1"/><span class="lab"><font color="Green" title="E53">A1</font></span>: 
( <font color="Maroon" title="c1">C</font> is 3 <a href="glib_013.html#V3" title="GLIB_013:attr.3">-vertex</a>  &amp; <font color="Maroon" title="c1">C</font> is  <a href="glib_000.html#V7" title="GLIB_000:attr.7">simple</a>  &amp; <font color="Maroon" title="c1">C</font> is  <a href="chord.html#V2" title="CHORD:attr.2">complete</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">C</font> is  <a href="glpacy00.html#V4" title="GLPACY00:attr.4">Cycle-like</a> </span><br/>

<span class="kw">hence </span><a NAME="E2:112_1_1"/>
<font color="Maroon" title="c1">C</font> is  <a href="glib_002.html#V1" title="GLIB_002:attr.1">connected</a> 
 ; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="glpacy00.html#D6" target="_self" onmouseover="rs('glpacy00/D6')" onmouseout="rh()">GLPACY00:def 6</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">C</font> is  <a href="glib_002.html#V2" title="GLIB_002:attr.2">acyclic</a>  &amp; <font color="Maroon" title="c1">C</font> is 2 <a href="glib_016.html#V2" title="GLIB_016:attr.2">-regular</a>  )</span><br/>

<a NAME="E3:112_1_1"/>
<font color="Maroon" title="c1">C</font> <a href="glib_000.html#K14" title="GLIB_000:func.14">.order()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:112_1_1"><span class="lab"><font color="Green" title="E53">A1</font></span></a>, <a class="ref" href="glib_013.html#D3" onmouseover="rs('glib_013/D3')" onmouseout="rh()">GLIB_013:def 3</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:112_1_1"/>
 not <font color="Maroon" title="c1">C</font> is  <a href="glib_002.html#V2" title="GLIB_002:attr.2">acyclic</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:112_1_1"><span class="lab"><font color="Green" title="E53">A1</font></span></a>, <a class="txt" href="glpacy00.html#E11"><span class="lab"><font color="Green" title="E11">Th8</font></span></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"> <font color="Maroon" title="c1">C</font> is 2 <a href="glib_016.html#V2" title="GLIB_016:attr.2">-regular</a> </span><br/>

<a NAME="E5:112_1_1"/>
<font color="Maroon" title="c1">C</font> is 2 <a href="card_2.html#K1" title="CARD_2:func.1">+`</a> 1 <a href="glib_013.html#V3" title="GLIB_013:attr.3">-vertex</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:112_1_1"><span class="lab"><font color="Green" title="E53">A1</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E6:112_1_1"/>
<font color="Maroon" title="c1">C</font> is 2 <a href="glib_016.html#V2" title="GLIB_016:attr.2">-regular</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:112_1_1"><span class="lab"><font color="Green" title="E53">A1</font></span></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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