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<span class="kw">let </span><font color="Maroon" title="c1">H</font> be   <a href="modelc_1.html#NM1" title="MODELC_1:NM.1">CTL-formula</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">H</font> is  <a href="modelc_1.html#V2" title="MODELC_1:attr.2">atomic</a>  or <font color="Maroon" title="c1">H</font> is  <a href="modelc_1.html#V3" title="MODELC_1:attr.3">negative</a>  or <font color="Maroon" title="c1">H</font> is  <a href="modelc_1.html#V4" title="MODELC_1:attr.4">conjunctive</a>  or <font color="Maroon" title="c1">H</font> is  <a href="modelc_1.html#V5" title="MODELC_1:attr.5">ExistNext</a>  or <font color="Maroon" title="c1">H</font> is  <a href="modelc_1.html#V6" title="MODELC_1:attr.6">ExistGlobal</a>  or <font color="Maroon" title="c1">H</font> is  <a href="modelc_1.html#V7" title="MODELC_1:attr.7">ExistUntill</a>  )</span><br/>

<a NAME="E1:21"/><span class="lab"><font color="Green" title="E18">A1</font></span>: 
<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_1.html#K13" title="MODELC_1:func.13">CTL_WFF</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="modelc_1.html#D13" target="_self" title="MODELC_1:def.13">Def13</a></span>;<br/>
<span class="kw">assume </span><a NAME="E2:21"/><span class="lab"><font color="Green" title="E19">A2</font></span>: 
( not <font color="Maroon" title="c1">H</font> is  <a href="modelc_1.html#V2" title="MODELC_1:attr.2">atomic</a>  &amp; not <font color="Maroon" title="c1">H</font> is  <a href="modelc_1.html#V3" title="MODELC_1:attr.3">negative</a>  &amp; not <font color="Maroon" title="c1">H</font> is  <a href="modelc_1.html#V4" title="MODELC_1:attr.4">conjunctive</a>  &amp; not <font color="Maroon" title="c1">H</font> is  <a href="modelc_1.html#V5" title="MODELC_1:attr.5">ExistNext</a>  &amp; not <font color="Maroon" title="c1">H</font> is  <a href="modelc_1.html#V6" title="MODELC_1:attr.6">ExistGlobal</a>  &amp; not <font color="Maroon" title="c1">H</font> is  <a href="modelc_1.html#V7" title="MODELC_1:attr.7">ExistUntill</a>  )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E3:21"/><span class="kw">then </span>
 <a href="modelc_1.html#K7" title="MODELC_1:func.7">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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="modelc_1.html#D14" target="_self" title="MODELC_1:def.14">Def14</a></span>;<br/>
<a NAME="E4:21"/><span class="kw">then </span><span class="lab"><font color="Green" title="E20">A3</font></span>: 
not  <a href="modelc_1.html#K7" title="MODELC_1:func.7">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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/>
<div><span class="lab"><font color="Green" title="E21">A4</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="21_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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_1.html#K13" title="MODELC_1:func.13">CTL_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_1.html#K11" title="MODELC_1:func.11">EG</a> <font color="Maroon" title="c2">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <a href="modelc_1.html#K13" title="MODELC_1:func.13">CTL_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/><span class="kw">assume </span><a NAME="E1:21_1"/><span class="lab"><font color="Green" title="E22">A5</font></span>: 
<font color="Maroon" title="c2">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <a href="modelc_1.html#K13" title="MODELC_1:func.13">CTL_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:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="modelc_1.html#K11" title="MODELC_1:func.11">EG</a> <font color="Maroon" title="c2">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <a href="modelc_1.html#K13" title="MODELC_1:func.13">CTL_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/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c3">H1</font> = <font color="Maroon" title="c2">p</font> as   <a href="modelc_1.html#NM1" title="MODELC_1:NM.1">CTL-formula</a> <span class="kw">by</span> <span class="lab"><a class="ref" href="modelc_1.html#D13" target="_self" title="MODELC_1:def.13">Def13</a></span>;<br/><a NAME="E3:21_1"/>
 <a href="modelc_1.html#K11" title="MODELC_1:func.11">EG</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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:21"><span class="lab"><font color="Green" title="E19">A2</font></span></a>, <a class="ref" href="modelc_1.html#D18" target="_self" title="MODELC_1:def.18">Def18</a></span>;<br/><a NAME="E4:21_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E23">A6</font></span>: 
not  <a href="modelc_1.html#K11" title="MODELC_1:func.11">EG</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>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/><a NAME="E5:21_1"/>
