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

<b>let </b><font color="Maroon">O</font> be  non <a href="struct_0.html#V3">empty</a>  <a href="oposet_1.html#L1" target="_self">OrthoRelStr</a> ;<br/>

<b>thus </b><a NAME="E1:95"/>
( <font color="Maroon">O</font> is <a href="oposet_1.html#V13" target="_self">SubPartialOrdered</a> implies <font color="Maroon">O</font> is <a href="oposet_1.html#V14" target="_self">PartialOrdered</a> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="95_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:95_1"/>
<font color="Maroon">O</font> is <a href="oposet_1.html#V13" target="_self">SubPartialOrdered</a>
 ;<br/>

<b>then reconsider </b><font color="Maroon">O</font> = <font color="Maroon">O</font> as  non <a href="struct_0.html#V3">empty</a> <a href="orders_2.html#V2">reflexive</a> <a href="oposet_1.html#V7" target="_self">SubAntisymmetric</a> <a href="oposet_1.html#V9" target="_self">SubTransitive</a>  <a href="oposet_1.html#L1" target="_self">OrthoRelStr</a>  <b>by </b><i/>;<br/>
<a NAME="E3:95_1"/>
( <font color="Maroon">O</font> is <a href="oposet_1.html#V7" target="_self">SubAntisymmetric</a> &amp; <font color="Maroon">O</font> is <a href="oposet_1.html#V9" target="_self">SubTransitive</a> )
 
;<br/>
<b>hence </b><a NAME="E4:95_1"/>
<font color="Maroon">O</font> is <a href="oposet_1.html#V14" target="_self">PartialOrdered</a>
 <b>by </b><i><a class="ref" href="oposet_1.html#D3" target="_self">Def3</a></i>;<br/>


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

<b>assume </b><a NAME="E2:95"/>
<font color="Maroon">O</font> is <a href="oposet_1.html#V14" target="_self">PartialOrdered</a>
 ;<br/>

<b>then reconsider </b><font color="Maroon">O</font> = <font color="Maroon">O</font> as  non <a href="struct_0.html#V3">empty</a> <a href="orders_2.html#V2">reflexive</a> <a href="orders_2.html#V3">transitive</a> <a href="orders_2.html#V4">antisymmetric</a>  <a href="oposet_1.html#L1" target="_self">OrthoRelStr</a>  <b>by </b><i><a class="ref" href="oposet_1.html#D3" target="_self">Def3</a></i>;<br/>
<a NAME="E4:95"/>
<font color="Maroon">O</font> is <a href="oposet_1.html#V9" target="_self">SubTransitive</a>
 
;<br/>
<b>hence </b><a NAME="E5:95"/>
<font color="Maroon">O</font> is <a href="oposet_1.html#V13" target="_self">SubPartialOrdered</a>
 <b>by </b><i/>;<br/>


</div>
