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<div class="add">

<b>let </b><font color="Maroon" title="c1">H</font> be   <a href="modelc_2.html#NM2" title="MODELC_2:NM.2">LTL-formula</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">H</font> is <a href="modelc_2.html#V2" title="MODELC_2:attr.2">atomic</a> or <font color="Maroon" title="c1">H</font> is <a href="modelc_2.html#V3" title="MODELC_2:attr.3">negative</a> or <font color="Maroon" title="c1">H</font> is <a href="modelc_2.html#V4" title="MODELC_2:attr.4">conjunctive</a> or <font color="Maroon" title="c1">H</font> is <a href="modelc_2.html#V5" title="MODELC_2:attr.5">disjunctive</a> or <font color="Maroon" title="c1">H</font> is <a href="modelc_2.html#V6" title="MODELC_2:attr.6">next</a> or <font color="Maroon" title="c1">H</font> is <a href="modelc_2.html#V7" title="MODELC_2:attr.7">Until</a> or <font color="Maroon" title="c1">H</font> is <a href="modelc_2.html#V8" title="MODELC_2:attr.8">Release</a> )</span><br/>

<a NAME="E1:16"/><i><font color="Green" title="E15">A1</font></i>: 
<font color="Maroon" title="c1">H</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="modelc_2.html#K9" title="MODELC_2:func.9">LTL_WFF</a> 
 
<b>by </b><i><a class="ref" href="modelc_2.html#D10" target="_self" title="MODELC_2:def.10">Def13</a></i>;<br/>
<b>assume </b><a NAME="E2:16"/><i><font color="Green" title="E16">A2</font></i>: 
( not <font color="Maroon" title="c1">H</font> is <a href="modelc_2.html#V2" title="MODELC_2:attr.2">atomic</a> &amp; not <font color="Maroon" title="c1">H</font> is <a href="modelc_2.html#V3" title="MODELC_2:attr.3">negative</a> &amp; not <font color="Maroon" title="c1">H</font> is <a href="modelc_2.html#V4" title="MODELC_2:attr.4">conjunctive</a> &amp; not <font color="Maroon" title="c1">H</font> is <a href="modelc_2.html#V5" title="MODELC_2:attr.5">disjunctive</a> &amp; not <font color="Maroon" title="c1">H</font> is <a href="modelc_2.html#V6" title="MODELC_2:attr.6">next</a> &amp; not <font color="Maroon" title="c1">H</font> is <a href="modelc_2.html#V7" title="MODELC_2:attr.7">Until</a> &amp; not <font color="Maroon" title="c1">H</font> is <a href="modelc_2.html#V8" title="MODELC_2:attr.8">Release</a> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E3:16"/><i><font color="Green" title="E17">A3</font></i>: 
not <a href="modelc_2.html#K9" title="MODELC_2:func.9">LTL_WFF</a>  <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c1">H</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_1"><b>proof </b></a><div class="add">

<a NAME="E1:16_1"/><i><font color="Green" title="E18">A4</font></i>: 
 <a href="modelc_2.html#K2" title="MODELC_2:func.2">atom.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_2.html#K9" title="MODELC_2:func.9">LTL_WFF</a> 
 
<b>by </b><i><a class="ref" href="modelc_2.html#D9" target="_self" title="MODELC_2:def.9">Def12</a></i>;<br/>
<a NAME="E2:16_1"/>
 <a href="modelc_2.html#K2" title="MODELC_2:func.2">atom.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c1">H</font>
 
<b>by </b><i><a class="txt" href="modelc_2.html#E2:16"><i><font color="Green" title="E16">A2</font></i></a>, <a class="ref" href="modelc_2.html#D11" target="_self" title="MODELC_2:def.11">Def14</a></i>;<br/>
<a NAME="E3:16_1"/><b>then </b>
not  <a href="modelc_2.html#K2" title="MODELC_2:func.2">atom.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c1">H</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<b>by </b><i><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/>
<b>hence </b><a NAME="E4:16_1"/>
not <a href="modelc_2.html#K9" title="MODELC_2:func.9">LTL_WFF</a>  <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c1">H</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>
 <b>by </b><i><a class="txt" href="modelc_2.html#E1:16_1"><i><font color="Green" title="E18">A4</font></i></a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<a NAME="E4:16"/><i><font color="Green" title="E18">A5</font></i>: 
for <font color="Olive" title="b1">a</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <a href="modelc_2.html#K9" title="MODELC_2:func.9">LTL_WFF</a>  <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c1">H</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> holds <br/><font color="Olive" title="b1">a</font> is    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> 
 
<b>by </b><i><a class="ref" href="modelc_2.html#D9" target="_self" title="MODELC_2:def.9">Def12</a></i>;<br/>
