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

<span class="kw">let </span><font color="Maroon" title="c3">P</font> be   <a href="ltlaxio3.html#NM1" title="LTLAXIO3:NM.1">PNPair</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">Q</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ltlaxio4.html#K8" title="LTLAXIO4:func.8">untn</a> <font color="Maroon" title="c3">P</font> holds   <a href="subset_1.html#K1" title="SUBSET_1:func.1">{}</a> <a href="ltlaxio1.html#NK1" title="LTLAXIO1:NK.1">LTLB_WFF</a> <a href="ltlaxio1.html#R8" title="LTLAXIO1:pred.8">|-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">P</font> <a href="ltlaxio3.html#K12" title="LTLAXIO3:func.12">^</a></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="Olive" title="b1">Q</font> <a href="ltlaxio3.html#K12" title="LTLAXIO3:func.12">^</a></span>)</span></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c4">Q</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ltlaxio4.html#K8" title="LTLAXIO4:func.8">untn</a> <font color="Maroon" title="c3">P</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="subset_1.html#K1" title="SUBSET_1:func.1">{}</a> <a href="ltlaxio1.html#NK1" title="LTLAXIO1:NK.1">LTLB_WFF</a> <a href="ltlaxio1.html#R8" title="LTLAXIO1:pred.8">|-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">P</font> <a href="ltlaxio3.html#K12" title="LTLAXIO3:func.12">^</a></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="c4">Q</font> <a href="ltlaxio3.html#K12" title="LTLAXIO3:func.12">^</a></span>)</span></span>)</span></span><br/>



<span class="kw">set </span><font color="Maroon" title="c5">p</font> =  <a href="ltlaxio1.html#K2" title="LTLAXIO1:func.2">'X'</a> <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon" title="c4">Q</font> <a href="ltlaxio3.html#K8" title="LTLAXIO3:func.8">`1</a> );<br/>
<span class="kw">set </span><font color="Maroon" title="c6">q</font> =  <a href="ltlaxio1.html#K2" title="LTLAXIO1:func.2">'X'</a> <font color="Maroon">H<sub>2</sub></font>( <a href="ltlaxio2.html#K4" title="LTLAXIO2:func.4">nega</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">Q</font> <a href="ltlaxio3.html#K9" title="LTLAXIO3:func.9">`2</a></span>)</span>);<br/>
<a NAME="E1:38"/>
<font color="Maroon" title="c4">Q</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="ltlaxio4.html#K8" title="LTLAXIO4:func.8">untn</a> <font color="Maroon" title="c3">P</font>
 
;<br/>
<a NAME="E2:38"/><span class="kw">then </span><span class="lab"><font color="Green" title="E20">A1</font></span>: 
 ex <font color="Olive" title="b1">Q1</font> being   <a href="ltlaxio3.html#NM1" title="LTLAXIO3:NM.1">PNPair</a> st <br/>( <font color="Maroon" title="c4">Q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">Q1</font> &amp;  <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">Q1</font> <a href="ltlaxio3.html#K8" title="LTLAXIO3:func.8">`1</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ltlaxio4.html#K7" title="LTLAXIO4:func.7">untn</a> <span class="p1">(<span class="default"><a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">P</font> <a href="ltlaxio3.html#K8" title="LTLAXIO3:func.8">`1</a></span>)</span></span>)</span> &amp;  <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">Q1</font> <a href="ltlaxio3.html#K9" title="LTLAXIO3:func.9">`2</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ltlaxio4.html#K7" title="LTLAXIO4:func.7">untn</a> <span class="p1">(<span class="default"><a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">P</font> <a href="ltlaxio3.html#K9" title="LTLAXIO3:func.9">`2</a></span>)</span></span>)</span> )
 
;<br/>
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="38_1"><span class="kw">now </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">  for <font color="Olive" title="b1">i</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st <font color="Olive" title="b1">i</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="ltlaxio2.html#K5" title="LTLAXIO2:func.5">nex</a> <span class="p2">(<span class="default"><a href="ltlaxio2.html#K4" title="LTLAXIO2:func.4">nega</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">Q</font> <a href="ltlaxio3.html#K9" title="LTLAXIO3:func.9">`2</a></span>)</span></span>)</span></span>)</span> holds <br/> <a href="subset_1.html#K1" title="SUBSET_1:func.1">{}</a> <a href="ltlaxio1.html#NK1" title="LTLAXIO1:NK.1">LTLB_WFF</a> <a href="ltlaxio1.html#R8" title="LTLAXIO1:pred.8">|-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">P</font> <a href="ltlaxio3.html#K12" title="LTLAXIO3:func.12">^</a></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="ltlaxio2.html#K5" title="LTLAXIO2:func.5">nex</a> <span class="p3">(<span class="default"><a href="ltlaxio2.html#K4" title="LTLAXIO2:func.4">nega</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">Q</font> <a href="ltlaxio3.html#K9" title="LTLAXIO3:func.9">`2</a></span>)</span></span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Olive" title="b1">i</font></span>)</span></span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c7">i</font> be   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</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="c7">i</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="ltlaxio2.html#K5" title="LTLAXIO2:func.5">nex</a> <span class="p2">(<span