 <a href="modelc_1.html#K11" title="MODELC_1:func.11">EG</a> <font color="Maroon" title="c2">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_1.html#K13" title="MODELC_1:func.13">CTL_WFF</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:21_1"><span class="lab"><font color="Green" title="E22">A5</font></span></a>, <a class="ref" href="modelc_1.html#D12" target="_self" title="MODELC_1:def.12">Def12</a></span>;<br/><span class="kw">hence </span><a NAME="E6:21_1"/>
 <a href="modelc_1.html#K11" title="MODELC_1:func.11">EG</a> <font color="Maroon" title="c2">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <a href="modelc_1.html#K13" title="MODELC_1:func.13">CTL_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 class="kw">by</span> <span class="lab"><a class="txt" href="#E4:21_1"><span class="lab"><font color="Green" title="E23">A6</font></span></a>, <a class="ref" href="xboole_0.html#D5" title="XBOOLE_0:def.5">XBOOLE_0:def 5</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<div><span class="lab"><font color="Green" title="E22">A7</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="21_2"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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_1.html#K13" title="MODELC_1:func.13">CTL_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_1.html#K10" title="MODELC_1:func.10">EX</a> <font color="Maroon" title="c2">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <a href="modelc_1.html#K13" title="MODELC_1:func.13">CTL_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/><span class="kw">assume </span><a NAME="E1:21_2"/><span class="lab"><font color="Green" title="E23">A8</font></span>: 
<font color="Maroon" title="c2">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <a href="modelc_1.html#K13" title="MODELC_1:func.13">CTL_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:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="modelc_1.html#K10" title="MODELC_1:func.10">EX</a> <font color="Maroon" title="c2">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <a href="modelc_1.html#K13" title="MODELC_1:func.13">CTL_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/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c3">H1</font> = <font color="Maroon" title="c2">p</font> as   <a href="modelc_1.html#NM1" title="MODELC_1:NM.1">CTL-formula</a> <span class="kw">by</span> <span class="lab"><a class="ref" href="modelc_1.html#D13" target="_self" title="MODELC_1:def.13">Def13</a></span>;<br/><a NAME="E3:21_2"/>
 <a href="modelc_1.html#K10" title="MODELC_1:func.10">EX</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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:21"><span class="lab"><font color="Green" title="E19">A2</font></span></a>, <a class="ref" href="modelc_1.html#D17" target="_self" title="MODELC_1:def.17">Def17</a></span>;<br/><a NAME="E4:21_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E24">A9</font></span>: 
not  <a href="modelc_1.html#K10" title="MODELC_1:func.10">EX</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>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/><a NAME="E5:21_2"/>
 <a href="modelc_1.html#K10" title="MODELC_1:func.10">EX</a> <font color="Maroon" title="c2">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_1.html#K13" title="MODELC_1:func.13">CTL_WFF</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:21_2"><span class="lab"><font color="Green" title="E23">A8</font></span></a>, <a class="ref" href="modelc_1.html#D12" target="_self" title="MODELC_1:def.12">Def12</a></span>;<br/><span class="kw">hence </span><a NAME="E6:21_2"/>
 <a href="modelc_1.html#K10" title="MODELC_1:func.10">EX</a> <font color="Maroon" title="c2">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <a href="modelc_1.html#K13" title="MODELC_1:func.13">CTL_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 class="kw">by</span> <span class="lab"><a class="txt" href="#E4:21_2"><span class="lab"><font color="Green" title="E24">A9</font></span></a>, <a class="ref" href="xboole_0.html#D5" title="XBOOLE_0:def.5">XBOOLE_0:def 5</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<div><span class="lab"><font color="Green" title="E23">A10</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="21_3"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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_1.html#K13" title="MODELC_1:func.13">CTL_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_1.html#K13" title="MODELC_1:func.13">CTL_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_1.html#K9" title="MODELC_1:func.9">'&amp;'</a> <font color="Maroon" title="c3">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <a href="modelc_1.html#K13" title="MODELC_1:func.13">CTL_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/><span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:21_3"/><span class="lab"><font color="Green" title="E24">A11</font></span>: 