<div><i><font color="Green" title="E19">A6</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="16_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c2">n</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="modelc_2.html#K2" title="MODELC_2:func.2">atom.</a> <font color="Maroon" title="c2">n</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <a href="modelc_2.html#K9" title="MODELC_2:func.9">LTL_WFF</a>  <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c1">H</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span><br/><a NAME="E1:16_2"/><i><font color="Green" title="E20">A7</font></i>: 
 <a href="modelc_2.html#K2" title="MODELC_2:func.2">atom.</a> <font color="Maroon" title="c2">n</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_2.html#K9" title="MODELC_2:func.9">LTL_WFF</a> 
 <b>by </b><i><a class="ref" href="modelc_2.html#D9" target="_self" title="MODELC_2:def.9">Def12</a></i>;<br/><a NAME="E2:16_2"/>
 <a href="modelc_2.html#K2" title="MODELC_2:func.2">atom.</a> <font color="Maroon" title="c2">n</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c1">H</font>
 <b>by </b><i><a class="txt" href="modelc_2.html#E2:16"><i><font color="Green" title="E16">A2</font></i></a>, <a class="ref" href="modelc_2.html#D11" target="_self" title="MODELC_2:def.11">Def14</a></i>;<br/><a NAME="E3:16_2"/><b>then </b>
not  <a href="modelc_2.html#K2" title="MODELC_2:func.2">atom.</a> <font color="Maroon" title="c2">n</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c1">H</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <b>by </b><i><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/><b>hence </b><a NAME="E4:16_2"/>
 <a href="modelc_2.html#K2" title="MODELC_2:func.2">atom.</a> <font color="Maroon" title="c2">n</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <a href="modelc_2.html#K9" title="MODELC_2:func.9">LTL_WFF</a>  <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c1">H</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <b>by </b><i><a class="txt" href="modelc_2.html#E1:16_2"><i><font color="Green" title="E20">A7</font></i></a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<div><i><font color="Green" title="E20">A8</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="16_3"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c2">p</font> be    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c2">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <a href="modelc_2.html#K9" title="MODELC_2:func.9">LTL_WFF</a>  <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c1">H</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> implies  <a href="modelc_2.html#K3" title="MODELC_2:func.3">'not'</a> <font color="Maroon" title="c2">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <a href="modelc_2.html#K9" title="MODELC_2:func.9">LTL_WFF</a>  <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c1">H</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> )</span><br/><b>assume </b><a NAME="E1:16_3"/><i><font color="Green" title="E21">A9</font></i>: 
<font color="Maroon" title="c2">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <a href="modelc_2.html#K9" title="MODELC_2:func.9">LTL_WFF</a>  <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c1">H</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="modelc_2.html#K3" title="MODELC_2:func.3">'not'</a> <font color="Maroon" title="c2">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <a href="modelc_2.html#K9" title="MODELC_2:func.9">LTL_WFF</a>  <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c1">H</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span><br/><a NAME="E2:16_3"/><b>then </b><i><font color="Green" title="E22">A10</font></i>: 
 <a href="modelc_2.html#K3" title="MODELC_2:func.3">'not'</a> <font color="Maroon" title="c2">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_2.html#K9" title="MODELC_2:func.9">LTL_WFF</a> 
 <b>by </b><i><a class="ref" href="modelc_2.html#D9" target="_self" title="MODELC_2:def.9">Def12</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c3">H1</font> = <font color="Maroon" title="c2">p</font> as   <a href="modelc_2.html#NM2" title="MODELC_2:NM.2">LTL-formula</a> <b>by </b><i><a class="txt" href="modelc_2.html#E1:16_3"><i><font color="Green" title="E21">A9</font></i></a>, <a class="ref" href="modelc_2.html#D10" target="_self" title="MODELC_2:def.10">Def13</a></i>;<br/><a NAME="E4:16_3"/>
 <a href="modelc_2.html#K3" title="MODELC_2:func.3">'not'</a> <font color="Maroon" title="c3">H1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c1">H</font>
 <b>by </b><i><a class="txt" href="modelc_2.html#E2:16"><i><font color="Green" title="E16">A2</font></i></a>, <a class="ref" href="modelc_2.html#D12" target="_self" title="MODELC_2:def.12">Def15</a></i>;<br/><a NAME="E5:16_3"/><b>then </b>