class="default"><a href="ltlaxio2.html#K4" title="LTLAXIO2:func.4">nega</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">Q</font> <a href="ltlaxio3.html#K9" title="LTLAXIO3:func.9">`2</a></span>)</span></span>)</span></span>)</span> implies  <a href="subset_1.html#K1" title="SUBSET_1:func.1">{}</a> <a href="ltlaxio1.html#NK1" title="LTLAXIO1:NK.1">LTLB_WFF</a> <a href="ltlaxio1.html#R8" title="LTLAXIO1:pred.8">|-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">P</font> <a href="ltlaxio3.html#K12" title="LTLAXIO3:func.12">^</a></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="ltlaxio2.html#K5" title="LTLAXIO2:func.5">nex</a> <span class="p3">(<span class="default"><a href="ltlaxio2.html#K4" title="LTLAXIO2:func.4">nega</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">Q</font> <a href="ltlaxio3.html#K9" title="LTLAXIO3:func.9">`2</a></span>)</span></span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c7">i</font></span>)</span> )</span><br/><span class="kw">assume </span><a NAME="E1:38_1"/><span class="lab"><font color="Green" title="E21">A2</font></span>: 
<font color="Maroon" title="c7">i</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="ltlaxio2.html#K5" title="LTLAXIO2:func.5">nex</a> <span class="p2">(<span class="default"><a href="ltlaxio2.html#K4" title="LTLAXIO2:func.4">nega</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">Q</font> <a href="ltlaxio3.html#K9" title="LTLAXIO3:func.9">`2</a></span>)</span></span>)</span></span>)</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">  <a href="subset_1.html#K1" title="SUBSET_1:func.1">{}</a> <a href="ltlaxio1.html#NK1" title="LTLAXIO1:NK.1">LTLB_WFF</a> <a href="ltlaxio1.html#R8" title="LTLAXIO1:pred.8">|-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">P</font> <a href="ltlaxio3.html#K12" title="LTLAXIO3:func.12">^</a></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="ltlaxio2.html#K5" title="LTLAXIO2:func.5">nex</a> <span class="p3">(<span class="default"><a href="ltlaxio2.html#K4" title="LTLAXIO2:func.4">nega</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">Q</font> <a href="ltlaxio3.html#K9" title="LTLAXIO3:func.9">`2</a></span>)</span></span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c7">i</font></span>)</span></span><br/><a NAME="E2:38_1"/><span class="lab"><font color="Green" title="E22">A3</font></span>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="ltlaxio2.html#K5" title="LTLAXIO2:func.5">nex</a> <span class="p2">(<span class="default"><a href="ltlaxio2.html#K4" title="LTLAXIO2:func.4">nega</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">Q</font> <a href="ltlaxio3.html#K9" title="LTLAXIO3:func.9">`2</a></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="ltlaxio2.html#K4" title="LTLAXIO2:func.4">nega</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">Q</font> <a href="ltlaxio3.html#K9" title="LTLAXIO3:func.9">`2</a></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="ltlaxio2.html#D5" onmouseover="rs('ltlaxio2/D5')" onmouseout="rh()">LTLAXIO2:def 5</a></span>;<br/><a NAME="E3:38_1"/><span class="kw">then </span>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="ltlaxio2.html#K5" title="LTLAXIO2:func.5">nex</a> <span class="p2">(<span class="default"><a href="ltlaxio2.html#K4" title="LTLAXIO2:func.4">nega</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">Q</font> <a href="ltlaxio3.html#K9" title="LTLAXIO3:func.9">`2</a></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">Q</font> <a href="ltlaxio3.html#K9" title="LTLAXIO3:func.9">`2</a></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="ltlaxio2.html#D4" onmouseover="rs('ltlaxio2/D4')" onmouseout="rh()">LTLAXIO2:def 4</a></span>;<br/><a NAME="E4:38_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E23">A4</font></span>: 
<font color="Maroon" title="c7">i</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">Q</font> <a href="ltlaxio3.html#K9" title="LTLAXIO3:func.9">`2</a></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_3.html#T29" onmouseover="rs('finseq_3/T29')" onmouseout="rh()">FINSEQ_3:29</a>, <a class="txt" href="#E1:38_1"><span class="lab"><font color="Green" title="E21">A2</font></span></a></span>;<br/><a NAME="E5:38_1"/><span class="kw">then </span>
<span class="p1">(<span class="default"><font color="Maroon" title="c4">Q</font> <a href="ltlaxio3.html#K9" title="LTLAXIO3:func.9">`2</a></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c7">i</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="ltlaxio4.html#K7" title="LTLAXIO4:func.7">untn</a> <span class="p1">(<span class="default"><a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">P</font> <a href="ltlaxio3.html#K9" title="LTLAXIO3:func.9">`2</a></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="partfun2.html#T2" onmouseover="rs('partfun2/T2')" onmouseout="rh()">PARTFUN2:2</a>, <a class="txt" href="#E2:38"><span class="lab"><font color="Green" title="E20">A1</font></span></a></span>;<br/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c8">A</font>, <font color="Maroon" title="c9">B</font> being    <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> <span class="kw"> such that </span><br/><a NAME="E7:38_1"/><span class="lab"><font color="Green" title="E24">A5</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">Q</font> <a href="ltlaxio3.html#K9" title="LTLAXIO3:func.9">`2</a></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c7">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ltlaxio2.html#K1" title="LTLAXIO2:func.1">untn</a> (<font color="Maroon" title="c8">A</font>,<font color="Maroon" title="c9">B</font>)
