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

<span class="kw">set </span><font color="Maroon" title="c3">Q</font> = <span class="p1"><a href="ltlaxio3.html#K11" title="LTLAXIO3:func.11">[</a><span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K6" title="FINSEQ_1:func.6">&lt;*&gt;</a> <a href="ltlaxio1.html#NK1" title="LTLAXIO1:NK.1">LTLB_WFF</a></span>)</span>,<span class="p2">(<span class="default"><a href="finseq_1.html#K6" title="FINSEQ_1:func.6">&lt;*&gt;</a> <a href="ltlaxio1.html#NK1" title="LTLAXIO1:NK.1">LTLB_WFF</a></span>)</span></span><a href="ltlaxio3.html#K11" title="LTLAXIO3:func.11">]</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c4">t</font> =  <a href="ltlaxio1.html#K3" title="LTLAXIO1:func.3">TVERUM</a> ;<br/>
<div><span class="kw">hereby </span> <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="tarski.html#D3" onmouseover="rs('tarski/D3')" onmouseout="rh()">TARSKI:def 3</a>,<a class="ref" href="xboole_0.html#D10" onmouseover="rs('xboole_0/D10')" onmouseout="rh()">XBOOLE_0:def 10</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"> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2">(<span class="default"><a href="ltlaxio1.html#K3" title="LTLAXIO1:func.3">TVERUM</a> <a href="ltlaxio1.html#K4" title="LTLAXIO1:func.4">'&amp;&amp;'</a> <a href="ltlaxio1.html#K3" title="LTLAXIO1:func.3">TVERUM</a></span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2"><a href="ltlaxio3.html#K11" title="LTLAXIO3:func.11">[</a><span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K6" title="FINSEQ_1:func.6">&lt;*&gt;</a> <a href="ltlaxio1.html#NK1" title="LTLAXIO1:NK.1">LTLB_WFF</a></span>)</span>,<span class="p3">(<span class="default"><a href="finseq_1.html#K6" title="FINSEQ_1:func.6">&lt;*&gt;</a> <a href="ltlaxio1.html#NK1" title="LTLAXIO1:NK.1">LTLB_WFF</a></span>)</span></span><a href="ltlaxio3.html#K11" title="LTLAXIO3:func.11">]</a></span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="ltlaxio4.html#K3" title="LTLAXIO4:func.3">^</a> </span>
<div class="add"><span class="kw">let </span><font color="Maroon" title="c5">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</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="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2"><a href="ltlaxio3.html#K11" title="LTLAXIO3:func.11">[</a><span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K6" title="FINSEQ_1:func.6">&lt;*&gt;</a> <a href="ltlaxio1.html#NK1" title="LTLAXIO1:NK.1">LTLB_WFF</a></span>)</span>,<span class="p3">(<span class="default"><a href="finseq_1.html#K6" title="FINSEQ_1:func.6">&lt;*&gt;</a> <a href="ltlaxio1.html#NK1" title="LTLAXIO1:NK.1">LTLB_WFF</a></span>)</span></span><a href="ltlaxio3.html#K11" title="LTLAXIO3:func.11">]</a></span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="ltlaxio4.html#K3" title="LTLAXIO4:func.3">^</a>  implies <font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2">(<span class="default"><a href="ltlaxio1.html#K3" title="LTLAXIO1:func.3">TVERUM</a> <a href="ltlaxio1.html#K4" title="LTLAXIO1:func.4">'&amp;&amp;'</a> <a href="ltlaxio1.html#K3" title="LTLAXIO1:func.3">TVERUM</a></span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> )</span><br/><span class="kw">assume </span><a NAME="E1:21_1"/>
<font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2"><a href="ltlaxio3.html#K11" title="LTLAXIO3:func.11">[</a><span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K6" title="FINSEQ_1:func.6">&lt;*&gt;</a> <a href="ltlaxio1.html#NK1" title="LTLAXIO1:NK.1">LTLB_WFF</a></span>)</span>,<span class="p3">(<span class="default"><a href="finseq_1.html#K6" title="FINSEQ_1:func.6">&lt;*&gt;</a> <a href="ltlaxio1.html#NK1" title="LTLAXIO1:NK.1">LTLB_WFF</a></span>)</span></span><a href="ltlaxio3.html#K11" title="LTLAXIO3:func.11">]</a></span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="ltlaxio4.html#K3" title="LTLAXIO4:func.3">^</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="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2">(<span class="default"><a href="ltlaxio1.html#K3" title="LTLAXIO1:func.3">TVERUM</a> <a href="ltlaxio1.html#K4" title="LTLAXIO1:func.4">'&amp;&amp;'</a> <a href="ltlaxio1.html#K3" title="LTLAXIO1:func.3">TVERUM</a></span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span><br/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c6">P</font> being   <a href="ltlaxio3.html#NM1" title="LTLAXIO3:NM.1">PNPair</a><span class="kw"> such that </span><br/><a NAME="E3:21_1"/><span class="lab"><font color="Green" title="E13">A1</font></span>: 