not  <a href="modelc_2.html#K3" title="MODELC_2:func.3">'not'</a> <font color="Maroon" title="c2">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c1">H</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <b>by </b><i><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/><b>hence </b><a NAME="E6:16_3"/>
 <a href="modelc_2.html#K3" title="MODELC_2:func.3">'not'</a> <font color="Maroon" title="c2">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <a href="modelc_2.html#K9" title="MODELC_2:func.9">LTL_WFF</a>  <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c1">H</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <b>by </b><i><a class="txt" href="modelc_2.html#E2:16_3"><i><font color="Green" title="E22">A10</font></i></a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<div><i><font color="Green" title="E21">A11</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="16_4"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c2">p</font>, <font color="Maroon" title="c3">q</font> be    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c2">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <a href="modelc_2.html#K9" title="MODELC_2:func.9">LTL_WFF</a>  <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c1">H</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> &amp; <font color="Maroon" title="c3">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <a href="modelc_2.html#K9" title="MODELC_2:func.9">LTL_WFF</a>  <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c1">H</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> implies <font color="Maroon" title="c2">p</font> <a href="modelc_2.html#K4" title="MODELC_2:func.4">'&amp;'</a> <font color="Maroon" title="c3">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <a href="modelc_2.html#K9" title="MODELC_2:func.9">LTL_WFF</a>  <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c1">H</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> )</span><br/><b>assume </b><a NAME="E1:16_4"/><i><font color="Green" title="E22">A12</font></i>: 
( <font color="Maroon" title="c2">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <a href="modelc_2.html#K9" title="MODELC_2:func.9">LTL_WFF</a>  <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c1">H</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> &amp; <font color="Maroon" title="c3">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <a href="modelc_2.html#K9" title="MODELC_2:func.9">LTL_WFF</a>  <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c1">H</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">p</font> <a href="modelc_2.html#K4" title="MODELC_2:func.4">'&amp;'</a> <font color="Maroon" title="c3">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <a href="modelc_2.html#K9" title="MODELC_2:func.9">LTL_WFF</a>  <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c1">H</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span><br/><a NAME="E2:16_4"/><b>then </b><i><font color="Green" title="E23">A13</font></i>: 
<font color="Maroon" title="c2">p</font> <a href="modelc_2.html#K4" title="MODELC_2:func.4">'&amp;'</a> <font color="Maroon" title="c3">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_2.html#K9" title="MODELC_2:func.9">LTL_WFF</a> 
 <b>by </b><i><a class="ref" href="modelc_2.html#D9" target="_self" title="MODELC_2:def.9">Def12</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c4">F</font> = <font color="Maroon" title="c2">p</font>, <font color="Maroon" title="c5">G</font> = <font color="Maroon" title="c3">q</font> as   <a href="modelc_2.html#NM2" title="MODELC_2:NM.2">LTL-formula</a> <b>by </b><i><a class="txt" href="modelc_2.html#E1:16_4"><i><font color="Green" title="E22">A12</font></i></a>, <a class="ref" href="modelc_2.html#D10" target="_self" title="MODELC_2:def.10">Def13</a></i>;<br/><a NAME="E4:16_4"/>
<font color="Maroon" title="c4">F</font> <a href="modelc_2.html#K4" title="MODELC_2:func.4">'&amp;'</a> <font color="Maroon" title="c5">G</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c1">H</font>
 <b>by </b><i><a class="txt" href="modelc_2.html#E2:16"><i><font color="Green" title="E16">A2</font></i></a>, <a class="ref" href="modelc_2.html#D13" target="_self" title="MODELC_2:def.13">Def16</a></i>;<br/><a NAME="E5:16_4"/><b>then </b>
not <font color="Maroon" title="c2">p</font> <a href="modelc_2.html#K4" title="MODELC_2:func.4">'&amp;'</a> <font color="Maroon" title="c3">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c1">H</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <b>by </b><i><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/><b>hence </b><a NAME="E6:16_4"/>
