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<b>let </b><font color="Maroon">PO</font> be  non <a href="struct_0.html#V3">empty</a>  <a href="oposet_1.html#L1" target="_self">OrthoRelStr</a> ;<br/><b>let </b><font color="Maroon">g</font> be   <a href="binop_1.html#NM1">UnOp</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">PO</font>;<br/>



<b>assume </b><a NAME="E1:128"/><i><font color="Green">E22</font></i>: 
<font color="Maroon">g</font> <a href="oposet_1.html#R2" target="_self">OrthoComplement_on</a> <font color="Maroon">PO</font>
 ;<br/>

<a NAME="E2:128"/><b>then </b><i><font color="Green">E23</font></i>: 
for <font color="Olive">x</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">PO</font> holds <br/> (  <a href="yellow_0.html#R1">ex_sup_of</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Olive">x</font>,<span class="p2">(<span class="default"><font color="Maroon">g</font> <a href="funct_2.html#K3">.</a> <font color="Olive">x</font></span>)</span></span><a href="domain_1.html#K7">}</a></span>,<font color="Maroon">PO</font> &amp;  <a href="yellow_0.html#R2">ex_inf_of</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Olive">x</font>,<span class="p2">(<span class="default"><font color="Maroon">g</font> <a href="funct_2.html#K3">.</a> <font color="Olive">x</font></span>)</span></span><a href="domain_1.html#K7">}</a></span>,<font color="Maroon">PO</font> )
 
<b>by </b><i><a class="ref" href="oposet_1.html#D13" target="_self">Def13</a></i>;<br/>
<a NAME="E3:128"/>
<font color="Maroon">g</font> is <a href="oposet_1.html#V18" target="_self">Orderinvolutive</a>
 
<b>by </b><i><a class="ref" href="oposet_1.html#T27" target="_self">Th27</a>, <a class="ref" href="oposet_1.html#D13" target="_self">Def13</a></i>;<br/>
<b>hence </b><a NAME="E4:128"/>
<font color="Maroon">g</font> <a href="oposet_1.html#R1" target="_self">QuasiOrthoComplement_on</a> <font color="Maroon">PO</font>
 <b>by </b><i><a class="ref" href="oposet_1.html#D15" target="_self">Def15</a>, <a class="ref" href="oposet_1.html#T24" target="_self">Th24</a></i>;<br/>


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