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<b>let </b><font color="Maroon" title="c1">O</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  <a href="qmax_1.html#L2" title="QMAX_1:struct.2">OrthoRelStr</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">O</font> is <a href="oposet_1.html#V12" title="OPOSET_1:attr.12">SubPartialOrdered</a> iff <font color="Maroon" title="c1">O</font> is <a href="oposet_1.html#V13" title="OPOSET_1:attr.13">PartialOrdered</a> )</span><br/>

<b>thus </b><a NAME="E1:94"/>
( <font color="Maroon" title="c1">O</font> is <a href="oposet_1.html#V12" title="OPOSET_1:attr.12">SubPartialOrdered</a> implies <font color="Maroon" title="c1">O</font> is <a href="oposet_1.html#V13" title="OPOSET_1:attr.13">PartialOrdered</a> )
  <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">O</font> is <a href="oposet_1.html#V13" title="OPOSET_1:attr.13">PartialOrdered</a> implies <font color="Maroon" title="c1">O</font> is <a href="oposet_1.html#V12" title="OPOSET_1:attr.12">SubPartialOrdered</a> )</span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="94_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:94_1"/>
<font color="Maroon" title="c1">O</font> is <a href="oposet_1.html#V12" title="OPOSET_1:attr.12">SubPartialOrdered</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c1">O</font> is <a href="oposet_1.html#V13" title="OPOSET_1:attr.13">PartialOrdered</a></span><br/>

<b>then reconsider </b><font color="Maroon" title="c2">O</font> = <font color="Maroon" title="c1">O</font> as  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="orders_2.html#V3" title="ORDERS_2:attr.3">reflexive</a> <a href="oposet_1.html#V6" title="OPOSET_1:attr.6">SubAntisymmetric</a> <a href="oposet_1.html#V8" title="OPOSET_1:attr.8">SubTransitive</a>  <a href="qmax_1.html#L2" title="QMAX_1:struct.2">OrthoRelStr</a>  <b>by </b><i><a class="ref" href="oposet_1.html#D24" target="_self" title="OPOSET_1:def.24">Def24</a></i>;<br/>
<a NAME="E3:94_1"/>
( <font color="Maroon" title="c2">O</font> is <a href="oposet_1.html#V6" title="OPOSET_1:attr.6">SubAntisymmetric</a> &amp; <font color="Maroon" title="c2">O</font> is <a href="oposet_1.html#V8" title="OPOSET_1:attr.8">SubTransitive</a> )
 
;<br/>
<b>hence </b><a NAME="E4:94_1"/>
<font color="Maroon" title="c1">O</font> is <a href="oposet_1.html#V13" title="OPOSET_1:attr.13">PartialOrdered</a>
 <b>by </b><i><a class="ref" href="oposet_1.html#D25" target="_self" title="OPOSET_1:def.25">Def25</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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

<b>assume </b><a NAME="E2:94"/>
<font color="Maroon" title="c1">O</font> is <a href="oposet_1.html#V13" title="OPOSET_1:attr.13">PartialOrdered</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c1">O</font> is <a href="oposet_1.html#V12" title="OPOSET_1:attr.12">SubPartialOrdered</a></span><br/>

<b>then reconsider </b><font color="Maroon" title="c2">O</font> = <font color="Maroon" title="c1">O</font> as  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="orders_2.html#V3" title="ORDERS_2:attr.3">reflexive</a> <a href="orders_2.html#V4" title="ORDERS_2:attr.4">transitive</a> <a href="orders_2.html#V5" title="ORDERS_2:attr.5">antisymmetric</a>  <a href="qmax_1.html#L2" title="QMAX_1:struct.2">OrthoRelStr</a>  <b>by </b><i><a class="ref" href="oposet_1.html#D25" target="_self" title="OPOSET_1:def.25">Def25</a></i>;<br/>
<a NAME="E4:94"/>
<font color="Maroon" title="c2">O</font> is <a href="oposet_1.html#V8" title="OPOSET_1:attr.8">SubTransitive</a>
 
;<br/>
<b>hence </b><a NAME="E5:94"/>
<font color="Maroon" title="c1">O</font> is <a href="oposet_1.html#V12" title="OPOSET_1:attr.12">SubPartialOrdered</a>
 <b>by </b><i><a class="ref" href="oposet_1.html#D24" target="_self" title="OPOSET_1:def.24">Def24</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
