<?xml version="1.0"?>
<div class="add">

<span class="kw">let </span><font color="Maroon" title="c3">p</font>, <font color="Maroon" title="c4">q</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ltlaxio1.html#NK1" title="LTLAXIO1:NK.1">LTLB_WFF</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">  for <font color="Olive" title="b1">X</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <a href="ltlaxio1.html#NK1" title="LTLAXIO1:NK.1">LTLB_WFF</a> holds  <font color="Olive" title="b1">X</font> <a href="ltlaxio1.html#R8" title="LTLAXIO1:pred.8">|-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ltlaxio1.html#K2" title="LTLAXIO1:func.2">'X'</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="ltlaxio1.html#K5" title="LTLAXIO1:func.5">'or'</a> <span class="p2">(<span class="default"><a href="ltlaxio1.html#K2" title="LTLAXIO1:func.2">'X'</a> <font color="Maroon" title="c4">q</font></span>)</span></span>)</span> <a href="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</a> <span class="p1">(<span class="default"><a href="ltlaxio1.html#K2" title="LTLAXIO1:func.2">'X'</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="ltlaxio1.html#K5" title="LTLAXIO1:func.5">'or'</a> <font color="Maroon" title="c4">q</font></span>)</span></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c5">X</font> be   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <a href="ltlaxio1.html#NK1" title="LTLAXIO1:NK.1">LTLB_WFF</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"> <font color="Maroon" title="c5">X</font> <a href="ltlaxio1.html#R8" title="LTLAXIO1:pred.8">|-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ltlaxio1.html#K2" title="LTLAXIO1:func.2">'X'</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="ltlaxio1.html#K5" title="LTLAXIO1:func.5">'or'</a> <span class="p2">(<span class="default"><a href="ltlaxio1.html#K2" title="LTLAXIO1:func.2">'X'</a> <font color="Maroon" title="c4">q</font></span>)</span></span>)</span> <a href="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</a> <span class="p1">(<span class="default"><a href="ltlaxio1.html#K2" title="LTLAXIO1:func.2">'X'</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="ltlaxio1.html#K5" title="LTLAXIO1:func.5">'or'</a> <font color="Maroon" title="c4">q</font></span>)</span></span>)</span></span><br/>





<span class="kw">set </span><font color="Maroon" title="c6">xp</font> =  <a href="ltlaxio1.html#K2" title="LTLAXIO1:func.2">'X'</a> <font color="Maroon" title="c3">p</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c7">xq</font> =  <a href="ltlaxio1.html#K2" title="LTLAXIO1:func.2">'X'</a> <font color="Maroon" title="c4">q</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c8">np</font> =  <a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <font color="Maroon" title="c3">p</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c9">nq</font> =  <a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <font color="Maroon" title="c4">q</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c10">xnp</font> =  <a href="ltlaxio1.html#K2" title="LTLAXIO1:func.2">'X'</a> <span class="p1">(<span class="default"><a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <font color="Maroon" title="c3">p</font></span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c11">xnq</font> =  <a href="ltlaxio1.html#K2" title="LTLAXIO1:func.2">'X'</a> <span class="p1">(<span class="default"><a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <font color="Maroon" title="c4">q</font></span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c12">nxp</font> =  <a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <span class="p1">(<span class="default"><a href="ltlaxio1.html#K2" title="LTLAXIO1:func.2">'X'</a> <font color="Maroon" title="c3">p</font></span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c13">nxq</font> =  <a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <span class="p1">(<span class="default"><a href="ltlaxio1.html#K2" title="LTLAXIO1:func.2">'X'</a> <font color="Maroon" title="c4">q</font></span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c14">npq</font> = <span class="p1">(<span class="default"><a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="ltlaxio1.html#K4" title="LTLAXIO1:func.4">'&amp;&amp;'</a> <span class="p1">(<span class="default"><a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <font color="Maroon" title="c4">q</font></span>)</span>;<br/>
<a NAME="E1:69"/>
