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<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="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> <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="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</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="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> <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="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</a> <font color="Maroon" title="c4">q</font></span>)</span></span>)</span></span><br/>





<span class="kw">set </span><font color="Maroon" title="c6">pq</font> = <font color="Maroon" title="c3">p</font> <a href="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</a> <font color="Maroon" title="c4">q</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c7">npq</font> =  <a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</a> <font color="Maroon" title="c4">q</font></span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c8">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="c9">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="c10">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="c11">xnpq</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> <span class="p2">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</a> <font color="Maroon" title="c4">q</font></span>)</span></span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c12">xpq</font> =  <a href="ltlaxio1.html#K2" title="LTLAXIO1:func.2">'X'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</a> <font color="Maroon" title="c4">q</font></span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c13">nxpq</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> <span class="p2">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</a> <font color="Maroon" title="c4">q</font></span>)</span></span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c14">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="c15">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/>
<a NAME="E1:66"/>
<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"><font color="Maroon" title="c3">p</font> <a href="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</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"><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"><font color="Maroon" title="c3">p</font> <a href="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</a> <font color="Maroon" title="c4">q</font></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="E2:66"/><span class="kw">then </span><span class="lab"><font color="Green" title="E40">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"><font color="Maroon" title="c3">p</font> <a href="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</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"><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"><font color="Maroon" title="c3">p</font> <a href="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</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#T42" onmouseover="rs('ltlaxio1/T42')" onmouseout="rh()">LTLAXIO1:42</a></span>;<br/>
<a NAME="E3:66"/>
<span class="p1">(<span class="default"><a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</a> <font color="Maroon" title="c4">q</font></span>)</span></span>)</span> <a href="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</a> <font color="Maroon" title="c3">p</font> 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#T31" target="_self" onmouseover="rs('ltlaxio2/T31')" onmouseout="rh()">Th31</a></span>;<br/>
<a NAME="E4:66"/><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"><font color="Maroon" title="c3">p</font> <a href="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</a> <font color="Maroon" title="c4">q</font></span>)</span></span>)</span> <a href="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</a> <font color="Maroon" title="c3">p</font> <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="E5:66"/><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"><font color="Maroon" title="c3">p</font> <a href="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</a> <font color="Maroon" title="c4">q</font></span>)</span></span>)</span> <a href="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</a> <font color="Maroon" title="c3">p</font>
 
<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="E6:66"/><span class="kw">then </span><span class="lab"><font color="Green" title="E41">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"><font color="Maroon" title="c3">p</font> <a href="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</a> <font color="Maroon" title="c4">q</font></span>)</span></span>)</span> <a href="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</a> <font color="Maroon" title="c3">p</font></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="E7:66"/>
<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> <span class="p4">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</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="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="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</a> <span class="p1">(<span class="default"><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> <span class="p5">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</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="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> <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> <span class="p4">(<span class="default"><a href="ltlaxio1.html#K2" title="LTLAXIO1:func.2">'X'</a> <span class="p5">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</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="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#K2" title="LTLAXIO1:func.2">'X'</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</a> <span class="p5">(<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></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#T47" target="_self" onmouseover="rs('ltlaxio2/T47')" onmouseout="rh()">Th47</a></span>;<br/>
<a NAME="E8:66"/><span class="kw">then </span>
<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> <span class="p4">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</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="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="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</a> <span class="p1">(<span class="default"><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> <span class="p5">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</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="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> <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> <span class="p4">(<span class="default"><a href="ltlaxio1.html#K2" title="LTLAXIO1:func.2">'X'</a> <span class="p5">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</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="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#K2" title="LTLAXIO1:func.2">'X'</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</a> <span class="p5">(<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></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="E9:66"/><span class="kw">then </span><span class="lab"><font color="Green" title="E42">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"><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"><font color="Maroon" title="c3">p</font> <a href="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</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="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="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</a> <span class="p1">(<span class="default"><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> <span class="p5">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</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="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> <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> <span class="p4">(<span class="default"><a href="ltlaxio1.html#K2" title="LTLAXIO1:func.2">'X'</a> <span class="p5">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</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="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#K2" title="LTLAXIO1:func.2">'X'</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</a> <span class="p5">(<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></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="E10:66"/>
