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

<b>set </b><font color="Maroon">c<sub>1</sub></font> = <span class="p1"><a href="domain_1.html#K7">{</a><span class="default">0,1</span><a href="domain_1.html#K7">}</a></span>;<br/>
<b>set </b><font color="Maroon">c<sub>2</sub></font> =  <a href="toler_1.html#NK1" target="_self">Total</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default">0,1</span><a href="domain_1.html#K7">}</a></span>;<br/>
<b>set </b><font color="Maroon">c<sub>3</sub></font> =  <a href="orders_2.html#G1">RelStr</a>(# <span class="p1"><a href="domain_1.html#K7">{</a><span class="default">0,1</span><a href="domain_1.html#K7">}</a></span>,<span class="p1">(<span class="default"><a href="toler_1.html#NK1" target="_self">Total</a> <span class="p2"><a href="domain_1.html#K7">{</a><span class="default">0,1</span><a href="domain_1.html#K7">}</a></span></span>)</span> #);<br/>
<b>reconsider </b><font color="Maroon">c<sub>4</sub></font> =  <a href="orders_2.html#G1">RelStr</a>(# <span class="p1"><a href="domain_1.html#K7">{</a><span class="default">0,1</span><a href="domain_1.html#K7">}</a></span>,<span class="p1">(<span class="default"><a href="toler_1.html#NK1" target="_self">Total</a> <span class="p2"><a href="domain_1.html#K7">{</a><span class="default">0,1</span><a href="domain_1.html#K7">}</a></span></span>)</span> #) as  non <a href="struct_0.html#V3">empty</a>  <a href="orders_2.html#L1">RelStr</a>  ;<br/>
<a NAME="E2:25_2_1"/><i><font color="Green">E12</font></i>: 
<font color="Maroon">c<sub>4</sub></font> is <a href="roughs_1.html#V2" target="_self">with_equivalence</a>
 
<b>by </b><i><a class="ref" href="roughs_1.html#D2" target="_self">Def2</a></i>;<br/>
<a NAME="E3:25_2_1"/>
not <font color="Maroon">c<sub>4</sub></font> is <a href="roughs_1.html#V1" target="_self">diagonal</a>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="25_2_1_1"><b>proof </b></a><div class="add">

<a NAME="E1:25_2_1_1"/>
not <span class="p1"><a href="domain_1.html#K7">{</a><span class="default">0,1</span><a href="domain_1.html#K7">}</a></span> is <a href="realset1.html#V1">trivial</a>
 
<b>by </b><i><a class="ref" href="chain_1.html#T4">CHAIN_1:4</a></i>;<br/>
<a NAME="E2:25_2_1_1"/><b>then </b>
not the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">c<sub>4</sub></font> <a href="tarski.html#R1">c=</a>  <a href="partfun1.html#K6">id</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="ref" href="roughs_1.html#T1" target="_self">Th1</a></i>;<br/>
<b>hence </b><a NAME="E3:25_2_1_1"/>
not <font color="Maroon">c<sub>4</sub></font> is <a href="roughs_1.html#V1" target="_self">diagonal</a>
 <b>by </b><i><a class="ref" href="roughs_1.html#D1" target="_self">Def1</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E4:25_2_1"/>
ex <font color="Olive">b<sub>1</sub></font> being   <a href="orders_2.html#L1">RelStr</a>  st <br/>( not <font color="Olive">b<sub>1</sub></font> is <a href="roughs_1.html#V1" target="_self">diagonal</a> &amp; <font color="Olive">b<sub>1</sub></font> is <a href="group_1.html#V6">finite</a> &amp; <font color="Olive">b<sub>1</sub></font> is <a href="roughs_1.html#V2" target="_self">with_equivalence</a> &amp; not <font color="Olive">b<sub>1</sub></font> is <a href="struct_0.html#V3">empty</a> )
 <b>by </b><i><a class="txt" href="roughs_1.html#E2:25_2_1"><i><font color="Green">E12</font></i></a></i>;<br/>


</div>