 <span class="kw">and </span><br/><a NAME="E8:38_1"/><span class="lab"><font color="Green" title="E25">A6</font></span>: 
<font color="Maroon" title="c8">A</font> <a href="ltlaxio1.html#NK3" title="LTLAXIO1:NK.3">'U'</a> <font color="Maroon" title="c9">B</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">P</font> <a href="ltlaxio3.html#K9" title="LTLAXIO3:func.9">`2</a></span>)</span>
 ;<br/><a NAME="E9:38_1"/>
<font color="Maroon" title="c7">i</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="ltlaxio2.html#K4" title="LTLAXIO2:func.4">nega</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">Q</font> <a href="ltlaxio3.html#K9" title="LTLAXIO3:func.9">`2</a></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:38_1"><span class="lab"><font color="Green" title="E22">A3</font></span></a>, <a class="txt" href="#E1:38_1"><span class="lab"><font color="Green" title="E21">A2</font></span></a>, <a class="ref" href="finseq_3.html#T29" onmouseover="rs('finseq_3/T29')" onmouseout="rh()">FINSEQ_3:29</a></span>;<br/><span class="kw">then </span><span class="lab"><font color="Green" title="E26">A7</font></span>: <span class="p1">(<span class="default"><a href="ltlaxio2.html#K5" title="LTLAXIO2:func.5">nex</a> <span class="p2">(<span class="default"><a href="ltlaxio2.html#K4" title="LTLAXIO2:func.4">nega</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">Q</font> <a href="ltlaxio3.html#K9" title="LTLAXIO3:func.9">`2</a></span>)</span></span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c7">i</font> = 
 <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="ltlaxio2.html#K4" title="LTLAXIO2:func.4">nega</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">Q</font> <a href="ltlaxio3.html#K9" title="LTLAXIO3:func.9">`2</a></span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c7">i</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="ltlaxio2.html#T9" onmouseover="rs('ltlaxio2/T9')" onmouseout="rh()">LTLAXIO2:9</a></span>
<br/>.= 
 <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"><span class="p3">(<span class="default"><font color="Maroon" title="c4">Q</font> <a href="ltlaxio3.html#K9" title="LTLAXIO3:func.9">`2</a></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c7">i</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="ltlaxio2.html#T8" onmouseover="rs('ltlaxio2/T8')" onmouseout="rh()">LTLAXIO2:8</a>, <a class="txt" href="#E4:38_1"><span class="lab"><font color="Green" title="E23">A4</font></span></a></span>
;<br/><a NAME="E11:38_1"/>
(  <a href="subset_1.html#K1" title="SUBSET_1:func.1">{}</a> <a href="ltlaxio1.html#NK1" title="LTLAXIO1:NK.1">LTLB_WFF</a> <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="c8">A</font> <a href="ltlaxio1.html#NK3" title="LTLAXIO1:NK.3">'U'</a> <font color="Maroon" title="c9">B</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"><a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <span class="p3">(<span class="default"><a href="ltlaxio2.html#K1" title="LTLAXIO2:func.1">untn</a> (<font color="Maroon" title="c8">A</font>,<font color="Maroon" title="c9">B</font>)</span>)</span></span>)</span></span>)</span> &amp;  <a href="subset_1.html#K1" title="SUBSET_1:func.1">{}</a> <a href="ltlaxio1.html#NK1" title="LTLAXIO1:NK.1">LTLB_WFF</a> <a href="ltlaxio1.html#R8" title="LTLAXIO1:pred.8">|-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">P</font> <a href="ltlaxio3.html#K12" title="LTLAXIO3:func.12">^</a></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"><font color="Maroon" title="c8">A</font> <a href="ltlaxio1.html#NK3" title="LTLAXIO1:NK.3">'U'</a> <font color="Maroon" title="c9">B</font></span>)</span></span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="ltlaxio2.html#T63" onmouseover="rs('ltlaxio2/T63')" onmouseout="rh()">LTLAXIO2:63</a>, <a class="ref" href="ltlaxio3.html#T29" onmouseover="rs('ltlaxio3/T29')" onmouseout="rh()">LTLAXIO3:29</a>, <a class="txt" href="#E8:38_1"><span class="lab"><font color="Green" title="E25">A6</font></span></a></span>;<br/><span class="kw">hence </span><a NAME="E12:38_1"/>
 <a href="subset_1.html#K1" title="SUBSET_1:func.1">{}</a> <a href="ltlaxio1.html#NK1" title="LTLAXIO1:NK.1">LTLB_WFF</a> <a href="ltlaxio1.html#R8" title="LTLAXIO1:pred.8">|-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">P</font> <a href="ltlaxio3.html#K12" title="LTLAXIO3:func.12">^</a></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="ltlaxio2.html#K5" title="LTLAXIO2:func.5">nex</a> <span class="p3">(<span class="default"><a href="ltlaxio2.html#K4" title="LTLAXIO2:func.4">nega</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">Q</font> <a href="ltlaxio3.html#K9" title="LTLAXIO3:func.9">`2</a></span>)</span></span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c7">i</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:38_1"><span class="lab"><font color="Green" title="E26">A7</font></span></a>, <a class="ref" href="ltlaxio1.html#T47" onmouseover="rs('ltlaxio1/T47')" onmouseout="rh()">LTLAXIO1:47</a>, <a class="txt" href="#E7:38_1"><span class="lab"><font color="Green" title="E24">A5</font></span></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/></div><span class="kw">end;</span></div>
