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<b>let </b><font color="Maroon">O</font> be  non <a href="struct_0.html#V3">empty</a> <a href="oposet_1.html#V14">PartialOrdered</a> <a href="oposet_1.html#V19">OrderInvolutive</a>  <a href="oposet_1.html#L1">OrthoRelStr</a> ;<br/><b>let </b><font color="Maroon">x</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">O</font>, <font color="Maroon">y</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">O</font>;<br/>



<b>assume </b><a NAME="E1:12"/><i><font color="Green">E22</font></i>: 
<font color="Maroon">x</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">y</font>
 ;<br/>

<b>consider </b><font color="Maroon">f</font> being   <a href="struct_0.html#NM6">Function</a> of <font color="Maroon">O</font>,<font color="Maroon">O</font><b> such that </b><br/><a NAME="E3:12"/><i><font color="Green">E23</font></i>: 
( <font color="Maroon">f</font> <a href="funct_2.html#R2">=</a> the <a href="robbins1.html#U1">Compl</a> of <font color="Maroon">O</font> &amp; <font color="Maroon">f</font> is <a href="oposet_1.html#V18">Orderinvolutive</a> )
 <b>by </b><i><a class="ref" href="oposet_1.html#D33">OPOSET_1:def 33</a></i>;<br/>
<b>consider </b><font color="Maroon">g</font> being   <a href="struct_0.html#NM6">Function</a> of <font color="Maroon">O</font>,<font color="Maroon">O</font><b> such that </b><br/><a NAME="E5:12"/><i><font color="Green">E26</font></i>: 
( <font color="Maroon">g</font> <a href="funct_2.html#R2">=</a> <font color="Maroon">f</font> &amp; <font color="Maroon">g</font> is <a href="oposet_1.html#V2">dneg</a> &amp; <font color="Maroon">g</font> is <a href="waybel_0.html#V5">antitone</a> )
 <b>by </b><i>, <a class="ref" href="oposet_1.html#D32">OPOSET_1:def 32</a></i>;<br/>
<a NAME="E6:12"/>
<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> <a href="orders_2.html#NR2" target="_self">&gt;=</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font>
 
<b>by </b><i>, , <a class="ref" href="waybel_9.html#D1">WAYBEL_9:def 1</a></i>;<br/>
<a NAME="E7:12"/><b>then </b>
<font color="Maroon">x</font> <a href="robbins1.html#K3">`</a>  <a href="orders_2.html#NR2" target="_self">&gt;=</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font>
 
<b>by </b><i>, <a class="ref" href="robbins1.html#D3">ROBBINS1:def 3</a></i>;<br/>
<b>hence </b><a NAME="E8:12"/>
<font color="Maroon">y</font> <a href="robbins1.html#K3">`</a>  <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">x</font> <a href="robbins1.html#K3">`</a> 
 <b>by </b><i>, <a class="ref" href="robbins1.html#D3">ROBBINS1:def 3</a></i>;<br/>


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