<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="E11:66"/><span class="kw">then </span><span class="lab"><font color="Green" title="E43">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#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="E12:66"/>
<span class="p1">(<span class="default"><a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</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> <font color="Maroon" title="c4">q</font></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#T32" target="_self" onmouseover="rs('ltlaxio2/T32')" onmouseout="rh()">Th32</a></span>;<br/>
<a NAME="E13:66"/><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"><font color="Maroon" title="c3">p</font> <a href="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</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> <font color="Maroon" title="c4">q</font></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="E14:66"/><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"><font color="Maroon" title="c3">p</font> <a href="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</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> <font color="Maroon" title="c4">q</font></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="E15:66"/><span class="kw">then </span><span class="lab"><font color="Green" title="E44">A5</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"><font color="Maroon" title="c3">p</font> <a href="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</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="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#T44" onmouseover="rs('ltlaxio1/T44')" onmouseout="rh()">LTLAXIO1:44</a></span>;<br/>
<a NAME="E16:66"/>
<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"><font color="Maroon" title="c3">p</font> <a href="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</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"><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"><font color="Maroon" title="c3">p</font> <a href="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</a> <font color="Maroon" title="c4">q</font></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="E17:66"/><span class="kw">then </span><span class="lab"><font color="Green" title="E45">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#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"><font color="Maroon" title="c3">p</font> <a href="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</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"><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"><font color="Maroon" title="c3">p</font> <a href="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</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#T42" onmouseover="rs('ltlaxio1/T42')" onmouseout="rh()">LTLAXIO1:42</a></span>;<br/>
<a NAME="E18:66"/>
<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"><font color="Maroon" title="c3">p</font> <a href="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</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="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> <span class="p4">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</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="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="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="E19:66"/><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"><font color="Maroon" title="c3">p</font> <a href="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</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="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> <span class="p4">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</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="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#T42" onmouseover="rs('ltlaxio1/T42')" onmouseout="rh()">LTLAXIO1:42</a></span>;<br/>
<a NAME="E20:66"/><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"><font color="Maroon" title="c3">p</font> <a href="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</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"><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>
 
<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="#E15:66"><span class="lab"><font color="Green" title="E44">A5</font></span></a></span>;<br/>
<a NAME="E21:66"/><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"><font color="Maroon" title="c3">p</font> <a href="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</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"><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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:66"><span class="lab"><font color="Green" title="E40">A1</font></span></a>, <a class="txt" href="#E17:66"><span class="lab"><font color="Green" title="E45">A6</font></span></a>, <a class="ref" href="ltlaxio2.html#T54" target="_self" onmouseover="rs('ltlaxio2/T54')" onmouseout="rh()">Th54</a></span>;<br/>
<a NAME="E22:66"/><span class="kw">then </span><span class="lab"><font color="Green" title="E46">A7</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"><font color="Maroon" title="c3">p</font> <a href="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</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"><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="txt" href="#E11:66"><span class="lab"><font color="Green" title="E43">A4</font></span></a>, <a class="ref" href="ltlaxio1.html#T47" onmouseover="rs('ltlaxio1/T47')" onmouseout="rh()">LTLAXIO1:47</a></span>;<br/>
<a NAME="E23:66"/>
<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"><font color="Maroon" title="c3">p</font> <a href="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</a> <font color="Maroon" title="c4">q</font></span>)</span></span>)</span> <a href="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</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"><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"><font color="Maroon" title="c3">p</font> <a href="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</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="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="E24:66"/><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"><font color="Maroon" title="c3">p</font> <a href="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</a> <font color="Maroon" title="c4">q</font></span>)</span></span>)</span> <a href="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</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"><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"><font color="Maroon" title="c3">p</font> <a href="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</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="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="E25:66"/><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"><font color="Maroon" title="c3">p</font> <a href="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</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"><a href="ltlaxio1.html#K2" title="LTLAXIO1:func.2">'X'</a> <font color="Maroon" title="c3">p</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:66"><span class="lab"><font color="Green" title="E41">A2</font></span></a>, <a class="ref" href="ltlaxio1.html#T43" onmouseover="rs('ltlaxio1/T43')" onmouseout="rh()">LTLAXIO1:43</a></span>;<br/>
