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<span class="kw">let </span><font color="Maroon" title="c2">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="c2">G</font> is <font color="Maroon" title="c1">n</font> <a href="glib_013.html#V4" title="GLIB_013:attr.4">-edge</a>  &amp; <font color="Maroon" title="c2">G</font> is  <a href="glpacy00.html#V4" title="GLPACY00:attr.4">Cycle-like</a>  implies <font color="Maroon" title="c2">G</font> is <font color="Maroon" title="c1">n</font> <a href="glib_013.html#V3" title="GLIB_013:attr.3">-vertex</a>  )</span><br/>

<span class="kw">assume </span><a NAME="E1:98_2_1"/><span class="lab"><font color="Green" title="E49">A2</font></span>: 
( <font color="Maroon" title="c2">G</font> is <font color="Maroon" title="c1">n</font> <a href="glib_013.html#V4" title="GLIB_013:attr.4">-edge</a>  &amp; <font color="Maroon" title="c2">G</font> is  <a href="glpacy00.html#V4" title="GLPACY00:attr.4">Cycle-like</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="c2">G</font> is <font color="Maroon" title="c1">n</font> <a href="glib_013.html#V3" title="GLIB_013:attr.3">-vertex</a> </span><br/>

<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c3">C</font> = <font color="Maroon" title="c2">G</font> as   <a href="glpacy00.html#V4" title="GLPACY00:attr.4">Cycle-like</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a> ;<br/>
<span class="kw">set </span><font color="Maroon" title="c4">e</font> =  the   <a href="glib_008.html#NM1" title="GLIB_008:NM.1">Edge</a> of <font color="Maroon" title="c3">C</font>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c5">P</font> =  the   <a href="glib_000.html#NM8" title="GLIB_000:NM.8">removeEdge</a> of <font color="Maroon" title="c3">C</font>, the   <a href="glib_008.html#NM1" title="GLIB_008:NM.1">Edge</a> of <font color="Maroon" title="c3">C</font> as   <a href="glib_000.html#V2" title="GLIB_000:attr.2">_finite</a>   <a href="glpacy00.html#V1" title="GLPACY00:attr.1">Path-like</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a> ;<br/>
<font color="Maroon" title="c2">G</font> <a href="glib_000.html#K14" title="GLIB_000:func.14">.order()</a>  = 
<font color="Maroon" title="c5">P</font> <a href="glib_013.html#K1" title="GLIB_013:func.1">.order()</a> 
<span class="kw">by</span> <span class="lab"><a class="ref" href="glib_000.html#D33" onmouseover="rs('glib_000/D33')" onmouseout="rh()">GLIB_000:def 33</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">P</font> <a href="glib_013.html#K2" title="GLIB_013:func.2">.size()</a></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1
<span class="kw">by</span> <span class="lab"><a class="ref" href="glib_002.html#T46" onmouseover="rs('glib_002/T46')" onmouseout="rh()">GLIB_002:46</a></span>
<br/>.= 
<font color="Maroon" title="c3">C</font> <a href="glib_013.html#K2" title="GLIB_013:func.2">.size()</a> 
<span class="kw">by</span> <span class="lab"><a class="ref" href="glib_000.html#T52" onmouseover="rs('glib_000/T52')" onmouseout="rh()">GLIB_000:52</a></span>
<br/>.= 
<font color="Maroon" title="c1">n</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:98_2_1"><span class="lab"><font color="Green" title="E49">A2</font></span></a>, <a class="ref" href="glib_013.html#D4" onmouseover="rs('glib_013/D4')" onmouseout="rh()">GLIB_013:def 4</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E5:98_2_1"/>
<font color="Maroon" title="c2">G</font> is <font color="Maroon" title="c1">n</font> <a href="glib_013.html#V3" title="GLIB_013:attr.3">-vertex</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="glib_013.html#D3" onmouseover="rs('glib_013/D3')" onmouseout="rh()">GLIB_013:def 3</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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