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<span class="kw">consider </span><font color="Maroon" title="c4">Q</font> being   <a href="ltlaxio3.html#NV3" title="LTLAXIO3:NV.3">consistent</a>  <a href="ltlaxio3.html#NM1" title="LTLAXIO3:NM.1">PNPair</a><span class="kw"> such that </span><br/><a NAME="E2:27_1_1"/><span class="lab"><font color="Green" title="E15">A1</font></span>: 
(  <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">P</font> <a href="ltlaxio3.html#K8" title="LTLAXIO3:func.8">`1</a></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">Q</font> <a href="ltlaxio3.html#K8" title="LTLAXIO3:func.8">`1</a></span>)</span> &amp;  <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">P</font> <a href="ltlaxio3.html#K9" title="LTLAXIO3:func.9">`2</a></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">Q</font> <a href="ltlaxio3.html#K9" title="LTLAXIO3:func.9">`2</a></span>)</span> &amp;  <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="c3">P</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">Q</font> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="ltlaxio3.html#T34" onmouseover="rs('ltlaxio3/T34')" onmouseout="rh()">LTLAXIO3:34</a></span>;<br/>
<a NAME="E3:27_1_1"/>
<font color="Maroon" title="c4">Q</font> <a href="ltlaxio4.html#R1" title="LTLAXIO4:pred.1">is_completion_of</a> <font color="Maroon" title="c3">P</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:27_1_1"><span class="lab"><font color="Green" title="E15">A1</font></span></a></span>;<br/>
<a NAME="E4:27_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c4">Q</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <span class="p1"> { <span class="default"> <font color="Olive" title="b1">R</font> where <font color="Olive" title="b1">R</font> is   <a href="ltlaxio3.html#NV3" title="LTLAXIO3:NV.3">consistent</a>  <a href="ltlaxio3.html#NM1" title="LTLAXIO3:NM.1">PNPair</a> : <font color="Olive" title="b1">R</font> <a href="ltlaxio4.html#R1" title="LTLAXIO4:pred.1">is_completion_of</a> <font color="Maroon" title="c3">P</font> </span> } </span> 
 
;<br/>
<span class="kw">hence </span><a NAME="E5:27_1_1"/>
 not  <a href="ltlaxio4.html#K5" title="LTLAXIO4:func.5">comp</a> <font color="Maroon" title="c3">P</font> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</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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