<span class="p1">(<span class="default"><a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <span class="p2">(<span class="default"><a href="ltlaxio1.html#K2" title="LTLAXIO1:func.2">'X'</a> <span class="p3">(<span class="default"><a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="ltlaxio1.html#K4" title="LTLAXIO1:func.4">'&amp;&amp;'</a> <span class="p5">(<span class="default"><a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <font color="Maroon" title="c4">q</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</a> <span class="p1">(<span class="default"><a href="ltlaxio1.html#K2" title="LTLAXIO1:func.2">'X'</a> <span class="p2">(<span class="default"><a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <span class="p3">(<span class="default"><a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="ltlaxio1.html#K4" title="LTLAXIO1:func.4">'&amp;&amp;'</a> <span class="p5">(<span class="default"><a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <font color="Maroon" title="c4">q</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="ltlaxio1.html#K13" title="LTLAXIO1:func.13">LTL_axioms</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="ltlaxio1.html#D17" onmouseover="rs('ltlaxio1/D17')" onmouseout="rh()">LTLAXIO1:def 17</a></span>;<br/>
<a NAME="E2:69"/><span class="kw">then </span><span class="lab"><font color="Green" title="E41">A1</font></span>: 
<font color="Maroon" title="c5">X</font> <a href="ltlaxio1.html#R8" title="LTLAXIO1:pred.8">|-</a> <span class="p1">(<span class="default"><a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <span class="p2">(<span class="default"><a href="ltlaxio1.html#K2" title="LTLAXIO1:func.2">'X'</a> <span class="p3">(<span class="default"><a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="ltlaxio1.html#K4" title="LTLAXIO1:func.4">'&amp;&amp;'</a> <span class="p5">(<span class="default"><a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <font color="Maroon" title="c4">q</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</a> <span class="p1">(<span class="default"><a href="ltlaxio1.html#K2" title="LTLAXIO1:func.2">'X'</a> <span class="p2">(<span class="default"><a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <span class="p3">(<span class="default"><a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="ltlaxio1.html#K4" title="LTLAXIO1:func.4">'&amp;&amp;'</a> <span class="p5">(<span class="default"><a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <font color="Maroon" title="c4">q</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="ltlaxio1.html#T42" onmouseover="rs('ltlaxio1/T42')" onmouseout="rh()">LTLAXIO1:42</a></span>;<br/>
<a NAME="E3:69"/>
<span class="p1">(<span class="default"><a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <span class="p2">(<span class="default"><a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="ltlaxio1.html#K4" title="LTLAXIO1:func.4">'&amp;&amp;'</a> <span class="p4">(<span class="default"><a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <font color="Maroon" title="c4">q</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="ltlaxio1.html#K4" title="LTLAXIO1:func.4">'&amp;&amp;'</a> <span class="p2">(<span class="default"><a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <font color="Maroon" title="c4">q</font></span>)</span></span>)</span> is  <a href="ltlaxio2.html#NV1" title="LTLAXIO2:NV.1">ctaut</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="ltlaxio2.html#T25" target="_self" onmouseover="rs('ltlaxio2/T25')" onmouseout="rh()">Th25</a></span>;<br/>
<a NAME="E4:69"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <span class="p2">(<span class="default"><a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="ltlaxio1.html#K4" title="LTLAXIO1:func.4">'&amp;&amp;'</a> <span class="p4">(<span class="default"><a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <font color="Maroon" title="c4">q</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="ltlaxio1.html#K4" title="LTLAXIO1:func.4">'&amp;&amp;'</a> <span class="p2">(<span class="default"><a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <font color="Maroon" title="c4">q</font></span>)</span></span>)</span> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="ltlaxio1.html#K13" title="LTLAXIO1:func.13">LTL_axioms</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="ltlaxio1.html#D17" onmouseover="rs('ltlaxio1/D17')" onmouseout="rh()">LTLAXIO1:def 17</a></span>;<br/>
<a NAME="E5:69"/><span class="kw">then </span>
<font color="Maroon" title="c5">X</font> <a href="ltlaxio1.html#R8" title="LTLAXIO1:pred.8">|-</a> <span class="p1">(<span class="default"><a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <span class="p2">(<span class="default"><a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="ltlaxio1.html#K4" title="LTLAXIO1:func.4">'&amp;&amp;'</a> <span class="p4">(<span class="default"><a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <font color="Maroon" title="c4">q</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="ltlaxio1.html#K4" title="LTLAXIO1:func.4">'&amp;&amp;'</a> <span class="p2">(<span class="default"><a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <font color="Maroon" title="c4">q</font></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="ltlaxio1.html#T42" onmouseover="rs('ltlaxio1/T42')" onmouseout="rh()">LTLAXIO1:42</a></span>;<br/>
