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<span class="kw">let </span><font color="Maroon" title="c4">x</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ltlaxio4.html#K4" title="LTLAXIO4:func.4">comp</a> <font color="Maroon" title="c3">F</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c4">x</font> is  <a href="ltlaxio3.html#V3" title="LTLAXIO3:attr.3">complete</a> </span><br/>

<a NAME="E1:23_1_1"/>
<font color="Maroon" title="c4">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="ltlaxio4.html#K4" title="LTLAXIO4:func.4">comp</a> <font color="Maroon" title="c3">F</font>
 
;<br/>
<a NAME="E2:23_1_1"/><span class="kw">then </span>
 ex <font color="Olive" title="b1">Q</font> being   <a href="ltlaxio3.html#NM1" title="LTLAXIO3:NM.1">PNPair</a> st <br/>( <font color="Olive" title="b1">Q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">x</font> &amp;  <a href="ltlaxio3.html#K10" title="LTLAXIO3:func.10">rng</a> <font color="Olive" title="b1">Q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ltlaxio3.html#K5" title="LTLAXIO3:func.5">tau</a> <font color="Maroon" title="c3">F</font> &amp;  <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">Q</font> <a href="ltlaxio3.html#K8" title="LTLAXIO3:func.8">`1</a></span>)</span> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">Q</font> <a href="ltlaxio3.html#K9" title="LTLAXIO3:func.9">`2</a></span>)</span> )
 
;<br/>
<a NAME="E3:23_1_1"/><span class="kw">then </span>
 <a href="ltlaxio3.html#K5" title="LTLAXIO3:func.5">tau</a> <span class="p1">(<span class="default"><a href="ltlaxio3.html#K10" title="LTLAXIO3:func.10">rng</a> <font color="Maroon" title="c4">x</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ltlaxio3.html#K10" title="LTLAXIO3:func.10">rng</a> <font color="Maroon" title="c4">x</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="ltlaxio3.html#T17" onmouseover="rs('ltlaxio3/T17')" onmouseout="rh()">LTLAXIO3:17</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:23_1_1"/>
<font color="Maroon" title="c4">x</font> is  <a href="ltlaxio3.html#V3" title="LTLAXIO3:attr.3">complete</a> 
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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