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<span class="kw">let </span><font color="Maroon" title="c1">T</font> be   <a href="helly.html#NM1" title="HELLY:NM.1">_Tree</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">P</font> being   <a href="glib_001.html#NM5" title="GLIB_001:NM.5">Path</a> of <font color="Maroon" title="c1">T</font>  st  not <font color="Olive" title="b1">P</font> is  <a href="glib_001.html#V3" title="GLIB_001:attr.3">trivial</a>  holds <br/> not <font color="Olive" title="b1">P</font> is  <a href="glib_001.html#V1" title="GLIB_001:attr.1">closed</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c2">P</font> be   <a href="glib_001.html#NM5" title="GLIB_001:NM.5">Path</a> of <font color="Maroon" title="c1">T</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c2">P</font> is  <a href="glib_001.html#V3" title="GLIB_001:attr.3">trivial</a>  implies  not <font color="Maroon" title="c2">P</font> is  <a href="glib_001.html#V1" title="GLIB_001:attr.1">closed</a>  )</span><br/>



<span class="kw">assume </span><a NAME="E1:29"/>
(  not <font color="Maroon" title="c2">P</font> is  <a href="glib_001.html#V3" title="GLIB_001:attr.3">trivial</a>  &amp; <font color="Maroon" title="c2">P</font> is  <a href="glib_001.html#V1" title="GLIB_001:attr.1">closed</a>  )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:29"/><span class="kw">then </span>
<font color="Maroon" title="c2">P</font> is  <a href="glib_001.html#V8" title="GLIB_001:attr.8">Cycle-like</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="glib_001.html#D31" title="GLIB_001:def.31">GLIB_001:def 31</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:29"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="ref" href="glib_002.html#D2" title="GLIB_002:def.2">GLIB_002:def 2</a></span>; <a class="txt" 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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