<a NAME="E6:69"/><span class="kw">then </span><span class="lab"><font color="Green" title="E42">A2</font></span>: 
<font color="Maroon" title="c5">X</font> <a href="ltlaxio1.html#R8" title="LTLAXIO1:pred.8">|-</a>  <a href="ltlaxio1.html#K2" title="LTLAXIO1:func.2">'X'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <span class="p3">(<span class="default"><a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="ltlaxio1.html#K4" title="LTLAXIO1:func.4">'&amp;&amp;'</a> <span class="p5">(<span class="default"><a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <font color="Maroon" title="c4">q</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="ltlaxio1.html#K4" title="LTLAXIO1:func.4">'&amp;&amp;'</a> <span class="p3">(<span class="default"><a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <font color="Maroon" title="c4">q</font></span>)</span></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="ltlaxio1.html#T44" onmouseover="rs('ltlaxio1/T44')" onmouseout="rh()">LTLAXIO1:44</a></span>;<br/>
<a NAME="E7:69"/>
<span class="p1">(<span class="default"><a href="ltlaxio1.html#K2" title="LTLAXIO1:func.2">'X'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <span class="p4">(<span class="default"><a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="ltlaxio1.html#K4" title="LTLAXIO1:func.4">'&amp;&amp;'</a> <span class="p0">(<span class="default"><a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <font color="Maroon" title="c4">q</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="ltlaxio1.html#K4" title="LTLAXIO1:func.4">'&amp;&amp;'</a> <span class="p4">(<span class="default"><a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <font color="Maroon" title="c4">q</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ltlaxio1.html#K2" title="LTLAXIO1:func.2">'X'</a> <span class="p3">(<span class="default"><a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <span class="p4">(<span class="default"><a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="ltlaxio1.html#K4" title="LTLAXIO1:func.4">'&amp;&amp;'</a> <span class="p0">(<span class="default"><a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <font color="Maroon" title="c4">q</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</a> <span class="p2">(<span class="default"><a href="ltlaxio1.html#K2" title="LTLAXIO1:func.2">'X'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="ltlaxio1.html#K4" title="LTLAXIO1:func.4">'&amp;&amp;'</a> <span class="p4">(<span class="default"><a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <font color="Maroon" title="c4">q</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="ltlaxio1.html#K13" title="LTLAXIO1:func.13">LTL_axioms</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="ltlaxio1.html#D17" onmouseover="rs('ltlaxio1/D17')" onmouseout="rh()">LTLAXIO1:def 17</a></span>;<br/>
<a NAME="E8:69"/><span class="kw">then </span>
<font color="Maroon" title="c5">X</font> <a href="ltlaxio1.html#R8" title="LTLAXIO1:pred.8">|-</a> <span class="p1">(<span class="default"><a href="ltlaxio1.html#K2" title="LTLAXIO1:func.2">'X'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <span class="p4">(<span class="default"><a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="ltlaxio1.html#K4" title="LTLAXIO1:func.4">'&amp;&amp;'</a> <span class="p0">(<span class="default"><a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <font color="Maroon" title="c4">q</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="ltlaxio1.html#K4" title="LTLAXIO1:func.4">'&amp;&amp;'</a> <span class="p4">(<span class="default"><a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <font color="Maroon" title="c4">q</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ltlaxio1.html#K2" title="LTLAXIO1:func.2">'X'</a> <span class="p3">(<span class="default"><a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <span class="p4">(<span class="default"><a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="ltlaxio1.html#K4" title="LTLAXIO1:func.4">'&amp;&amp;'</a> <span class="p0">(<span class="default"><a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <font color="Maroon" title="c4">q</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</a> <span class="p2">(<span class="default"><a href="ltlaxio1.html#K2" title="LTLAXIO1:func.2">'X'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="ltlaxio1.html#K4" title="LTLAXIO1:func.4">'&amp;&amp;'</a> <span class="p4">(<span class="default"><a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <font color="Maroon" title="c4">q</font></span>)</span></span>)</span></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="ltlaxio1.html#T42" onmouseover="rs('ltlaxio1/T42')" onmouseout="rh()">LTLAXIO1:42</a></span>;<br/>
