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<div class="add">

<a NAME="E1:15_2_1"/>
 ex <font color="Olive" title="b1">Y</font> being non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="orders_2.html#NM1" title="ORDERS_2:NM.1">Poset</a> st <br/>( <font color="Olive" title="b1">Y</font> is <a href="orders_2.html#V1" title="ORDERS_2:attr.1">strict</a> &amp; <font color="Olive" title="b1">Y</font> is <a href="orders_3.html#V3" title="ORDERS_3:attr.3">disconnected</a> &amp; <font color="Olive" title="b1">Y</font> is <a href="orders_3.html#V1" title="ORDERS_3:attr.1">discrete</a> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_2_1_1"><b>proof </b></a><div class="add">

<b>reconsider </b><font color="Maroon" title="c1">A</font> =  <a href="orders_2.html#G1" title="ORDERS_2:aggr.1">RelStr</a>(# <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default">1,2</span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>,<span class="p1">(<span class="default"><a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> <span class="p2"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default">1,2</span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span></span>)</span> #) as  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="orders_2.html#NM1" title="ORDERS_2:NM.1">Poset</a> ;<br/>
<b>reconsider </b><font color="Maroon" title="c2">A</font> = <font color="Maroon" title="c1">A</font> as  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="orders_3.html#V1" title="ORDERS_3:attr.1">discrete</a> <a href="orders_2.html#NM1" title="ORDERS_2:NM.1">Poset</a> <b>by </b><i><a class="ref" href="orders_3.html#D1" target="_self" title="ORDERS_3:def.1">Def1</a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c2">A</font>
;<br/>

<a NAME="E3:15_2_1_1"/>
 ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">A</font> st <font color="Olive" title="b1">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b2">b</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_2_1_1_1"><b>proof </b></a><div class="add">

<b>set </b><font color="Maroon" title="c3">a</font> = 1;<br/>
<b>set </b><font color="Maroon" title="c4">b</font> = 2;<br/>
<b>reconsider </b><font color="Maroon" title="c5">a</font> = 1, <font color="Maroon" title="c6">b</font> = 2 as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">A</font> <b>by </b><i><a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c5">a</font>
;<br/>

<b>take </b>
<font color="Maroon" title="c6">b</font>
;<br/>

<b>thus </b><a NAME="E2:15_2_1_1_1"/>
<font color="Maroon" title="c5">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">b</font>
 ;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E4:15_2_1_1"/>
( <font color="Maroon" title="c2">A</font> is <a href="orders_2.html#V1" title="ORDERS_2:attr.1">strict</a> &amp; <font color="Maroon" title="c2">A</font> is <a href="orders_3.html#V3" title="ORDERS_3:attr.3">disconnected</a> &amp; <font color="Maroon" title="c2">A</font> is <a href="orders_3.html#V1" title="ORDERS_3:attr.1">discrete</a> )
 <b>by </b><i><a class="ref" href="orders_3.html#T5" target="_self" title="ORDERS_3:th.5">Th5</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E2:15_2_1"/>
 ex <font color="Olive">b<sub>1</sub></font> being non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="orders_2.html#NM1" title="ORDERS_2:NM.1">Poset</a> st <br/>( <font color="Olive">b<sub>1</sub></font> is <a href="orders_2.html#V1" title="ORDERS_2:attr.1">strict</a> &amp; <font color="Olive">b<sub>1</sub></font> is <a href="orders_3.html#V3" title="ORDERS_3:attr.3">disconnected</a> &amp; <font color="Olive">b<sub>1</sub></font> is <a href="orders_3.html#V1" title="ORDERS_3:attr.1">discrete</a> )
 ;<br/>


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