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

<b>let </b><font color="Maroon" title="c1">G</font> be   <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">W</font> being   <a href="glib_001.html#M3" title="GLIB_001:mode.3">Walk</a> of <font color="Maroon" title="c1">G</font><br/> for <font color="Olive" title="b2">m</font>, <font color="Olive" title="b3">n</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st not <font color="Olive" title="b1">W</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> <font color="Olive" title="b2">m</font>,<font color="Olive" title="b3">n</font> is <a href="glib_001.html#V3" title="GLIB_001:attr.3">trivial</a> holds <br/> not <font color="Olive" title="b1">W</font> is <a href="glib_001.html#V3" title="GLIB_001:attr.3">trivial</a></span><br/><b>let </b><font color="Maroon" title="c2">W</font> be    <a href="glib_001.html#M3" title="GLIB_001:mode.3">Walk</a> of <font color="Maroon" title="c1">G</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">m</font>, <font color="Olive" title="b2">n</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st not <font color="Maroon" title="c2">W</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> <font color="Olive" title="b1">m</font>,<font color="Olive" title="b2">n</font> is <a href="glib_001.html#V3" title="GLIB_001:attr.3">trivial</a> holds <br/> not <font color="Maroon" title="c2">W</font> is <a href="glib_001.html#V3" title="GLIB_001:attr.3">trivial</a></span><br/><b>let </b><font color="Maroon" title="c3">m</font>, <font color="Maroon" title="c4">n</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( not <font color="Maroon" title="c2">W</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> <font color="Maroon" title="c3">m</font>,<font color="Maroon" title="c4">n</font> is <a href="glib_001.html#V3" title="GLIB_001:attr.3">trivial</a> implies  not <font color="Maroon" title="c2">W</font> is <a href="glib_001.html#V3" title="GLIB_001:attr.3">trivial</a> )</span><br/>





<b>assume </b><b>that </b><br/><a NAME="E1:12"/><i><font color="Green" title="E10">A1</font></i>: 
not <font color="Maroon" title="c2">W</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> <font color="Maroon" title="c3">m</font>,<font color="Maroon" title="c4">n</font> is <a href="glib_001.html#V3" title="GLIB_001:attr.3">trivial</a>
 <b>and </b><br/><a NAME="E2:12"/><i><font color="Green" title="E11">A2</font></i>: 
<font color="Maroon" title="c2">W</font> is <a href="glib_001.html#V3" title="GLIB_001:attr.3">trivial</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<b>reconsider </b><font color="Maroon" title="c5">m'</font> = <font color="Maroon" title="c3">m</font>, <font color="Maroon" title="c6">n'</font> = <font color="Maroon" title="c4">n</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  <b>by </b><i><a class="ref" href="ordinal1.html#D13" title="ORDINAL1:def.13">ORDINAL1:def 13</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c7">W</font> = <font color="Maroon" title="c2">W</font> as  <a href="glib_001.html#V3" title="GLIB_001:attr.3">trivial</a>  <a href="glib_001.html#M3" title="GLIB_001:mode.3">Walk</a> of <font color="Maroon" title="c1">G</font> <b>by </b><i><a class="txt" href="#E2:12"><i><font color="Green" title="E11">A2</font></i></a></i>;<br/>
<a NAME="E5:12"/>
<font color="Maroon" title="c7">W</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> <font color="Maroon" title="c5">m'</font>,<font color="Maroon" title="c6">n'</font> is <a href="glib_001.html#V3" title="GLIB_001:attr.3">trivial</a>
 
;<br/>
<b>hence </b><a NAME="E6:12"/>
contradiction
 <b>by </b><i><a class="txt" href="#E1:12"><i><font color="Green" title="E10">A1</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