<a NAME="E9:69"/><span class="kw">then </span>
<font color="Maroon" title="c5">X</font> <a href="ltlaxio1.html#R8" title="LTLAXIO1:pred.8">|-</a> <span class="p1">(<span class="default"><a href="ltlaxio1.html#K2" title="LTLAXIO1:func.2">'X'</a> <span class="p2">(<span class="default"><a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <span class="p3">(<span class="default"><a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="ltlaxio1.html#K4" title="LTLAXIO1:func.4">'&amp;&amp;'</a> <span class="p5">(<span class="default"><a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <font color="Maroon" title="c4">q</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</a> <span class="p1">(<span class="default"><a href="ltlaxio1.html#K2" title="LTLAXIO1:func.2">'X'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="ltlaxio1.html#K4" title="LTLAXIO1:func.4">'&amp;&amp;'</a> <span class="p3">(<span class="default"><a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <font color="Maroon" title="c4">q</font></span>)</span></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="ltlaxio1.html#T43" onmouseover="rs('ltlaxio1/T43')" onmouseout="rh()">LTLAXIO1:43</a>, <a class="txt" href="#E6:69"><span class="lab"><font color="Green" title="E42">A2</font></span></a></span>;<br/>
<a NAME="E10:69"/><span class="kw">then </span><span class="lab"><font color="Green" title="E43">A3</font></span>: 
<font color="Maroon" title="c5">X</font> <a href="ltlaxio1.html#R8" title="LTLAXIO1:pred.8">|-</a> <span class="p1">(<span class="default"><a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <span class="p2">(<span class="default"><a href="ltlaxio1.html#K2" title="LTLAXIO1:func.2">'X'</a> <span class="p3">(<span class="default"><a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="ltlaxio1.html#K4" title="LTLAXIO1:func.4">'&amp;&amp;'</a> <span class="p5">(<span class="default"><a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <font color="Maroon" title="c4">q</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</a> <span class="p1">(<span class="default"><a href="ltlaxio1.html#K2" title="LTLAXIO1:func.2">'X'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="ltlaxio1.html#K4" title="LTLAXIO1:func.4">'&amp;&amp;'</a> <span class="p3">(<span class="default"><a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <font color="Maroon" title="c4">q</font></span>)</span></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="ltlaxio1.html#T47" onmouseover="rs('ltlaxio1/T47')" onmouseout="rh()">LTLAXIO1:47</a>, <a class="txt" href="#E2:69"><span class="lab"><font color="Green" title="E41">A1</font></span></a></span>;<br/>
<a NAME="E11:69"/>
<font color="Maroon" title="c5">X</font> <a href="ltlaxio1.html#R8" title="LTLAXIO1:pred.8">|-</a> <span class="p1">(<span class="default"><a href="ltlaxio1.html#K2" title="LTLAXIO1:func.2">'X'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="ltlaxio1.html#K4" title="LTLAXIO1:func.4">'&amp;&amp;'</a> <span class="p3">(<span class="default"><a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <font color="Maroon" title="c4">q</font></span>)</span></span>)</span></span>)</span> <a href="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ltlaxio1.html#K2" title="LTLAXIO1:func.2">'X'</a> <span class="p3">(<span class="default"><a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <font color="Maroon" title="c3">p</font></span>)</span></span>)</span> <a href="ltlaxio1.html#K4" title="LTLAXIO1:func.4">'&amp;&amp;'</a> <span class="p2">(<span class="default"><a href="ltlaxio1.html#K2" title="LTLAXIO1:func.2">'X'</a> <span class="p3">(<span class="default"><a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <font color="Maroon" title="c4">q</font></span>)</span></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="ltlaxio2.html#T59" target="_self" onmouseover="rs('ltlaxio2/T59')" onmouseout="rh()">Th59</a></span>;<br/>
<a NAME="E12:69"/><span class="kw">then </span><span class="lab"><font color="Green" title="E44">A4</font></span>: 