<font color="Maroon" title="c5">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">P</font> <a href="ltlaxio3.html#K12" title="LTLAXIO3:func.12">^</a> 
 <span class="kw">and </span><br/><a NAME="E4:21_1"/><span class="lab"><font color="Green" title="E14">A2</font></span>: 
<font color="Maroon" title="c6">P</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2"><a href="ltlaxio3.html#K11" title="LTLAXIO3:func.11">[</a><span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K6" title="FINSEQ_1:func.6">&lt;*&gt;</a> <a href="ltlaxio1.html#NK1" title="LTLAXIO1:NK.1">LTLB_WFF</a></span>)</span>,<span class="p3">(<span class="default"><a href="finseq_1.html#K6" title="FINSEQ_1:func.6">&lt;*&gt;</a> <a href="ltlaxio1.html#NK1" title="LTLAXIO1:NK.1">LTLB_WFF</a></span>)</span></span><a href="ltlaxio3.html#K11" title="LTLAXIO3:func.11">]</a></span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>
 ;<br/><a NAME="E5:21_1"/>
<font color="Maroon" title="c6">P</font> <a href="ltlaxio3.html#K12" title="LTLAXIO3:func.12">^</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="ltlaxio1.html#K3" title="LTLAXIO1:func.3">TVERUM</a> <a href="ltlaxio1.html#K4" title="LTLAXIO1:func.4">'&amp;&amp;'</a> <a href="ltlaxio1.html#K3" title="LTLAXIO1:func.3">TVERUM</a>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:21_1"><span class="lab"><font color="Green" title="E14">A2</font></span></a>, <a class="ref" href="tarski.html#D1" onmouseover="rs('tarski/D1')" onmouseout="rh()">TARSKI:def 1</a>, <a class="ref" href="ltlaxio3.html#T27" onmouseover="rs('ltlaxio3/T27')" onmouseout="rh()">LTLAXIO3:27</a></span>;<br/><span class="kw">hence </span><a NAME="E6:21_1"/>
<font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2">(<span class="default"><a href="ltlaxio1.html#K3" title="LTLAXIO1:func.3">TVERUM</a> <a href="ltlaxio1.html#K4" title="LTLAXIO1:func.4">'&amp;&amp;'</a> <a href="ltlaxio1.html#K3" title="LTLAXIO1:func.3">TVERUM</a></span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:21_1"><span class="lab"><font color="Green" title="E13">A1</font></span></a>, <a class="ref" href="tarski.html#D1" onmouseover="rs('tarski/D1')" onmouseout="rh()">TARSKI:def 1</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>

<span class="kw">let </span><font color="Maroon" title="c5">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> ; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="tarski.html#D3" onmouseover="rs('tarski/D3')" onmouseout="rh()">TARSKI:def 3</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"> (  not <font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2">(<span class="default"><a href="ltlaxio1.html#K3" title="LTLAXIO1:func.3">TVERUM</a> <a href="ltlaxio1.html#K4" title="LTLAXIO1:func.4">'&amp;&amp;'</a> <a href="ltlaxio1.html#K3" title="LTLAXIO1:func.3">TVERUM</a></span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> or <font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2"><a href="ltlaxio3.html#K11" title="LTLAXIO3:func.11">[</a><span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K6" title="FINSEQ_1:func.6">&lt;*&gt;</a> <a href="ltlaxio1.html#NK1" title="LTLAXIO1:NK.1">LTLB_WFF</a></span>)</span>,<span class="p3">(<span class="default"><a href="finseq_1.html#K6" title="FINSEQ_1:func.6">&lt;*&gt;</a> <a href="ltlaxio1.html#NK1" title="LTLAXIO1:NK.1">LTLB_WFF</a></span>)</span></span><a href="ltlaxio3.html#K11" title="LTLAXIO3:func.11">]</a></span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="ltlaxio4.html#K3" title="LTLAXIO4:func.3">^</a>  )</span><br/>