<font color="Maroon" title="c2">p</font> <a href="modelc_2.html#K4" title="MODELC_2:func.4">'&amp;'</a> <font color="Maroon" title="c3">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <a href="modelc_2.html#K9" title="MODELC_2:func.9">LTL_WFF</a>  <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c1">H</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <b>by </b><i><a class="txt" href="modelc_2.html#E2:16_4"><i><font color="Green" title="E23">A13</font></i></a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<div><i><font color="Green" title="E22">A14</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="16_5"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c2">p</font>, <font color="Maroon" title="c3">q</font> be    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c2">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <a href="modelc_2.html#K9" title="MODELC_2:func.9">LTL_WFF</a>  <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c1">H</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> &amp; <font color="Maroon" title="c3">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <a href="modelc_2.html#K9" title="MODELC_2:func.9">LTL_WFF</a>  <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c1">H</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> implies <font color="Maroon" title="c2">p</font> <a href="modelc_2.html#K5" title="MODELC_2:func.5">'or'</a> <font color="Maroon" title="c3">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <a href="modelc_2.html#K9" title="MODELC_2:func.9">LTL_WFF</a>  <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c1">H</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> )</span><br/><b>assume </b><a NAME="E1:16_5"/><i><font color="Green" title="E23">A15</font></i>: 
( <font color="Maroon" title="c2">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <a href="modelc_2.html#K9" title="MODELC_2:func.9">LTL_WFF</a>  <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c1">H</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> &amp; <font color="Maroon" title="c3">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <a href="modelc_2.html#K9" title="MODELC_2:func.9">LTL_WFF</a>  <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c1">H</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">p</font> <a href="modelc_2.html#K5" title="MODELC_2:func.5">'or'</a> <font color="Maroon" title="c3">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <a href="modelc_2.html#K9" title="MODELC_2:func.9">LTL_WFF</a>  <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c1">H</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span><br/><a NAME="E2:16_5"/><b>then </b><i><font color="Green" title="E24">A16</font></i>: 
<font color="Maroon" title="c2">p</font> <a href="modelc_2.html#K5" title="MODELC_2:func.5">'or'</a> <font color="Maroon" title="c3">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_2.html#K9" title="MODELC_2:func.9">LTL_WFF</a> 
 <b>by </b><i><a class="ref" href="modelc_2.html#D9" target="_self" title="MODELC_2:def.9">Def12</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c4">F</font> = <font color="Maroon" title="c2">p</font>, <font color="Maroon" title="c5">G</font> = <font color="Maroon" title="c3">q</font> as   <a href="modelc_2.html#NM2" title="MODELC_2:NM.2">LTL-formula</a> <b>by </b><i><a class="txt" href="modelc_2.html#E1:16_5"><i><font color="Green" title="E23">A15</font></i></a>, <a class="ref" href="modelc_2.html#D10" target="_self" title="MODELC_2:def.10">Def13</a></i>;<br/><a NAME="E4:16_5"/>
<font color="Maroon" title="c4">F</font> <a href="modelc_2.html#K5" title="MODELC_2:func.5">'or'</a> <font color="Maroon" title="c5">G</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c1">H</font>
 <b>by </b><i><a class="txt" href="modelc_2.html#E2:16"><i><font color="Green" title="E16">A2</font></i></a>, <a class="ref" href="modelc_2.html#D14" target="_self" title="MODELC_2:def.14">Def17</a></i>;<br/><a NAME="E5:16_5"/><b>then </b>
not <font color="Maroon" title="c2">p</font> <a href="modelc_2.html#K5" title="MODELC_2:func.5">'or'</a> <font color="Maroon" title="c3">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c1">H</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <b>by </b><i><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/><b>hence </b><a NAME="E6:16_5"/>