<font color="Maroon" title="c5">X</font> <a href="ltlaxio1.html#R8" title="LTLAXIO1:pred.8">|-</a> <span class="p1">(<span class="default"><a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <span class="p2">(<span class="default"><a href="ltlaxio1.html#K2" title="LTLAXIO1:func.2">'X'</a> <span class="p3">(<span class="default"><a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="ltlaxio1.html#K4" title="LTLAXIO1:func.4">'&amp;&amp;'</a> <span class="p5">(<span class="default"><a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <font color="Maroon" title="c4">q</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ltlaxio1.html#K2" title="LTLAXIO1:func.2">'X'</a> <span class="p3">(<span class="default"><a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <font color="Maroon" title="c3">p</font></span>)</span></span>)</span> <a href="ltlaxio1.html#K4" title="LTLAXIO1:func.4">'&amp;&amp;'</a> <span class="p2">(<span class="default"><a href="ltlaxio1.html#K2" title="LTLAXIO1:func.2">'X'</a> <span class="p3">(<span class="default"><a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <font color="Maroon" title="c4">q</font></span>)</span></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="ltlaxio1.html#T47" onmouseover="rs('ltlaxio1/T47')" onmouseout="rh()">LTLAXIO1:47</a>, <a class="txt" href="#E10:69"><span class="lab"><font color="Green" title="E43">A3</font></span></a></span>;<br/>
<a NAME="E13:69"/>
<span class="p1">(<span class="default"><a href="ltlaxio1.html#K2" title="LTLAXIO1:func.2">'X'</a> <span class="p2">(<span class="default"><a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <font color="Maroon" title="c4">q</font></span>)</span></span>)</span> <a href="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</a> <span class="p1">(<span class="default"><a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <span class="p2">(<span class="default"><a href="ltlaxio1.html#K2" title="LTLAXIO1:func.2">'X'</a> <font color="Maroon" title="c4">q</font></span>)</span></span>)</span> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="ltlaxio1.html#K13" title="LTLAXIO1:func.13">LTL_axioms</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="ltlaxio1.html#D17" onmouseover="rs('ltlaxio1/D17')" onmouseout="rh()">LTLAXIO1:def 17</a></span>;<br/>
<a NAME="E14:69"/><span class="kw">then </span><span class="lab"><font color="Green" title="E45">A5</font></span>: 
<font color="Maroon" title="c5">X</font> <a href="ltlaxio1.html#R8" title="LTLAXIO1:pred.8">|-</a> <span class="p1">(<span class="default"><a href="ltlaxio1.html#K2" title="LTLAXIO1:func.2">'X'</a> <span class="p2">(<span class="default"><a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <font color="Maroon" title="c4">q</font></span>)</span></span>)</span> <a href="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</a> <span class="p1">(<span class="default"><a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <span class="p2">(<span class="default"><a href="ltlaxio1.html#K2" title="LTLAXIO1:func.2">'X'</a> <font color="Maroon" title="c4">q</font></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="ltlaxio1.html#T42" onmouseover="rs('ltlaxio1/T42')" onmouseout="rh()">LTLAXIO1:42</a></span>;<br/>
<a NAME="E15:69"/>
<span class="p1">(<span class="default"><a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <span class="p2">(<span class="default"><a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <span class="p3">(<span class="default"><a href="ltlaxio1.html#K2" title="LTLAXIO1:func.2">'X'</a> <span class="p4">(<span class="default"><a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="ltlaxio1.html#K4" title="LTLAXIO1:func.4">'&amp;&amp;'</a> <span class="p0">(<span class="default"><a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <font color="Maroon" title="c4">q</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</a> <span class="p1">(<span class="default"><a href="ltlaxio1.html#K2" title="LTLAXIO1:func.2">'X'</a> <span class="p2">(<span class="default"><a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="ltlaxio1.html#K4" title="LTLAXIO1:func.4">'&amp;&amp;'</a> <span class="p4">(<span class="default"><a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <font color="Maroon" title="c4">q</font></span>)</span></span>)</span></span>)</span></span>)</span> is  <a href="ltlaxio2.html#NV1" title="LTLAXIO2:NV.1">ctaut</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="ltlaxio2.html#T25" target="_self" onmouseover="rs('ltlaxio2/T25')" onmouseout="rh()">Th25</a></span>;<br/>