<span class="kw">assume </span><a NAME="E2:21"/>
<font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2">(<span class="default"><a href="ltlaxio1.html#K3" title="LTLAXIO1:func.3">TVERUM</a> <a href="ltlaxio1.html#K4" title="LTLAXIO1:func.4">'&amp;&amp;'</a> <a href="ltlaxio1.html#K3" title="LTLAXIO1:func.3">TVERUM</a></span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</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"> <font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2"><a href="ltlaxio3.html#K11" title="LTLAXIO3:func.11">[</a><span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K6" title="FINSEQ_1:func.6">&lt;*&gt;</a> <a href="ltlaxio1.html#NK1" title="LTLAXIO1:NK.1">LTLB_WFF</a></span>)</span>,<span class="p3">(<span class="default"><a href="finseq_1.html#K6" title="FINSEQ_1:func.6">&lt;*&gt;</a> <a href="ltlaxio1.html#NK1" title="LTLAXIO1:NK.1">LTLB_WFF</a></span>)</span></span><a href="ltlaxio3.html#K11" title="LTLAXIO3:func.11">]</a></span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="ltlaxio4.html#K3" title="LTLAXIO4:func.3">^</a> </span><br/>

<a NAME="E3:21"/><span class="kw">then </span><span class="lab"><font color="Green" title="E13">A3</font></span>: 
<font color="Maroon" title="c5">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="ltlaxio1.html#K3" title="LTLAXIO1:func.3">TVERUM</a> <a href="ltlaxio1.html#K4" title="LTLAXIO1:func.4">'&amp;&amp;'</a> <a href="ltlaxio1.html#K3" title="LTLAXIO1:func.3">TVERUM</a>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D1" onmouseover="rs('tarski/D1')" onmouseout="rh()">TARSKI:def 1</a></span>;<br/>
<a NAME="E4:21"/>
<span class="p1"><a href="ltlaxio3.html#K11" title="LTLAXIO3:func.11">[</a><span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K6" title="FINSEQ_1:func.6">&lt;*&gt;</a> <a href="ltlaxio1.html#NK1" title="LTLAXIO1:NK.1">LTLB_WFF</a></span>)</span>,<span class="p2">(<span class="default"><a href="finseq_1.html#K6" title="FINSEQ_1:func.6">&lt;*&gt;</a> <a href="ltlaxio1.html#NK1" title="LTLAXIO1:NK.1">LTLB_WFF</a></span>)</span></span><a href="ltlaxio3.html#K11" title="LTLAXIO3:func.11">]</a></span> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2"><a href="ltlaxio3.html#K11" title="LTLAXIO3:func.11">[</a><span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K6" title="FINSEQ_1:func.6">&lt;*&gt;</a> <a href="ltlaxio1.html#NK1" title="LTLAXIO1:NK.1">LTLB_WFF</a></span>)</span>,<span class="p3">(<span class="default"><a href="finseq_1.html#K6" title="FINSEQ_1:func.6">&lt;*&gt;</a> <a href="ltlaxio1.html#NK1" title="LTLAXIO1:NK.1">LTLB_WFF</a></span>)</span></span><a href="ltlaxio3.html#K11" title="LTLAXIO3:func.11">]</a></span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D1" onmouseover="rs('tarski/D1')" onmouseout="rh()">TARSKI:def 1</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:21"/>
<font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2"><a href="ltlaxio3.html#K11" title="LTLAXIO3:func.11">[</a><span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K6" title="FINSEQ_1:func.6">&lt;*&gt;</a> <a href="ltlaxio1.html#NK1" title="LTLAXIO1:NK.1">LTLB_WFF</a></span>)</span>,<span class="p3">(<span class="default"><a href="finseq_1.html#K6" title="FINSEQ_1:func.6">&lt;*&gt;</a> <a href="ltlaxio1.html#NK1" title="LTLAXIO1:NK.1">LTLB_WFF</a></span>)</span></span><a href="ltlaxio3.html#K11" title="LTLAXIO3:func.11">]</a></span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="ltlaxio4.html#K3" title="LTLAXIO4:func.3">^</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="ltlaxio3.html#T27" onmouseover="rs('ltlaxio3/T27')" onmouseout="rh()">LTLAXIO3:27</a>, <a class="txt" href="#E3:21"><span class="lab"><font color="Green" title="E13">A3</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>
