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<b>let </b><font color="Maroon" title="c1">O</font> be  non <a href="struct_0.html#V3" title="STRUCT_0:attr.3">empty</a> <a href="oposet_1.html#V14" title="OPOSET_1:attr.14">PartialOrdered</a> <a href="oposet_1.html#V19" title="OPOSET_1:attr.19">OrderInvolutive</a>  <a href="oposet_1.html#L1" title="OPOSET_1:struct.1">OrthoRelStr</a> ;<br/><b>let </b><font color="Maroon" title="c2">x</font>, <font color="Maroon" title="c3">y</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">O</font>;<br/>



<b>assume </b><a NAME="E1:12"/><i><font color="Green" title="E11">A1</font></i>: 
<font color="Maroon" title="c2">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c3">y</font>
 ;<br/>

<b>consider </b><font color="Maroon" title="c4">f</font> being   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c1">O</font>,<font color="Maroon" title="c1">O</font><b> such that </b><br/><a NAME="E3:12"/><i><font color="Green" title="E12">A2</font></i>: 
( <font color="Maroon" title="c4">f</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> the <a href="robbins1.html#U1" title="ROBBINS1:sel.1">Compl</a> of <font color="Maroon" title="c1">O</font> &amp; <font color="Maroon" title="c4">f</font> is <a href="oposet_1.html#V18" title="OPOSET_1:attr.18">Orderinvolutive</a> )
 <b>by </b><i><a class="ref" href="oposet_1.html#D33" title="OPOSET_1:def.33">OPOSET_1:def 33</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c5">g</font> being   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c1">O</font>,<font color="Maroon" title="c1">O</font><b> such that </b><br/><a NAME="E5:12"/><i><font color="Green" title="E13">A3</font></i>: 
( <font color="Maroon" title="c5">g</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c4">f</font> &amp; <font color="Maroon" title="c5">g</font> is <a href="oposet_1.html#V2" title="OPOSET_1:attr.2">dneg</a> &amp; <font color="Maroon" title="c5">g</font> is <a href="waybel_0.html#V5" title="WAYBEL_0:attr.5">antitone</a> )
 <b>by </b><i><a class="txt" href="robbins3.html#E3:12"><i><font color="Green" title="E12">A2</font></i></a>, <a class="ref" href="oposet_1.html#D32" title="OPOSET_1:def.32">OPOSET_1:def 32</a></i>;<br/>
<a NAME="E6:12"/>
<font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">x</font> <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a> <font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">y</font>
 
<b>by </b><i><a class="txt" href="robbins3.html#E1:12"><i><font color="Green" title="E11">A1</font></i></a>, <a class="txt" href="robbins3.html#E5:12"><i><font color="Green" title="E13">A3</font></i></a>, <a class="ref" href="waybel_9.html#D1" title="WAYBEL_9:def.1">WAYBEL_9:def 1</a></i>;<br/>
<a NAME="E7:12"/><b>then </b>
<font color="Maroon" title="c2">x</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a>  <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a> <font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">y</font>
 
<b>by </b><i><a class="txt" href="robbins3.html#E3:12"><i><font color="Green" title="E12">A2</font></i></a>, <a class="ref" href="robbins1.html#D3" title="ROBBINS1:def.3">ROBBINS1:def 3</a></i>;<br/>
<b>hence </b><a NAME="E8:12"/>
<font color="Maroon" title="c3">y</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a>  <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c2">x</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> 
 <b>by </b><i><a class="txt" href="robbins3.html#E3:12"><i><font color="Green" title="E12">A2</font></i></a>, <a class="ref" href="robbins1.html#D3" title="ROBBINS1:def.3">ROBBINS1:def 3</a></i>;<br/>


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