<a NAME="E16:69"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <span class="p2">(<span class="default"><a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <span class="p3">(<span class="default"><a href="ltlaxio1.html#K2" title="LTLAXIO1:func.2">'X'</a> <span class="p4">(<span class="default"><a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="ltlaxio1.html#K4" title="LTLAXIO1:func.4">'&amp;&amp;'</a> <span class="p0">(<span class="default"><a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <font color="Maroon" title="c4">q</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</a> <span class="p1">(<span class="default"><a href="ltlaxio1.html#K2" title="LTLAXIO1:func.2">'X'</a> <span class="p2">(<span class="default"><a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="ltlaxio1.html#K4" title="LTLAXIO1:func.4">'&amp;&amp;'</a> <span class="p4">(<span class="default"><a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <font color="Maroon" title="c4">q</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="ltlaxio1.html#K13" title="LTLAXIO1:func.13">LTL_axioms</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="ltlaxio1.html#D17" onmouseover="rs('ltlaxio1/D17')" onmouseout="rh()">LTLAXIO1:def 17</a></span>;<br/>
<a NAME="E17:69"/><span class="kw">then </span><span class="lab"><font color="Green" title="E46">A6</font></span>: 
<font color="Maroon" title="c5">X</font> <a href="ltlaxio1.html#R8" title="LTLAXIO1:pred.8">|-</a> <span class="p1">(<span class="default"><a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <span class="p2">(<span class="default"><a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <span class="p3">(<span class="default"><a href="ltlaxio1.html#K2" title="LTLAXIO1:func.2">'X'</a> <span class="p4">(<span class="default"><a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="ltlaxio1.html#K4" title="LTLAXIO1:func.4">'&amp;&amp;'</a> <span class="p0">(<span class="default"><a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <font color="Maroon" title="c4">q</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</a> <span class="p1">(<span class="default"><a href="ltlaxio1.html#K2" title="LTLAXIO1:func.2">'X'</a> <span class="p2">(<span class="default"><a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="ltlaxio1.html#K4" title="LTLAXIO1:func.4">'&amp;&amp;'</a> <span class="p4">(<span class="default"><a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <font color="Maroon" title="c4">q</font></span>)</span></span>)</span></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="ltlaxio1.html#T42" onmouseover="rs('ltlaxio1/T42')" onmouseout="rh()">LTLAXIO1:42</a></span>;<br/>
<a NAME="E18:69"/>
<span class="p1">(<span class="default"><a href="ltlaxio1.html#K2" title="LTLAXIO1:func.2">'X'</a> <span class="p2">(<span class="default"><a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <font color="Maroon" title="c3">p</font></span>)</span></span>)</span> <a href="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</a> <span class="p1">(<span class="default"><a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <span class="p2">(<span class="default"><a href="ltlaxio1.html#K2" title="LTLAXIO1:func.2">'X'</a> <font color="Maroon" title="c3">p</font></span>)</span></span>)</span> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="ltlaxio1.html#K13" title="LTLAXIO1:func.13">LTL_axioms</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="ltlaxio1.html#D17" onmouseover="rs('ltlaxio1/D17')" onmouseout="rh()">LTLAXIO1:def 17</a></span>;<br/>
<a NAME="E19:69"/><span class="kw">then </span>
<font color="Maroon" title="c5">X</font> <a href="ltlaxio1.html#R8" title="LTLAXIO1:pred.8">|-</a> <span class="p1">(<span class="default"><a href="ltlaxio1.html#K2" title="LTLAXIO1:func.2">'X'</a> <span class="p2">(<span class="default"><a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <font color="Maroon" title="c3">p</font></span>)</span></span>)</span> <a href="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</a> <span class="p1">(<span class="default"><a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <span class="p2">(<span class="default"><a href="ltlaxio1.html#K2" title="LTLAXIO1:func.2">'X'</a> <font color="Maroon" title="c3">p</font></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="ltlaxio1.html#T42" onmouseover="rs('ltlaxio1/T42')" onmouseout="rh()">LTLAXIO1:42</a></span>;<br/>
<a NAME="E20:69"/><span class="kw">then </span>
<font color="Maroon" title="c5">X</font> <a href="ltlaxio1.html#R8" title="LTLAXIO1:pred.8">|-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ltlaxio1.html#K2" title="LTLAXIO1:func.2">'X'</a> <span class="p3">(<span class="default"><a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <font color="Maroon" title="c3">p</font></span>)</span></span>)</span> <a href="ltlaxio1.html#K4" title="LTLAXIO1:func.4">'&amp;&amp;'</a> <span class="p2">(<span class="default"><a href="ltlaxio1.html#K2" title="LTLAXIO1:func.2">'X'</a> <span class="p3">(<span class="default"><a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <font color="Maroon" title="c4">q</font></span>)</span></span>)</span></span>)</span> <a href="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <span class="p3">(<span class="default"><a href="ltlaxio1.html#K2" title="LTLAXIO1:func.2">'X'</a> <font color="Maroon" title="c3">p</font></span>)</span></span>)</span> <a href="ltlaxio1.html#K4" title="LTLAXIO1:func.4">'&amp;&amp;'</a> <span class="p2">(<span class="default"><a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <span class="p3">(<span class="default"><a href="ltlaxio1.html#K2" title="LTLAXIO1:func.2">'X'</a> <font color="Maroon" title="c4">q</font></span>)</span></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:69"><span class="lab"><font color="Green" title="E45">A5</font></span></a>, <a class="ref" href="ltlaxio2.html#T53" target="_self" onmouseover="rs('ltlaxio2/T53')" onmouseout="rh()">Th53</a></span>;<br/>
