<?xml version="1.0"?>
<div class="add">

<span class="kw">take </span><font color="Maroon" title="c2">P</font> =  the  <font color="Maroon" title="c1">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 <a href="glib_013.html#V3" title="GLIB_013:attr.3">-vertex</a>  <font color="Maroon" title="c1">n</font> <a href="glib_013.html#V4" title="GLIB_013:attr.4">-edge</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>; <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">P</font> is <font color="Maroon" title="c1">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 <a href="glib_013.html#V3" title="GLIB_013:attr.3">-vertex</a>  &amp; <font color="Maroon" title="c2">P</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">P</font> is  <a href="glpacy00.html#V1" title="GLPACY00:attr.1">Path-like</a>  &amp;  not <font color="Maroon" title="c2">P</font> is  <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>  )</span><br/>

<a NAME="E1:40_2_1"/>
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c1">n</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="chord.html#T1" onmouseover="rs('chord/T1')" onmouseout="rh()">CHORD:1</a></span>;<br/>
<a NAME="E2:40_2_1"/><span class="kw">then </span>
1 <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c1">n</font> <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="xreal_1.html#T8" onmouseover="rs('xreal_1/T8')" onmouseout="rh()">XREAL_1:8</a></span>;<br/>
<a NAME="E3:40_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c2">P</font> <a href="glib_013.html#K1" title="GLIB_013:func.1">.order()</a>  <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 1
 
<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>;<br/>
<span class="kw">hence </span><a NAME="E4:40_2_1"/>
( <font color="Maroon" title="c2">P</font> is <font color="Maroon" title="c1">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 <a href="glib_013.html#V3" title="GLIB_013:attr.3">-vertex</a>  &amp; <font color="Maroon" title="c2">P</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">P</font> is  <a href="glpacy00.html#V1" title="GLPACY00:attr.1">Path-like</a>  &amp;  not <font color="Maroon" title="c2">P</font> is  <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</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/>


</div>
