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

<b>set </b><font color="Maroon" title="c1">C</font> = <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1</span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>;<br/>
<b>set </b><font color="Maroon" title="c2">R</font> =  <a href="toler_1.html#NK1" title="TOLER_1:NK.1">Total</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1</span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>;<br/>
<b>set </b><font color="Maroon" title="c3">E</font> =  <a href="orders_2.html#G1" title="ORDERS_2:aggr.1">RelStr</a>(# <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1</span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<span class="p1">(<span class="default"><a href="toler_1.html#NK1" title="TOLER_1:NK.1">Total</a> <span class="p2"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1</span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span></span>)</span> #);<br/>
<b>reconsider </b><font color="Maroon" title="c4">E</font> =  <a href="orders_2.html#G1" title="ORDERS_2:aggr.1">RelStr</a>(# <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1</span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<span class="p1">(<span class="default"><a href="toler_1.html#NK1" title="TOLER_1:NK.1">Total</a> <span class="p2"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1</span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span></span>)</span> #) as  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  <a href="orders_2.html#L1" title="ORDERS_2:struct.1">RelStr</a>  ;<br/>
<a NAME="E2:25_2_1"/><i><font color="Green" title="E11">A1</font></i>: 
<font color="Maroon" title="c4">E</font> is <a href="roughs_1.html#V2" title="ROUGHS_1:attr.2">with_equivalence</a>
 
<b>by </b><i><a class="ref" href="roughs_1.html#D2" target="_self" title="ROUGHS_1:def.2">Def2</a></i>;<br/>
<a NAME="E3:25_2_1"/>
not <font color="Maroon" title="c4">E</font> is <a href="roughs_1.html#V1" title="ROUGHS_1:attr.1">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" title="DOMAIN_1:func.7">{</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1</span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> is <a href="zfmisc_1.html#V1" title="ZFMISC_1:attr.1">trivial</a>
 
<b>by </b><i><a class="ref" href="chain_1.html#T4" title="CHAIN_1:th.4">CHAIN_1:4</a></i>;<br/>
<b>hence </b><a NAME="E2:25_2_1_1"/>
not <font color="Maroon" title="c4">E</font> is <a href="roughs_1.html#V1" title="ROUGHS_1:attr.1">diagonal</a>
 ; <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>hence </b><a NAME="E4:25_2_1"/>
 ex <font color="Olive">b<sub>1</sub></font> being   <a href="orders_2.html#L1" title="ORDERS_2:struct.1">RelStr</a>  st <br/>( not <font color="Olive">b<sub>1</sub></font> is <a href="roughs_1.html#V1" title="ROUGHS_1:attr.1">diagonal</a> &amp; <font color="Olive">b<sub>1</sub></font> is <a href="struct_0.html#V8" title="STRUCT_0:attr.8">finite</a> &amp; <font color="Olive">b<sub>1</sub></font> is <a href="roughs_1.html#V2" title="ROUGHS_1:attr.2">with_equivalence</a> &amp; not <font color="Olive">b<sub>1</sub></font> is <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> )
 <b>by </b><i><a class="txt" href="#E2:25_2_1"><i><font color="Green" title="E11">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>