<font color="Maroon" title="c2">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <a href="modelc_1.html#K13" title="MODELC_1:func.13">CTL_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 class="kw">and </span><br/><a NAME="E2:21_3"/><span class="lab"><font color="Green" title="E25">A12</font></span>: 
<font color="Maroon" title="c3">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <a href="modelc_1.html#K13" title="MODELC_1:func.13">CTL_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:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">p</font> <a href="modelc_1.html#K9" title="MODELC_1:func.9">'&amp;'</a> <font color="Maroon" title="c3">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <a href="modelc_1.html#K13" title="MODELC_1:func.13">CTL_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/><span class="kw">reconsider </span><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_1.html#NM1" title="MODELC_1:NM.1">CTL-formula</a> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:21_3"><span class="lab"><font color="Green" title="E24">A11</font></span></a>, <a class="txt" href="#E2:21_3"><span class="lab"><font color="Green" title="E25">A12</font></span></a>, <a class="ref" href="modelc_1.html#D13" target="_self" title="MODELC_1:def.13">Def13</a></span>;<br/><a NAME="E4:21_3"/>
<font color="Maroon" title="c4">F</font> <a href="modelc_1.html#K9" title="MODELC_1:func.9">'&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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:21"><span class="lab"><font color="Green" title="E19">A2</font></span></a>, <a class="ref" href="modelc_1.html#D16" target="_self" title="MODELC_1:def.16">Def16</a></span>;<br/><a NAME="E5:21_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E26">A13</font></span>: 
not <font color="Maroon" title="c2">p</font> <a href="modelc_1.html#K9" title="MODELC_1:func.9">'&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>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/><a NAME="E6:21_3"/>
<font color="Maroon" title="c2">p</font> <a href="modelc_1.html#K9" title="MODELC_1:func.9">'&amp;'</a> <font color="Maroon" title="c3">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_1.html#K13" title="MODELC_1:func.13">CTL_WFF</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:21_3"><span class="lab"><font color="Green" title="E24">A11</font></span></a>, <a class="txt" href="#E2:21_3"><span class="lab"><font color="Green" title="E25">A12</font></span></a>, <a class="ref" href="modelc_1.html#D12" target="_self" title="MODELC_1:def.12">Def12</a></span>;<br/><span class="kw">hence </span><a NAME="E7:21_3"/>
<font color="Maroon" title="c2">p</font> <a href="modelc_1.html#K9" title="MODELC_1:func.9">'&amp;'</a> <font color="Maroon" title="c3">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <a href="modelc_1.html#K13" title="MODELC_1:func.13">CTL_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 class="kw">by</span> <span class="lab"><a class="txt" href="#E5:21_3"><span class="lab"><font color="Green" title="E26">A13</font></span></a>, <a class="ref" href="xboole_0.html#D5" title="XBOOLE_0:def.5">XBOOLE_0:def 5</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<div><span class="lab"><font color="Green" title="E24">A14</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="21_4"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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_1.html#K13" title="MODELC_1:func.13">CTL_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_1.html#K8" title="MODELC_1:func.8">'not'</a> <font color="Maroon" title="c2">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <a href="modelc_1.html#K13" title="MODELC_1:func.13">CTL_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/><span class="kw">assume </span><a NAME="E1:21_4"/><span class="lab"><font color="Green" title="E25">A15</font></span>: 
<font color="Maroon" title="c2">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <a href="modelc_1.html#K13" title="MODELC_1:func.13">CTL_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:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="modelc_1.html#K8" title="MODELC_1:func.8">'not'</a> <font color="Maroon" title="c2">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <a href="modelc_1.html#K13" title="MODELC_1:func.13">CTL_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/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c3">H1</font> = <font color="Maroon" title="c2">p</font> as   <a href="modelc_1.html#NM1" title="MODELC_1:NM.1">CTL-formula</a> <span class="kw">by</span> <span class="lab"><a class="ref" href="modelc_1.html#D13" target="_self" title="MODELC_1:def.13">Def13</a></span>;<br/><a NAME="E3:21_4"/>
