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<a NAME="E1:14_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" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="14_2_1_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">reconsider </span><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/>
<span class="kw">reconsider </span><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> <span class="kw">by</span> <span class="lab"><a class="ref" href="orders_3.html#D1" target="_self" onmouseover="rs('orders_3/D1')" onmouseout="rh()">Def1</a></span>;<br/>
<span class="kw">take </span>
<font color="Maroon" title="c2">A</font>
; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <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>  )</span><br/>

<a NAME="E3:14_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" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="14_2_1_1_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">set </span><font color="Maroon" title="c3">a</font> = 1;<br/>
<span class="kw">set </span><font color="Maroon" title="c4">b</font> = 2;<br/>
<span class="kw">reconsider </span><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> <span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D2" onmouseover="rs('tarski/D2')" onmouseout="rh()">TARSKI:def 2</a></span>;<br/>
<span class="kw">take </span>
<font color="Maroon" title="c5">a</font>
; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">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="Maroon" title="c5">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b1">b</font></span><br/>

<span class="kw">take </span>
<font color="Maroon" title="c6">b</font>
; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <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></span><br/>

<span class="kw">thus </span><a NAME="E2:14_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>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E4:14_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>  )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="orders_3.html#T5" target="_self" onmouseover="rs('orders_3/T5')" onmouseout="rh()">Th5</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E2:14_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>  )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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