<a NAME="E4:38"/><span class="kw">then </span>
(  <a href="subset_1.html#K1" title="SUBSET_1:func.1">{}</a> <a href="ltlaxio1.html#NK1" title="LTLAXIO1:NK.1">LTLB_WFF</a> <a href="ltlaxio1.html#R8" title="LTLAXIO1:pred.8">|-</a> <font color="Maroon">H<sub>2</sub></font>( <a href="ltlaxio2.html#K5" title="LTLAXIO2:func.5">nex</a> <span class="p1">(<span class="default"><a href="ltlaxio2.html#K4" title="LTLAXIO2:func.4">nega</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">Q</font> <a href="ltlaxio3.html#K9" title="LTLAXIO3:func.9">`2</a></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">H<sub>2</sub></font>( <a href="ltlaxio2.html#K4" title="LTLAXIO2:func.4">nega</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">Q</font> <a href="ltlaxio3.html#K9" title="LTLAXIO3:func.9">`2</a></span>)</span>)</span>)</span> &amp;  <a href="subset_1.html#K1" title="SUBSET_1:func.1">{}</a> <a href="ltlaxio1.html#NK1" title="LTLAXIO1:NK.1">LTLB_WFF</a> <a href="ltlaxio1.html#R8" title="LTLAXIO1:pred.8">|-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">P</font> <a href="ltlaxio3.html#K12" title="LTLAXIO3:func.12">^</a></span>)</span> <a href="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</a> <font color="Maroon">H<sub>2</sub></font>( <a href="ltlaxio2.html#K5" title="LTLAXIO2:func.5">nex</a> <span class="p1">(<span class="default"><a href="ltlaxio2.html#K4" title="LTLAXIO2:func.4">nega</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">Q</font> <a href="ltlaxio3.html#K9" title="LTLAXIO3:func.9">`2</a></span>)</span></span>)</span>) )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="ltlaxio2.html#T60" onmouseover="rs('ltlaxio2/T60')" onmouseout="rh()">LTLAXIO2:60</a>, <a class="ref" href="ltlaxio2.html#T56" onmouseover="rs('ltlaxio2/T56')" onmouseout="rh()">LTLAXIO2:56</a></span>;<br/>
<a NAME="E5:38"/><span class="kw">then </span><span class="lab"><font color="Green" title="E21">A8</font></span>: 
 <a href="subset_1.html#K1" title="SUBSET_1:func.1">{}</a> <a href="ltlaxio1.html#NK1" title="LTLAXIO1:NK.1">LTLB_WFF</a> <a href="ltlaxio1.html#R8" title="LTLAXIO1:pred.8">|-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">P</font> <a href="ltlaxio3.html#K12" title="LTLAXIO3:func.12">^</a></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">H<sub>2</sub></font>( <a href="ltlaxio2.html#K4" title="LTLAXIO2:func.4">nega</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">Q</font> <a href="ltlaxio3.html#K9" title="LTLAXIO3:func.9">`2</a></span>)</span>)</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></span>;<br/>
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="38_2"><span class="kw">now </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">  for <font color="Olive" title="b1">i</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st <font color="Olive" title="b1">i</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="ltlaxio2.html#K5" title="LTLAXIO2:func.5">nex</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">Q</font> <a href="ltlaxio3.html#K8" title="LTLAXIO3:func.8">`1</a></span>)</span></span>)</span> holds <br/> <a href="subset_1.html#K1" title="SUBSET_1:func.1">{}</a> <a href="ltlaxio1.html#NK1" title="LTLAXIO1:NK.1">LTLB_WFF</a> <a href="ltlaxio1.html#R8" title="LTLAXIO1:pred.8">|-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">P</font> <a href="ltlaxio3.html#K12" title="LTLAXIO3:func.12">^</a></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="ltlaxio2.html#K5" title="LTLAXIO2:func.5">nex</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">Q</font> <a href="ltlaxio3.html#K8" title="LTLAXIO3:func.8">`1</a></span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Olive" title="b1">i</font></span>)</span></span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c7">i</font> be   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</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="c7">i</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="ltlaxio2.html#K5" title="LTLAXIO2:func.5">nex</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">Q</font> <a href="ltlaxio3.html#K8" title="LTLAXIO3:func.8">`1</a></span>)</span></span>)</span> implies  <a href="subset_1.html#K1" title="SUBSET_1:func.1">{}</a> <a href="ltlaxio1.html#NK1" title="LTLAXIO1:NK.1">LTLB_WFF</a> <a href="ltlaxio1.html#R8" title="LTLAXIO1:pred.8">|-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">P</font> <a href="ltlaxio3.html#K12" title="LTLAXIO3:func.12">^</a></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="ltlaxio2.html#K5" title="LTLAXIO2:func.5">nex</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">Q</font> <a href="ltlaxio3.html#K8" title="LTLAXIO3:func.8">`1</a></span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c7">i</font></span>)</span> )</span><br/><span class="kw">assume </span><a NAME="E1:38_2"/><span class="lab"><font color="Green" title="E22">A9</font></span>: 
