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

<b>let </b><font color="Maroon">c<sub>1</sub></font> be    <a href="orders_2.html#L1">RelStr</a> ;<br/>

<b>thus </b><a NAME="E1:5"/>
( <font color="Maroon">c<sub>1</sub></font> is <a href="orders_2.html#V2">reflexive</a> implies <font color="Maroon">c<sub>1</sub></font> <a href="yellow_7.html#NK1" target="_self">opp</a>  is <a href="orders_2.html#V2">reflexive</a> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="5_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:5_1"/>
<font color="Maroon">c<sub>1</sub></font> is <a href="orders_2.html#V2">reflexive</a>
 ;<br/>

<a NAME="E2:5_1"/><b>then </b><i><font color="Green">E4</font></i>: 
the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">c<sub>1</sub></font> <a href="relat_2.html#R1">is_reflexive_in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="orders_2.html#D4">ORDERS_2:def 4</a></i>;<br/>
<b>let </b><font color="Maroon">c<sub>2</sub></font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="relat_2.html#D1">RELAT_2:def 1</a>,<a class="ref" href="orders_2.html#D4">ORDERS_2:def 4</a><br/>

<b>assume </b><a NAME="E3:5_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="yellow_7.html#NK1" target="_self">opp</a> </span>)</span>
 ;<br/>

<a NAME="E4:5_1"/><b>then </b>
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="txt" href="yellow_7.html#E2:5_1"><i><font color="Green">E4</font></i></a>, <a class="ref" href="relat_2.html#D1">RELAT_2:def 1</a></i>;<br/>
<b>hence </b><a NAME="E5:5_1"/>
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> the <a href="orders_2.html#U1">InternalRel</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="yellow_7.html#NK1" target="_self">opp</a> </span>)</span>
 <b>by </b><i><a class="ref" href="relat_1.html#D7">RELAT_1:def 7</a></i>;<br/>


</div><b>end;</b></div>

<b>assume </b><a NAME="E2:5"/>
<font color="Maroon">c<sub>1</sub></font> <a href="yellow_7.html#NK1" target="_self">opp</a>  is <a href="orders_2.html#V2">reflexive</a>
 ;<br/>

<a NAME="E3:5"/><b>then </b><i><font color="Green">E4</font></i>: 
the <a href="orders_2.html#U1">InternalRel</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="yellow_7.html#NK1" target="_self">opp</a> </span>)</span> <a href="relat_2.html#R1">is_reflexive_in</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="yellow_7.html#NK1" target="_self">opp</a> </span>)</span>
 
<b>by </b><i><a class="ref" href="orders_2.html#D4">ORDERS_2:def 4</a></i>;<br/>
<b>let </b><font color="Maroon">c<sub>2</sub></font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="relat_2.html#D1">RELAT_2:def 1</a>,<a class="ref" href="orders_2.html#D4">ORDERS_2:def 4</a><br/>

<b>assume </b><a NAME="E4:5"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>
 ;<br/>

<a NAME="E5:5"/><b>then </b>
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> the <a href="orders_2.html#U1">InternalRel</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="yellow_7.html#NK1" target="_self">opp</a> </span>)</span>
 
<b>by </b><i><a class="txt" href="yellow_7.html#E3:5"><i><font color="Green">E4</font></i></a>, <a class="ref" href="relat_2.html#D1">RELAT_2:def 1</a></i>;<br/>
<b>hence </b><a NAME="E6:5"/>
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="ref" href="relat_1.html#D7">RELAT_1:def 7</a></i>;<br/>


</div>