<font color="Maroon" title="c2">p</font> <a href="modelc_2.html#K5" title="MODELC_2:func.5">'or'</a> <font color="Maroon" title="c3">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <a href="modelc_2.html#K9" title="MODELC_2:func.9">LTL_WFF</a>  <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c1">H</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <b>by </b><i><a class="txt" href="modelc_2.html#E2:16_5"><i><font color="Green" title="E24">A16</font></i></a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<div><i><font color="Green" title="E23">A17</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="16_6"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c2">p</font> be    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c2">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <a href="modelc_2.html#K9" title="MODELC_2:func.9">LTL_WFF</a>  <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c1">H</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> implies  <a href="modelc_2.html#K6" title="MODELC_2:func.6">'X'</a> <font color="Maroon" title="c2">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <a href="modelc_2.html#K9" title="MODELC_2:func.9">LTL_WFF</a>  <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c1">H</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> )</span><br/><b>assume </b><a NAME="E1:16_6"/><i><font color="Green" title="E24">A18</font></i>: 
<font color="Maroon" title="c2">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <a href="modelc_2.html#K9" title="MODELC_2:func.9">LTL_WFF</a>  <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c1">H</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="modelc_2.html#K6" title="MODELC_2:func.6">'X'</a> <font color="Maroon" title="c2">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <a href="modelc_2.html#K9" title="MODELC_2:func.9">LTL_WFF</a>  <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c1">H</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span><br/><a NAME="E2:16_6"/><b>then </b><i><font color="Green" title="E25">A19</font></i>: 
 <a href="modelc_2.html#K6" title="MODELC_2:func.6">'X'</a> <font color="Maroon" title="c2">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_2.html#K9" title="MODELC_2:func.9">LTL_WFF</a> 
 <b>by </b><i><a class="ref" href="modelc_2.html#D9" target="_self" title="MODELC_2:def.9">Def12</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c3">H1</font> = <font color="Maroon" title="c2">p</font> as   <a href="modelc_2.html#NM2" title="MODELC_2:NM.2">LTL-formula</a> <b>by </b><i><a class="txt" href="modelc_2.html#E1:16_6"><i><font color="Green" title="E24">A18</font></i></a>, <a class="ref" href="modelc_2.html#D10" target="_self" title="MODELC_2:def.10">Def13</a></i>;<br/><a NAME="E4:16_6"/>
 <a href="modelc_2.html#K6" title="MODELC_2:func.6">'X'</a> <font color="Maroon" title="c3">H1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c1">H</font>
 <b>by </b><i><a class="txt" href="modelc_2.html#E2:16"><i><font color="Green" title="E16">A2</font></i></a>, <a class="ref" href="modelc_2.html#D15" target="_self" title="MODELC_2:def.15">Def18</a></i>;<br/><a NAME="E5:16_6"/><b>then </b>
not  <a href="modelc_2.html#K6" title="MODELC_2:func.6">'X'</a> <font color="Maroon" title="c2">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c1">H</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <b>by </b><i><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/><b>hence </b><a NAME="E6:16_6"/>
 <a href="modelc_2.html#K6" title="MODELC_2:func.6">'X'</a> <font color="Maroon" title="c2">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <a href="modelc_2.html#K9" title="MODELC_2:func.9">LTL_WFF</a>  <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c1">H</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <b>by </b><i><a class="txt" href="modelc_2.html#E2:16_6"><i><font color="Green" title="E25">A19</font></i></a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<div><i><font color="Green" title="E24">A20</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="16_7"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c2">p</font>, <font color="Maroon" title="c3">q</font> be    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c2">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <a href="modelc_2.html#K9" title="MODELC_2:func.9">LTL_WFF</a>  <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c1">H</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> &amp; <font color="Maroon" title="c3">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <a href="modelc_2.html#K9" title="MODELC_2:func.9">LTL_WFF</a>  <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c1">H</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> implies <font color="Maroon" title="c2">p</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c3">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <a href="modelc_2.html#K9" title="MODELC_2:func.9">LTL_WFF</a>  <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c1">H</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> )</span><br/><b>assume </b><a NAME="E1:16_7"/><i><font color="Green" title="E25">A21</font></i>: 
