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

<a NAME="E1:16_2_1"/>
ex <font color="Olive">b<sub>1</sub></font> being non <a href="struct_0.html#V3">empty</a> <a href="orders_2.html#NM1">Poset</a> st <br/>( <font color="Olive">b<sub>1</sub></font> is <a href="orders_2.html#V1">strict</a> &amp; <font color="Olive">b<sub>1</sub></font> is <a href="orders_3.html#V3" target="_self">disconnected</a> &amp; <font color="Olive">b<sub>1</sub></font> is <a href="orders_3.html#V1" target="_self">discrete</a> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_2_1_1"><b>proof </b></a><div class="add">

<b>reconsider </b><font color="Maroon">c<sub>1</sub></font> =  <a href="orders_2.html#G1">RelStr</a>(# <span class="p1"><a href="tarski.html#K2">{</a><span class="default">1,2</span><a href="tarski.html#K2">}</a></span>,<span class="p1">(<span class="default"><a href="partfun1.html#K6">id</a> <span class="p2"><a href="tarski.html#K2">{</a><span class="default">1,2</span><a href="tarski.html#K2">}</a></span></span>)</span> #) as  non <a href="struct_0.html#V3">empty</a> <a href="orders_2.html#NM1">Poset</a> ;<br/>
<b>reconsider </b><font color="Maroon">c<sub>2</sub></font> = <font color="Maroon">c<sub>1</sub></font> as  non <a href="struct_0.html#V3">empty</a> <a href="orders_3.html#V1" target="_self">discrete</a> <a href="orders_2.html#NM1">Poset</a> <b>by </b><i><a class="ref" href="orders_3.html#D1" target="_self">Def1</a></i>;<br/>
<b>take </b>
<font color="Maroon">c<sub>2</sub></font>
;<br/>

<a NAME="E3:16_2_1_1"/>
ex <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>2</sub></font> st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">b<sub>2</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_2_1_1_1"><b>proof </b></a><div class="add">

<b>set </b><font color="Maroon">c<sub>3</sub></font> = 1;<br/>
<b>set </b><font color="Maroon">c<sub>4</sub></font> = 2;<br/>
<b>reconsider </b><font color="Maroon">c<sub>5</sub></font> = 1, <font color="Maroon">c<sub>6</sub></font> = 2 as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>2</sub></font> <b>by </b><i><a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/>
<b>take </b>
<font color="Maroon">c<sub>5</sub></font>
;<br/>

<b>take </b>
<font color="Maroon">c<sub>6</sub></font>
;<br/>

<b>thus </b><a NAME="E2:16_2_1_1_1"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>6</sub></font>
 ;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E4:16_2_1_1"/>
( <font color="Maroon">c<sub>2</sub></font> is <a href="orders_2.html#V1">strict</a> &amp; <font color="Maroon">c<sub>2</sub></font> is <a href="orders_3.html#V3" target="_self">disconnected</a> &amp; <font color="Maroon">c<sub>2</sub></font> is <a href="orders_3.html#V1" target="_self">discrete</a> )
 <b>by </b><i><a class="ref" href="orders_3.html#T5" target="_self">Th5</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E2:16_2_1"/>
ex <font color="Olive">b<sub>1</sub></font> being non <a href="struct_0.html#V3">empty</a> <a href="orders_2.html#NM1">Poset</a> st <br/>( <font color="Olive">b<sub>1</sub></font> is <a href="orders_2.html#V1">strict</a> &amp; <font color="Olive">b<sub>1</sub></font> is <a href="orders_3.html#V3" target="_self">disconnected</a> &amp; <font color="Olive">b<sub>1</sub></font> is <a href="orders_3.html#V1" target="_self">discrete</a> )
 ;<br/>


</div>
