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<span class="kw">let </span><font color="Maroon" title="c1">PO</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:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">f</font> being  <a href="binop_1.html#NM1" title="BINOP_1:NM.1">UnOp</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">PO</font>  st <font color="Olive" title="b1">f</font> <a href="oposet_1.html#R2" title="OPOSET_1:pred.2">OrthoComplement_on</a> <font color="Maroon" title="c1">PO</font> holds <br/><font color="Olive" title="b1">f</font> <a href="oposet_1.html#R1" title="OPOSET_1:pred.1">QuasiOrthoComplement_on</a> <font color="Maroon" title="c1">PO</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">g</font> be   <a href="binop_1.html#NM1" title="BINOP_1:NM.1">UnOp</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">PO</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">g</font> <a href="oposet_1.html#R2" title="OPOSET_1:pred.2">OrthoComplement_on</a> <font color="Maroon" title="c1">PO</font> implies <font color="Maroon" title="c2">g</font> <a href="oposet_1.html#R1" title="OPOSET_1:pred.1">QuasiOrthoComplement_on</a> <font color="Maroon" title="c1">PO</font> )</span><br/>



<span class="kw">assume </span><a NAME="E1:133"/>
<font color="Maroon" title="c2">g</font> <a href="oposet_1.html#R2" title="OPOSET_1:pred.2">OrthoComplement_on</a> <font color="Maroon" title="c1">PO</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">g</font> <a href="oposet_1.html#R1" title="OPOSET_1:pred.1">QuasiOrthoComplement_on</a> <font color="Maroon" title="c1">PO</font></span><br/>

<a NAME="E2:133"/><span class="kw">then </span>
( ( for <font color="Olive" title="b1">x</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">PO</font> holds <br/> (  <a href="yellow_0.html#R1" title="YELLOW_0:pred.1">ex_sup_of</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Olive" title="b1">x</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">g</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">x</font></span>)</span></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c1">PO</font> &amp;  <a href="yellow_0.html#R2" title="YELLOW_0:pred.2">ex_inf_of</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Olive" title="b1">x</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">g</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">x</font></span>)</span></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c1">PO</font> ) ) &amp; <font color="Maroon" title="c2">g</font> is  <a href="oposet_1.html#V17" title="OPOSET_1:attr.17">Orderinvolutive</a>  )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="oposet_1.html#D36" target="_self" title="OPOSET_1:def.36">Def36</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:133"/>
<font color="Maroon" title="c2">g</font> <a href="oposet_1.html#R1" title="OPOSET_1:pred.1">QuasiOrthoComplement_on</a> <font color="Maroon" title="c1">PO</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="oposet_1.html#D34" target="_self" title="OPOSET_1:def.34">Def34</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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