( <font color="Maroon" title="c2">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <a href="modelc_2.html#K9" title="MODELC_2:func.9">LTL_WFF</a>  <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c1">H</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> &amp; <font color="Maroon" title="c3">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <a href="modelc_2.html#K9" title="MODELC_2:func.9">LTL_WFF</a>  <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c1">H</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">p</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c3">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <a href="modelc_2.html#K9" title="MODELC_2:func.9">LTL_WFF</a>  <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c1">H</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span><br/><a NAME="E2:16_7"/><b>then </b><i><font color="Green" title="E26">A22</font></i>: 
<font color="Maroon" title="c2">p</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c3">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_2.html#K9" title="MODELC_2:func.9">LTL_WFF</a> 
 <b>by </b><i><a class="ref" href="modelc_2.html#D9" target="_self" title="MODELC_2:def.9">Def12</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c4">F</font> = <font color="Maroon" title="c2">p</font>, <font color="Maroon" title="c5">G</font> = <font color="Maroon" title="c3">q</font> as   <a href="modelc_2.html#NM2" title="MODELC_2:NM.2">LTL-formula</a> <b>by </b><i><a class="txt" href="modelc_2.html#E1:16_7"><i><font color="Green" title="E25">A21</font></i></a>, <a class="ref" href="modelc_2.html#D10" target="_self" title="MODELC_2:def.10">Def13</a></i>;<br/><a NAME="E4:16_7"/>
<font color="Maroon" title="c4">F</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c5">G</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c1">H</font>
 <b>by </b><i><a class="txt" href="modelc_2.html#E2:16"><i><font color="Green" title="E16">A2</font></i></a>, <a class="ref" href="modelc_2.html#D16" target="_self" title="MODELC_2:def.16">Def19</a></i>;<br/><a NAME="E5:16_7"/><b>then </b>
not <font color="Maroon" title="c2">p</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c3">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c1">H</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <b>by </b><i><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/><b>hence </b><a NAME="E6:16_7"/>
<font color="Maroon" title="c2">p</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c3">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <a href="modelc_2.html#K9" title="MODELC_2:func.9">LTL_WFF</a>  <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c1">H</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <b>by </b><i><a class="txt" href="modelc_2.html#E2:16_7"><i><font color="Green" title="E26">A22</font></i></a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_8"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c2">p</font>, <font color="Maroon" title="c3">q</font> be    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c2">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <a href="modelc_2.html#K9" title="MODELC_2:func.9">LTL_WFF</a>  <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c1">H</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> &amp; <font color="Maroon" title="c3">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <a href="modelc_2.html#K9" title="MODELC_2:func.9">LTL_WFF</a>  <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c1">H</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> implies <font color="Maroon" title="c2">p</font> <a href="modelc_2.html#K8" title="MODELC_2:func.8">'R'</a> <font color="Maroon" title="c3">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <a href="modelc_2.html#K9" title="MODELC_2:func.9">LTL_WFF</a>  <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c1">H</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> )</span><br/><b>assume </b><a NAME="E1:16_8"/><i><font color="Green" title="E25">A23</font></i>: 
( <font color="Maroon" title="c2">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <a href="modelc_2.html#K9" title="MODELC_2:func.9">LTL_WFF</a>  <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c1">H</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> &amp; <font color="Maroon" title="c3">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <a href="modelc_2.html#K9" title="MODELC_2:func.9">LTL_WFF</a>  <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c1">H</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">p</font> <a href="modelc_2.html#K8" title="MODELC_2:func.8">'R'</a> <font color="Maroon" title="c3">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <a href="modelc_2.html#K9" title="MODELC_2:func.9">LTL_WFF</a>  <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c1">H</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span><br/><a NAME="E2:16_8"/><b>then </b><i><font color="Green" title="E26">A24</font></i>: 