<font color="Maroon" title="c7">i</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="ltlaxio2.html#K5" title="LTLAXIO2:func.5">nex</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">Q</font> <a href="ltlaxio3.html#K8" title="LTLAXIO3:func.8">`1</a></span>)</span></span>)</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">  <a href="subset_1.html#K1" title="SUBSET_1:func.1">{}</a> <a href="ltlaxio1.html#NK1" title="LTLAXIO1:NK.1">LTLB_WFF</a> <a href="ltlaxio1.html#R8" title="LTLAXIO1:pred.8">|-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">P</font> <a href="ltlaxio3.html#K12" title="LTLAXIO3:func.12">^</a></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="ltlaxio2.html#K5" title="LTLAXIO2:func.5">nex</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">Q</font> <a href="ltlaxio3.html#K8" title="LTLAXIO3:func.8">`1</a></span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c7">i</font></span>)</span></span><br/><a NAME="E2:38_2"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">Q</font> <a href="ltlaxio3.html#K8" title="LTLAXIO3:func.8">`1</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="ltlaxio2.html#K5" title="LTLAXIO2:func.5">nex</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">Q</font> <a href="ltlaxio3.html#K8" title="LTLAXIO3:func.8">`1</a></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="ltlaxio2.html#D5" onmouseover="rs('ltlaxio2/D5')" onmouseout="rh()">LTLAXIO2:def 5</a></span>;<br/><a NAME="E3:38_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E23">A10</font></span>: 
<font color="Maroon" title="c7">i</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">Q</font> <a href="ltlaxio3.html#K8" title="LTLAXIO3:func.8">`1</a></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:38_2"><span class="lab"><font color="Green" title="E22">A9</font></span></a>, <a class="ref" href="finseq_3.html#T29" onmouseover="rs('finseq_3/T29')" onmouseout="rh()">FINSEQ_3:29</a></span>;<br/><a NAME="E4:38_2"/><span class="kw">then </span>
<span class="p1">(<span class="default"><font color="Maroon" title="c4">Q</font> <a href="ltlaxio3.html#K8" title="LTLAXIO3:func.8">`1</a></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c7">i</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="ltlaxio4.html#K7" title="LTLAXIO4:func.7">untn</a> <span class="p1">(<span class="default"><a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">P</font> <a href="ltlaxio3.html#K8" title="LTLAXIO3:func.8">`1</a></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="partfun2.html#T2" onmouseover="rs('partfun2/T2')" onmouseout="rh()">PARTFUN2:2</a>, <a class="txt" href="#E2:38"><span class="lab"><font color="Green" title="E20">A1</font></span></a></span>;<br/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c8">A</font>, <font color="Maroon" title="c9">B</font> being    <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> <span class="kw"> such that </span><br/><a NAME="E6:38_2"/><span class="lab"><font color="Green" title="E24">A11</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">Q</font> <a href="ltlaxio3.html#K8" title="LTLAXIO3:func.8">`1</a></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c7">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ltlaxio2.html#K1" title="LTLAXIO2:func.1">untn</a> (<font color="Maroon" title="c8">A</font>,<font color="Maroon" title="c9">B</font>)
 <span class="kw">and </span><br/><a NAME="E7:38_2"/><span class="lab"><font color="Green" title="E25">A12</font></span>: 
<font color="Maroon" title="c8">A</font> <a href="ltlaxio1.html#NK3" title="LTLAXIO1:NK.3">'U'</a> <font color="Maroon" title="c9">B</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">P</font> <a href="ltlaxio3.html#K8" title="LTLAXIO3:func.8">`1</a></span>)</span>
 ;<br/><a NAME="E8:38_2"/><span class="lab"><font color="Green" title="E26">A13</font></span>: 
 <a href="subset_1.html#K1" title="SUBSET_1:func.1">{}</a> <a href="ltlaxio1.html#NK1" title="LTLAXIO1:NK.1">LTLB_WFF</a> <a href="ltlaxio1.html#R8" title="LTLAXIO1:pred.8">|-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">P</font> <a href="ltlaxio3.html#K12" title="LTLAXIO3:func.12">^</a></span>)</span> <a href="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">A</font> <a href="ltlaxio1.html#NK3" title="LTLAXIO1:NK.3">'U'</a> <font color="Maroon" title="c9">B</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="ltlaxio3.html#T28" onmouseover="rs('ltlaxio3/T28')" onmouseout="rh()">LTLAXIO3:28</a>, <a class="txt" href="#E7:38_2"><span class="lab"><font color="Green" title="E25">A12</font></span></a></span>;<br/><a NAME="E9:38_2"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c8">A</font> <a href="ltlaxio1.html#NK3" title="LTLAXIO1:NK.3">'U'</a> <font color="Maroon" title="c9">B</font></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="c9">B</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> <span class="p3">(<span class="default"><font color="Maroon" title="c8">A</font> <a href="ltlaxio1.html#K4" title="LTLAXIO1:func.4">'&amp;&amp;'</a> <span class="p4">(<span class="default"><font color="Maroon" title="c8">A</font> <a href="ltlaxio1.html#NK3" title="LTLAXIO1:NK.3">'U'</a> <font color="Maroon" title="c9">B</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="E10:38_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E27">A14</font></span>: 
