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<b>let </b><font color="Maroon" title="c1">G</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="necklace.html#V3" title="NECKLACE:attr.3">irreflexive</a>  <a href="orders_2.html#L1" title="ORDERS_2:struct.1">RelStr</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">G</font> is <a href="neckla_2.html#V1" title="NECKLA_2:attr.1">N-free</a> iff  <a href="necklace.html#K3" title="NECKLACE:func.3">ComplRelStr</a> <font color="Maroon" title="c1">G</font> is <a href="neckla_2.html#V1" title="NECKLA_2:attr.1">N-free</a> )</span><br/>

<b>thus </b><a NAME="E1:38"/>
( <font color="Maroon" title="c1">G</font> is <a href="neckla_2.html#V1" title="NECKLA_2:attr.1">N-free</a> implies  <a href="necklace.html#K3" title="NECKLACE:func.3">ComplRelStr</a> <font color="Maroon" title="c1">G</font> is <a href="neckla_2.html#V1" title="NECKLA_2:attr.1">N-free</a> )
  <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="necklace.html#K3" title="NECKLACE:func.3">ComplRelStr</a> <font color="Maroon" title="c1">G</font> is <a href="neckla_2.html#V1" title="NECKLA_2:attr.1">N-free</a> implies <font color="Maroon" title="c1">G</font> is <a href="neckla_2.html#V1" title="NECKLA_2:attr.1">N-free</a> )</span><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" title="E22">A1</font></i>: 
<font color="Maroon" title="c1">G</font> is <a href="neckla_2.html#V1" title="NECKLA_2:attr.1">N-free</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="necklace.html#K3" title="NECKLACE:func.3">ComplRelStr</a> <font color="Maroon" title="c1">G</font> is <a href="neckla_2.html#V1" title="NECKLA_2:attr.1">N-free</a></span><br/>

<b>assume </b><a NAME="E2:38_1"/>
not  <a href="necklace.html#K3" title="NECKLACE:func.3">ComplRelStr</a> <font color="Maroon" title="c1">G</font> is <a href="neckla_2.html#V1" title="NECKLA_2:attr.1">N-free</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E3:38_1"/><b>then </b>
 <a href="necklace.html#K3" title="NECKLACE:func.3">ComplRelStr</a> <font color="Maroon" title="c1">G</font> <a href="necklace.html#R2" title="NECKLACE:pred.2">embeds</a>  <a href="necklace.html#K4" title="NECKLACE:func.4">Necklace</a> 4
 
<b>by </b><i><a class="ref" href="neckla_2.html#D1" title="NECKLA_2:def.1">NECKLA_2:def 1</a></i>;<br/>
<a NAME="E4:38_1"/><b>then </b>
<font color="Maroon" title="c1">G</font> <a href="necklace.html#R2" title="NECKLACE:pred.2">embeds</a>  <a href="necklace.html#K4" title="NECKLACE:func.4">Necklace</a> 4
 
<b>by </b><i><a class="ref" href="neckla_3.html#T24" target="_self" title="NECKLA_3:th.24">Th24</a></i>;<br/>
<b>hence </b><a NAME="E5:38_1"/>
contradiction
 <b>by </b><i><a class="txt" href="#E1:38_1"><i><font color="Green" title="E22">A1</font></i></a>, <a class="ref" href="neckla_2.html#D1" title="NECKLA_2:def.1">NECKLA_2:def 1</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><b>end;</b></div>

<b>assume </b><a NAME="E2:38"/><i><font color="Green" title="E22">A2</font></i>: 
 <a href="necklace.html#K3" title="NECKLACE:func.3">ComplRelStr</a> <font color="Maroon" title="c1">G</font> is <a href="neckla_2.html#V1" title="NECKLA_2:attr.1">N-free</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c1">G</font> is <a href="neckla_2.html#V1" title="NECKLA_2:attr.1">N-free</a></span><br/>

<b>assume </b><a NAME="E3:38"/>
not <font color="Maroon" title="c1">G</font> is <a href="neckla_2.html#V1" title="NECKLA_2:attr.1">N-free</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E4:38"/><b>then </b>
<font color="Maroon" title="c1">G</font> <a href="necklace.html#R2" title="NECKLACE:pred.2">embeds</a>  <a href="necklace.html#K4" title="NECKLACE:func.4">Necklace</a> 4
 
<b>by </b><i><a class="ref" href="neckla_2.html#D1" title="NECKLA_2:def.1">NECKLA_2:def 1</a></i>;<br/>
<a NAME="E5:38"/><b>then </b>
 <a href="necklace.html#K3" title="NECKLACE:func.3">ComplRelStr</a> <font color="Maroon" title="c1">G</font> <a href="necklace.html#R2" title="NECKLACE:pred.2">embeds</a>  <a href="necklace.html#K4" title="NECKLACE:func.4">Necklace</a> 4
 
<b>by </b><i><a class="ref" href="neckla_3.html#T24" target="_self" title="NECKLA_3:th.24">Th24</a></i>;<br/>
<b>hence </b><a NAME="E6:38"/>
contradiction
 <b>by </b><i><a class="txt" href="#E2:38"><i><font color="Green" title="E22">A2</font></i></a>, <a class="ref" href="neckla_2.html#D1" title="NECKLA_2:def.1">NECKLA_2:def 1</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>