<font color="Maroon" title="c2">p</font> <a href="modelc_2.html#K8" title="MODELC_2:func.8">'R'</a> <font color="Maroon" title="c3">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_2.html#K9" title="MODELC_2:func.9">LTL_WFF</a> 
 <b>by </b><i><a class="ref" href="modelc_2.html#D9" target="_self" title="MODELC_2:def.9">Def12</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c4">F</font> = <font color="Maroon" title="c2">p</font>, <font color="Maroon" title="c5">G</font> = <font color="Maroon" title="c3">q</font> as   <a href="modelc_2.html#NM2" title="MODELC_2:NM.2">LTL-formula</a> <b>by </b><i><a class="txt" href="modelc_2.html#E1:16_8"><i><font color="Green" title="E25">A23</font></i></a>, <a class="ref" href="modelc_2.html#D10" target="_self" title="MODELC_2:def.10">Def13</a></i>;<br/><a NAME="E4:16_8"/>
<font color="Maroon" title="c4">F</font> <a href="modelc_2.html#K8" title="MODELC_2:func.8">'R'</a> <font color="Maroon" title="c5">G</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c1">H</font>
 <b>by </b><i><a class="txt" href="modelc_2.html#E2:16"><i><font color="Green" title="E16">A2</font></i></a>, <a class="ref" href="modelc_2.html#D17" target="_self" title="MODELC_2:def.17">Def1901</a></i>;<br/><a NAME="E5:16_8"/><b>then </b>
not <font color="Maroon" title="c2">p</font> <a href="modelc_2.html#K8" title="MODELC_2:func.8">'R'</a> <font color="Maroon" title="c3">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c1">H</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <b>by </b><i><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/><b>hence </b><a NAME="E6:16_8"/>
<font color="Maroon" title="c2">p</font> <a href="modelc_2.html#K8" title="MODELC_2:func.8">'R'</a> <font color="Maroon" title="c3">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <a href="modelc_2.html#K9" title="MODELC_2:func.9">LTL_WFF</a>  <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c1">H</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <b>by </b><i><a class="txt" href="modelc_2.html#E2:16_8"><i><font color="Green" title="E26">A24</font></i></a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<a NAME="E12:16"/><b>then </b>
 <a href="modelc_2.html#K9" title="MODELC_2:func.9">LTL_WFF</a>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <a href="modelc_2.html#K9" title="MODELC_2:func.9">LTL_WFF</a>  <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c1">H</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<b>by </b><i><a class="txt" href="modelc_2.html#E3:16"><i><font color="Green" title="E17">A3</font></i></a>, <a class="txt" href="modelc_2.html#E4:16"><i><font color="Green" title="E18">A5</font></i></a>, <a class="txt" href="modelc_2.html#E5:16"><i><font color="Green" title="E19">A6</font></i></a>, <a class="txt" href="modelc_2.html#E6:16"><i><font color="Green" title="E20">A8</font></i></a>, <a class="txt" href="modelc_2.html#E7:16"><i><font color="Green" title="E21">A11</font></i></a>, <a class="txt" href="modelc_2.html#E8:16"><i><font color="Green" title="E22">A14</font></i></a>, <a class="txt" href="modelc_2.html#E9:16"><i><font color="Green" title="E23">A17</font></i></a>, <a class="txt" href="modelc_2.html#E10:16"><i><font color="Green" title="E24">A20</font></i></a>, <a class="ref" href="modelc_2.html#D9" target="_self" title="MODELC_2:def.9">Def12</a></i>;<br/>
<a NAME="E13:16"/><b>then </b>
<font color="Maroon" title="c1">H</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <a href="modelc_2.html#K9" title="MODELC_2:func.9">LTL_WFF</a>  <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c1">H</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<b>by </b><i><a class="txt" href="modelc_2.html#E1:16"><i><font color="Green" title="E15">A1</font></i></a>, <a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a></i>;<br/>
<a NAME="E14:16"/><b>then </b>
( not <font color="Maroon" title="c1">H</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c1">H</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> &amp; <font color="Maroon" title="c1">H</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c1">H</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> )
 
<b>by </b><i><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></i>;<br/>
<b>hence </b><a NAME="E15:16"/>
contradiction
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