<a NAME="E21:69"/><span class="kw">then </span>
<font color="Maroon" title="c5">X</font> <a href="ltlaxio1.html#R8" title="LTLAXIO1:pred.8">|-</a> <span class="p1">(<span class="default"><a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <span class="p2">(<span class="default"><a href="ltlaxio1.html#K2" title="LTLAXIO1:func.2">'X'</a> <span class="p3">(<span class="default"><a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="ltlaxio1.html#K4" title="LTLAXIO1:func.4">'&amp;&amp;'</a> <span class="p5">(<span class="default"><a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <font color="Maroon" title="c4">q</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <span class="p3">(<span class="default"><a href="ltlaxio1.html#K2" title="LTLAXIO1:func.2">'X'</a> <font color="Maroon" title="c3">p</font></span>)</span></span>)</span> <a href="ltlaxio1.html#K4" title="LTLAXIO1:func.4">'&amp;&amp;'</a> <span class="p2">(<span class="default"><a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <span class="p3">(<span class="default"><a href="ltlaxio1.html#K2" title="LTLAXIO1:func.2">'X'</a> <font color="Maroon" title="c4">q</font></span>)</span></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="ltlaxio1.html#T47" onmouseover="rs('ltlaxio1/T47')" onmouseout="rh()">LTLAXIO1:47</a>, <a class="txt" href="#E12:69"><span class="lab"><font color="Green" title="E44">A4</font></span></a></span>;<br/>
<a NAME="E22:69"/><span class="kw">then </span>
<font color="Maroon" title="c5">X</font> <a href="ltlaxio1.html#R8" title="LTLAXIO1:pred.8">|-</a> <span class="p1">(<span class="default"><a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <span class="p4">(<span class="default"><a href="ltlaxio1.html#K2" title="LTLAXIO1:func.2">'X'</a> <font color="Maroon" title="c3">p</font></span>)</span></span>)</span> <a href="ltlaxio1.html#K4" title="LTLAXIO1:func.4">'&amp;&amp;'</a> <span class="p3">(<span class="default"><a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <span class="p4">(<span class="default"><a href="ltlaxio1.html#K2" title="LTLAXIO1:func.2">'X'</a> <font color="Maroon" title="c4">q</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</a> <span class="p1">(<span class="default"><a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <span class="p2">(<span class="default"><a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <span class="p3">(<span class="default"><a href="ltlaxio1.html#K2" title="LTLAXIO1:func.2">'X'</a> <span class="p4">(<span class="default"><a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="ltlaxio1.html#K4" title="LTLAXIO1:func.4">'&amp;&amp;'</a> <span class="p0">(<span class="default"><a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <font color="Maroon" title="c4">q</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="ltlaxio1.html#T52" onmouseover="rs('ltlaxio1/T52')" onmouseout="rh()">LTLAXIO1:52</a></span>;<br/>
<span class="kw">hence </span><a NAME="E23:69"/>
<font color="Maroon" title="c5">X</font> <a href="ltlaxio1.html#R8" title="LTLAXIO1:pred.8">|-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ltlaxio1.html#K2" title="LTLAXIO1:func.2">'X'</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="ltlaxio1.html#K5" title="LTLAXIO1:func.5">'or'</a> <span class="p2">(<span class="default"><a href="ltlaxio1.html#K2" title="LTLAXIO1:func.2">'X'</a> <font color="Maroon" title="c4">q</font></span>)</span></span>)</span> <a href="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</a> <span class="p1">(<span class="default"><a href="ltlaxio1.html#K2" title="LTLAXIO1:func.2">'X'</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="ltlaxio1.html#K5" title="LTLAXIO1:func.5">'or'</a> <font color="Maroon" title="c4">q</font></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E17:69"><span class="lab"><font color="Green" title="E46">A6</font></span></a>, <a class="ref" href="ltlaxio1.html#T47" onmouseover="rs('ltlaxio1/T47')" onmouseout="rh()">LTLAXIO1:47</a></span>; <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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