 <a href="subset_1.html#K1" title="SUBSET_1:func.1">{}</a> <a href="ltlaxio1.html#NK1" title="LTLAXIO1:NK.1">LTLB_WFF</a> <a href="ltlaxio1.html#R8" title="LTLAXIO1:pred.8">|-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">A</font> <a href="ltlaxio1.html#NK3" title="LTLAXIO1:NK.3">'U'</a> <font color="Maroon" title="c9">B</font></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="c9">B</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> <span class="p3">(<span class="default"><font color="Maroon" title="c8">A</font> <a href="ltlaxio1.html#K4" title="LTLAXIO1:func.4">'&amp;&amp;'</a> <span class="p4">(<span class="default"><font color="Maroon" title="c8">A</font> <a href="ltlaxio1.html#NK3" title="LTLAXIO1:NK.3">'U'</a> <font color="Maroon" title="c9">B</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="E11:38_2"/>
 <a href="subset_1.html#K1" title="SUBSET_1:func.1">{}</a> <a href="ltlaxio1.html#NK1" title="LTLAXIO1:NK.1">LTLB_WFF</a> <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="c9">B</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> <span class="p3">(<span class="default"><font color="Maroon" title="c8">A</font> <a href="ltlaxio1.html#K4" title="LTLAXIO1:func.4">'&amp;&amp;'</a> <span class="p4">(<span class="default"><font color="Maroon" title="c8">A</font> <a href="ltlaxio1.html#NK3" title="LTLAXIO1:NK.3">'U'</a> <font color="Maroon" title="c9">B</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"><a href="ltlaxio2.html#K1" title="LTLAXIO2:func.1">untn</a> (<font color="Maroon" title="c8">A</font>,<font color="Maroon" title="c9">B</font>)</span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="ltlaxio2.html#T61" onmouseover="rs('ltlaxio2/T61')" onmouseout="rh()">LTLAXIO2:61</a></span>;<br/><a NAME="E12:38_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E28">A15</font></span>: 
 <a href="subset_1.html#K1" title="SUBSET_1:func.1">{}</a> <a href="ltlaxio1.html#NK1" title="LTLAXIO1:NK.1">LTLB_WFF</a> <a href="ltlaxio1.html#R8" title="LTLAXIO1:pred.8">|-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">A</font> <a href="ltlaxio1.html#NK3" title="LTLAXIO1:NK.3">'U'</a> <font color="Maroon" title="c9">B</font></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="ltlaxio2.html#K1" title="LTLAXIO2:func.1">untn</a> (<font color="Maroon" title="c8">A</font>,<font color="Maroon" title="c9">B</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="#E10:38_2"><span class="lab"><font color="Green" title="E27">A14</font></span></a></span>;<br/><a NAME="E13:38_2"/>
<span class="p1">(<span class="default"><a href="ltlaxio2.html#K5" title="LTLAXIO2:func.5">nex</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">Q</font> <a href="ltlaxio3.html#K8" title="LTLAXIO3:func.8">`1</a></span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c7">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ltlaxio1.html#K2" title="LTLAXIO1:func.2">'X'</a> <span class="p1">(<span class="default"><a href="ltlaxio2.html#K1" title="LTLAXIO2:func.1">untn</a> (<font color="Maroon" title="c8">A</font>,<font color="Maroon" title="c9">B</font>)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:38_2"><span class="lab"><font color="Green" title="E24">A11</font></span></a>, <a class="ref" href="ltlaxio2.html#T9" onmouseover="rs('ltlaxio2/T9')" onmouseout="rh()">LTLAXIO2:9</a>, <a class="txt" href="#E3:38_2"><span class="lab"><font color="Green" title="E23">A10</font></span></a></span>;<br/><span class="kw">hence </span><a NAME="E14:38_2"/>
 <a href="subset_1.html#K1" title="SUBSET_1:func.1">{}</a> <a href="ltlaxio1.html#NK1" title="LTLAXIO1:NK.1">LTLB_WFF</a> <a href="ltlaxio1.html#R8" title="LTLAXIO1:pred.8">|-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">P</font> <a href="ltlaxio3.html#K12" title="LTLAXIO3:func.12">^</a></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="ltlaxio2.html#K5" title="LTLAXIO2:func.5">nex</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">Q</font> <a href="ltlaxio3.html#K8" title="LTLAXIO3:func.8">`1</a></span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c7">i</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:38_2"><span class="lab"><font color="Green" title="E28">A15</font></span></a>, <a class="ref" href="ltlaxio1.html#T47" onmouseover="rs('ltlaxio1/T47')" onmouseout="rh()">LTLAXIO1:47</a>, <a class="txt" href="#E8:38_2"><span class="lab"><font color="Green" title="E26">A13</font></span></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/></div><span class="kw">end;</span></div>
<a NAME="E7:38"/><span class="kw">then </span>
(  <a href="subset_1.html#K1" title="SUBSET_1:func.1">{}</a> <a href="ltlaxio1.html#NK1" title="LTLAXIO1:NK.1">LTLB_WFF</a> <a href="ltlaxio1.html#R8" title="LTLAXIO1:pred.8">|-</a> <font color="Maroon">H<sub>2</sub></font>( <a href="ltlaxio2.html#K5" title="LTLAXIO2:func.5">nex</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">Q</font> <a href="ltlaxio3.html#K8" title="LTLAXIO3:func.8">`1</a></span>)</span>) <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">H<sub>2</sub></font>(<font color="Maroon" title="c4">Q</font> <a href="ltlaxio3.html#K8" title="LTLAXIO3:func.8">`1</a> )</span>)</span> &amp;  <a href="subset_1.html#K1" title="SUBSET_1:func.1">{}</a> <a href="ltlaxio1.html#NK1" title="LTLAXIO1:NK.1">LTLB_WFF</a> <a href="ltlaxio1.html#R8" title="LTLAXIO1:pred.8">|-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">P</font> <a href="ltlaxio3.html#K12" title="LTLAXIO3:func.12">^</a></span>)</span> <a href="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</a> <font color="Maroon">H<sub>2</sub></font>( <a href="ltlaxio2.html#K5" title="LTLAXIO2:func.5">nex</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">Q</font> <a href="ltlaxio3.html#K8" title="LTLAXIO3:func.8">`1</a></span>)</span>) )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="ltlaxio2.html#T60" onmouseover="rs('ltlaxio2/T60')" onmouseout="rh()">LTLAXIO2:60</a>, <a class="ref" href="ltlaxio2.html#T56" onmouseover="rs('ltlaxio2/T56')" onmouseout="rh()">LTLAXIO2:56</a></span>;<br/>