<a NAME="E26:66"/><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"><font color="Maroon" title="c3">p</font> <a href="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</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"><a href="ltlaxio1.html#K2" title="LTLAXIO1:func.2">'X'</a> <font color="Maroon" title="c3">p</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E17:66"><span class="lab"><font color="Green" title="E45">A6</font></span></a>, <a class="ref" href="ltlaxio2.html#T54" target="_self" onmouseover="rs('ltlaxio2/T54')" onmouseout="rh()">Th54</a>, <a class="txt" href="#E2:66"><span class="lab"><font color="Green" title="E40">A1</font></span></a></span>;<br/>
<a NAME="E27:66"/><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#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"><font color="Maroon" title="c3">p</font> <a href="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</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="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> <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> <span class="p4">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</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="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#K2" title="LTLAXIO1:func.2">'X'</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:66"><span class="lab"><font color="Green" title="E42">A3</font></span></a>, <a class="ref" href="ltlaxio1.html#T43" onmouseover="rs('ltlaxio1/T43')" onmouseout="rh()">LTLAXIO1:43</a></span>;<br/>
<a NAME="E28:66"/><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"><font color="Maroon" title="c3">p</font> <a href="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</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"><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#K2" title="LTLAXIO1:func.2">'X'</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</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#T43" onmouseover="rs('ltlaxio1/T43')" onmouseout="rh()">LTLAXIO1:43</a>, <a class="txt" href="#E22:66"><span class="lab"><font color="Green" title="E46">A7</font></span></a></span>;<br/>
<a NAME="E29:66"/><span class="kw">then </span><span class="lab"><font color="Green" title="E47">A8</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"><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> <a href="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</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"><font color="Maroon" title="c3">p</font> <a href="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</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#T52" onmouseover="rs('ltlaxio1/T52')" onmouseout="rh()">LTLAXIO1:52</a></span>;<br/>
<a NAME="E30:66"/>
<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="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> <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#K1" title="LTLAXIO1:func.1">'not'</a> <span class="p3">(<span class="default"><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> <a href="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</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> 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#T26" target="_self" onmouseover="rs('ltlaxio2/T26')" onmouseout="rh()">Th26</a></span>;<br/>
<a NAME="E31:66"/><span class="kw">then </span>
<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="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> <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#K1" title="LTLAXIO1:func.1">'not'</a> <span class="p3">(<span class="default"><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> <a href="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</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="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="E32:66"/><span class="kw">then </span><span class="lab"><font color="Green" title="E48">A9</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"><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="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> <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#K1" title="LTLAXIO1:func.1">'not'</a> <span class="p3">(<span class="default"><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> <a href="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</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>
 
<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="E33:66"/>
<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#K2" title="LTLAXIO1:func.2">'X'</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</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"><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="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> <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="E34:66"/><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#K2" title="LTLAXIO1:func.2">'X'</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</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"><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="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> <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="E35:66"/><span class="kw">then </span><span class="lab"><font color="Green" title="E49">A10</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"><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> <a href="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</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"><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="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> <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="E36:66"/>
<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"><font color="Maroon" title="c3">p</font> <a href="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</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#K2" title="LTLAXIO1:func.2">'X'</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</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="E37:66"/><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"><font color="Maroon" title="c3">p</font> <a href="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</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#K2" title="LTLAXIO1:func.2">'X'</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</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="E38:66"/><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"><a href="ltlaxio1.html#K2" title="LTLAXIO1:func.2">'X'</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</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#K2" title="LTLAXIO1:func.2">'X'</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</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="E39:66"/><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#K2" title="LTLAXIO1:func.2">'X'</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</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#K2" title="LTLAXIO1:func.2">'X'</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</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#T47" onmouseover="rs('ltlaxio1/T47')" onmouseout="rh()">LTLAXIO1:47</a>, <a class="txt" href="#E29:66"><span class="lab"><font color="Green" title="E47">A8</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E40:66"/>
<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="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> <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="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</a> <font color="Maroon" title="c4">q</font></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E32:66"><span class="lab"><font color="Green" title="E48">A9</font></span></a>, <a class="txt" href="#E35:66"><span class="lab"><font color="Green" title="E49">A10</font></span></a>, <a class="ref" href="ltlaxio2.html#T54" target="_self" onmouseover="rs('ltlaxio2/T54')" onmouseout="rh()">Th54</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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