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

<b>let </b><font color="Maroon">G</font> be  non <a href="struct_0.html#V3">empty</a> <a href="necklace.html#V3">irreflexive</a>  <a href="orders_2.html#L1">RelStr</a> ;<br/>

<b>thus </b><a NAME="E1:38"/>
( <font color="Maroon">G</font> is <a href="neckla_2.html#V1">N-free</a> implies  <a href="necklace.html#K3">ComplRelStr</a> <font color="Maroon">G</font> is <a href="neckla_2.html#V1">N-free</a> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="38_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:38_1"/><i><font color="Green">E31</font></i>: 
<font color="Maroon">G</font> is <a href="neckla_2.html#V1">N-free</a>
 ;<br/>

<b>assume </b><a NAME="E2:38_1"/>
not  <a href="necklace.html#K3">ComplRelStr</a> <font color="Maroon">G</font> is <a href="neckla_2.html#V1">N-free</a>
 ;<br/>

<a NAME="E3:38_1"/><b>then </b>
 <a href="necklace.html#K3">ComplRelStr</a> <font color="Maroon">G</font> <a href="necklace.html#R2">embeds</a>  <a href="necklace.html#K4">Necklace</a> 4
 
<b>by </b><i><a class="ref" href="neckla_2.html#D1">NECKLA_2:def 1</a></i>;<br/>
<a NAME="E4:38_1"/><b>then </b>
<font color="Maroon">G</font> <a href="necklace.html#R2">embeds</a>  <a href="necklace.html#K4">Necklace</a> 4
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E5:38_1"/>
contradiction
 <b>by </b><i>, <a class="ref" href="neckla_2.html#D1">NECKLA_2:def 1</a></i>;<br/>


</div><b>end;</b></div>

<b>assume </b><a NAME="E2:38"/><i><font color="Green">E34</font></i>: 
 <a href="necklace.html#K3">ComplRelStr</a> <font color="Maroon">G</font> is <a href="neckla_2.html#V1">N-free</a>
 ;<br/>

<b>assume </b><a NAME="E3:38"/>
not <font color="Maroon">G</font> is <a href="neckla_2.html#V1">N-free</a>
 ;<br/>

<a NAME="E4:38"/><b>then </b>
<font color="Maroon">G</font> <a href="necklace.html#R2">embeds</a>  <a href="necklace.html#K4">Necklace</a> 4
 
<b>by </b><i><a class="ref" href="neckla_2.html#D1">NECKLA_2:def 1</a></i>;<br/>
<a NAME="E5:38"/><b>then </b>
 <a href="necklace.html#K3">ComplRelStr</a> <font color="Maroon">G</font> <a href="necklace.html#R2">embeds</a>  <a href="necklace.html#K4">Necklace</a> 4
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E6:38"/>
contradiction
 <b>by </b><i>, <a class="ref" href="neckla_2.html#D1">NECKLA_2:def 1</a></i>;<br/>


</div>