<a NAME="E8:38"/><span class="kw">then </span><span class="lab"><font color="Green" title="E22">A16</font></span>: 
 <a href="subset_1.html#K1" title="SUBSET_1:func.1">{}</a> <a href="ltlaxio1.html#NK1" title="LTLAXIO1:NK.1">LTLB_WFF</a> <a href="ltlaxio1.html#R8" title="LTLAXIO1:pred.8">|-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">P</font> <a href="ltlaxio3.html#K12" title="LTLAXIO3:func.12">^</a></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">H<sub>2</sub></font>(<font color="Maroon" title="c4">Q</font> <a href="ltlaxio3.html#K8" title="LTLAXIO3:func.8">`1</a> )</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></span>;<br/>
<a NAME="E9:38"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">P</font> <a href="ltlaxio3.html#K12" title="LTLAXIO3:func.12">^</a></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">H<sub>2</sub></font>(<font color="Maroon" title="c4">Q</font> <a href="ltlaxio3.html#K8" title="LTLAXIO3:func.8">`1</a> )</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"><font color="Maroon" title="c3">P</font> <a href="ltlaxio3.html#K12" title="LTLAXIO3:func.12">^</a></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">H<sub>2</sub></font>( <a href="ltlaxio2.html#K4" title="LTLAXIO2:func.4">nega</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">Q</font> <a href="ltlaxio3.html#K9" title="LTLAXIO3:func.9">`2</a></span>)</span>)</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"><font color="Maroon" title="c3">P</font> <a href="ltlaxio3.html#K12" title="LTLAXIO3:func.12">^</a></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#K2" title="LTLAXIO1:func.2">'X'</a> <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon" title="c4">Q</font> <a href="ltlaxio3.html#K8" title="LTLAXIO3:func.8">`1</a> )</span>)</span> <a href="ltlaxio1.html#K4" title="LTLAXIO1:func.4">'&amp;&amp;'</a> <span class="p4">(<span class="default"><a href="ltlaxio1.html#K2" title="LTLAXIO1:func.2">'X'</a> <font color="Maroon">H<sub>2</sub></font>( <a href="ltlaxio2.html#K4" title="LTLAXIO2:func.4">nega</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">Q</font> <a href="ltlaxio3.html#K9" title="LTLAXIO3:func.9">`2</a></span>)</span>)</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#T40" onmouseover="rs('ltlaxio2/T40')" onmouseout="rh()">LTLAXIO2:40</a></span>;<br/>
<a NAME="E10:38"/><span class="kw">then </span>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">P</font> <a href="ltlaxio3.html#K12" title="LTLAXIO3:func.12">^</a></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">H<sub>2</sub></font>(<font color="Maroon" title="c4">Q</font> <a href="ltlaxio3.html#K8" title="LTLAXIO3:func.8">`1</a> )</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"><font color="Maroon" title="c3">P</font> <a href="ltlaxio3.html#K12" title="LTLAXIO3:func.12">^</a></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">H<sub>2</sub></font>( <a href="ltlaxio2.html#K4" title="LTLAXIO2:func.4">nega</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">Q</font> <a href="ltlaxio3.html#K9" title="LTLAXIO3:func.9">`2</a></span>)</span>)</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"><font color="Maroon" title="c3">P</font> <a href="ltlaxio3.html#K12" title="LTLAXIO3:func.12">^</a></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#K2" title="LTLAXIO1:func.2">'X'</a> <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon" title="c4">Q</font> <a href="ltlaxio3.html#K8" title="LTLAXIO3:func.8">`1</a> )</span>)</span> <a href="ltlaxio1.html#K4" title="LTLAXIO1:func.4">'&amp;&amp;'</a> <span class="p4">(<span class="default"><a href="ltlaxio1.html#K2" title="LTLAXIO1:func.2">'X'</a> <font color="Maroon">H<sub>2</sub></font>( <a href="ltlaxio2.html#K4" title="LTLAXIO2:func.4">nega</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">Q</font> <a href="ltlaxio3.html#K9" title="LTLAXIO3:func.9">`2</a></span>)</span>)</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="E11:38"/><span class="kw">then </span>
 <a href="subset_1.html#K1" title="SUBSET_1:func.1">{}</a> <a href="ltlaxio1.html#NK1" title="LTLAXIO1:NK.1">LTLB_WFF</a> <a href="ltlaxio1.html#R8" title="LTLAXIO1:pred.8">|-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">P</font> <a href="ltlaxio3.html#K12" title="LTLAXIO3:func.12">^</a></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">H<sub>2</sub></font>(<font color="Maroon" title="c4">Q</font> <a href="ltlaxio3.html#K8" title="LTLAXIO3:func.8">`1</a> )</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"><font color="Maroon" title="c3">P</font> <a href="ltlaxio3.html#K12" title="LTLAXIO3:func.12">^</a></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">H<sub>2</sub></font>( <a href="ltlaxio2.html#K4" title="LTLAXIO2:func.4">nega</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">Q</font> <a href="ltlaxio3.html#K9" title="LTLAXIO3:func.9">`2</a></span>)</span>)</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"><font color="Maroon" title="c3">P</font> <a href="ltlaxio3.html#K12" title="LTLAXIO3:func.12">^</a></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#K2" title="LTLAXIO1:func.2">'X'</a> <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon" title="c4">Q</font> <a href="ltlaxio3.html#K8" title="LTLAXIO3:func.8">`1</a> )</span>)</span> <a href="ltlaxio1.html#K4" title="LTLAXIO1:func.4">'&amp;&amp;'</a> <span class="p4">(<span class="default"><a href="ltlaxio1.html#K2" title="LTLAXIO1:func.2">'X'</a> <font color="Maroon">H<sub>2</sub></font>( <a href="ltlaxio2.html#K4" title="LTLAXIO2:func.4">nega</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">Q</font> <a href="ltlaxio3.html#K9" title="LTLAXIO3:func.9">`2</a></span>)</span>)</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="E12:38"/><span class="kw">then </span>
 <a href="subset_1.html#K1" title="SUBSET_1:func.1">{}</a> <a href="ltlaxio1.html#NK1" title="LTLAXIO1:NK.1">LTLB_WFF</a> <a href="ltlaxio1.html#R8" title="LTLAXIO1:pred.8">|-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">P</font> <a href="ltlaxio3.html#K12" title="LTLAXIO3:func.12">^</a></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">H<sub>2</sub></font>( <a href="ltlaxio2.html#K4" title="LTLAXIO2:func.4">nega</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">Q</font> <a href="ltlaxio3.html#K9" title="LTLAXIO3:func.9">`2</a></span>)</span>)</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"><font color="Maroon" title="c3">P</font> <a href="ltlaxio3.html#K12" title="LTLAXIO3:func.12">^</a></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#K2" title="LTLAXIO1:func.2">'X'</a> <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon" title="c4">Q</font> <a href="ltlaxio3.html#K8" title="LTLAXIO3:func.8">`1</a> )</span>)</span> <a href="ltlaxio1.html#K4" title="LTLAXIO1:func.4">'&amp;&amp;'</a> <span class="p3">(<span class="default"><a href="ltlaxio1.html#K2" title="LTLAXIO1:func.2">'X'</a> <font color="Maroon">H<sub>2</sub></font>( <a href="ltlaxio2.html#K4" title="LTLAXIO2:func.4">nega</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">Q</font> <a href="ltlaxio3.html#K9" title="LTLAXIO3:func.9">`2</a></span>)</span>)</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="#E8:38"><span class="lab"><font color="Green" title="E22">A16</font></span></a></span>;<br/>
<a NAME="E13:38"/><span class="kw">then </span><span class="lab"><font color="Green" title="E23">A17</font></span>: 
 <a href="subset_1.html#K1" title="SUBSET_1:func.1">{}</a> <a href="ltlaxio1.html#NK1" title="LTLAXIO1:NK.1">LTLB_WFF</a> <a href="ltlaxio1.html#R8" title="LTLAXIO1:pred.8">|-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">P</font> <a href="ltlaxio3.html#K12" title="LTLAXIO3:func.12">^</a></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">H<sub>2</sub></font>(<font color="Maroon" title="c4">Q</font> <a href="ltlaxio3.html#K8" title="LTLAXIO3:func.8">`1</a> )</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> <font color="Maroon">H<sub>2</sub></font>( <a href="ltlaxio2.html#K4" title="LTLAXIO2:func.4">nega</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">Q</font> <a href="ltlaxio3.html#K9" title="LTLAXIO3:func.9">`2</a></span>)</span>)</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="#E5:38"><span class="lab"><font color="Green" title="E21">A8</font></span></a></span>;<br/>
<a NAME="E14:38"/>
 <a href="subset_1.html#K1" title="SUBSET_1:func.1">{}</a> <a href="ltlaxio1.html#NK1" title="LTLAXIO1:NK.1">LTLB_WFF</a> <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">H<sub>2</sub></font>(<font color="Maroon" title="c4">Q</font> <a href="ltlaxio3.html#K8" title="LTLAXIO3:func.8">`1</a> )</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> <font color="Maroon">H<sub>2</sub></font>( <a href="ltlaxio2.html#K4" title="LTLAXIO2:func.4">nega</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">Q</font> <a href="ltlaxio3.html#K9" title="LTLAXIO3:func.9">`2</a></span>)</span>)</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="c4">Q</font> <a href="ltlaxio3.html#K12" title="LTLAXIO3:func.12">^</a></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="ltlaxio1.html#T53" onmouseover="rs('ltlaxio1/T53')" onmouseout="rh()">LTLAXIO1:53</a></span>;<br/>
<span class="kw">hence </span><a NAME="E15:38"/>
 <a href="subset_1.html#K1" title="SUBSET_1:func.1">{}</a> <a href="ltlaxio1.html#NK1" title="LTLAXIO1:NK.1">LTLB_WFF</a> <a href="ltlaxio1.html#R8" title="LTLAXIO1:pred.8">|-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">P</font> <a href="ltlaxio3.html#K12" title="LTLAXIO3:func.12">^</a></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="c4">Q</font> <a href="ltlaxio3.html#K12" title="LTLAXIO3:func.12">^</a></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="#E13:38"><span class="lab"><font color="Green" title="E23">A17</font></span></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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