 <a href="modelc_1.html#K8" title="MODELC_1:func.8">'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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:21"><span class="lab"><font color="Green" title="E19">A2</font></span></a>, <a class="ref" href="modelc_1.html#D15" target="_self" title="MODELC_1:def.15">Def15</a></span>;<br/><a NAME="E4:21_4"/><span class="kw">then </span><span class="lab"><font color="Green" title="E26">A16</font></span>: 
not  <a href="modelc_1.html#K8" title="MODELC_1:func.8">'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>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/><a NAME="E5:21_4"/>
 <a href="modelc_1.html#K8" title="MODELC_1:func.8">'not'</a> <font color="Maroon" title="c2">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_1.html#K13" title="MODELC_1:func.13">CTL_WFF</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:21_4"><span class="lab"><font color="Green" title="E25">A15</font></span></a>, <a class="ref" href="modelc_1.html#D12" target="_self" title="MODELC_1:def.12">Def12</a></span>;<br/><span class="kw">hence </span><a NAME="E6:21_4"/>
 <a href="modelc_1.html#K8" title="MODELC_1:func.8">'not'</a> <font color="Maroon" title="c2">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <a href="modelc_1.html#K13" title="MODELC_1:func.13">CTL_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 class="kw">by</span> <span class="lab"><a class="txt" href="#E4:21_4"><span class="lab"><font color="Green" title="E26">A16</font></span></a>, <a class="ref" href="xboole_0.html#D5" title="XBOOLE_0:def.5">XBOOLE_0:def 5</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<div><span class="lab"><font color="Green" title="E25">A17</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="21_5"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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_1.html#K13" title="MODELC_1:func.13">CTL_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_1.html#K13" title="MODELC_1:func.13">CTL_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_1.html#K12" title="MODELC_1:func.12">EU</a> <font color="Maroon" title="c3">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <a href="modelc_1.html#K13" title="MODELC_1:func.13">CTL_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/><span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:21_5"/><span class="lab"><font color="Green" title="E26">A18</font></span>: 
<font color="Maroon" title="c2">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <a href="modelc_1.html#K13" title="MODELC_1:func.13">CTL_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 class="kw">and </span><br/><a NAME="E2:21_5"/><span class="lab"><font color="Green" title="E27">A19</font></span>: 
<font color="Maroon" title="c3">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <a href="modelc_1.html#K13" title="MODELC_1:func.13">CTL_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:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">p</font> <a href="modelc_1.html#K12" title="MODELC_1:func.12">EU</a> <font color="Maroon" title="c3">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <a href="modelc_1.html#K13" title="MODELC_1:func.13">CTL_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/><span class="kw">reconsider </span><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_1.html#NM1" title="MODELC_1:NM.1">CTL-formula</a> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:21_5"><span class="lab"><font color="Green" title="E26">A18</font></span></a>, <a class="txt" href="#E2:21_5"><span class="lab"><font color="Green" title="E27">A19</font></span></a>, <a class="ref" href="modelc_1.html#D13" target="_self" title="MODELC_1:def.13">Def13</a></span>;<br/><a NAME="E4:21_5"/>
<font color="Maroon" title="c4">F</font> <a href="modelc_1.html#K12" title="MODELC_1:func.12">EU</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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:21"><span class="lab"><font color="Green" title="E19">A2</font></span></a>, <a class="ref" href="modelc_1.html#D19" target="_self" title="MODELC_1:def.19">Def19</a></span>;<br/><a NAME="E5:21_5"/><span class="kw">then </span><span class="lab"><font color="Green" title="E28">A20</font></span>: 
not <font color="Maroon" title="c2">p</font> <a href="modelc_1.html#K12" title="MODELC_1:func.12">EU</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>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/><a NAME="E6:21_5"/>
<font color="Maroon" title="c2">p</font> <a href="modelc_1.html#K12" title="MODELC_1:func.12">EU</a> <font color="Maroon" title="c3">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_1.html#K13" title="MODELC_1:func.13">CTL_WFF</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:21_5"><span class="lab"><font color="Green" title="E26">A18</font></span></a>, <a class="txt" href="#E2:21_5"><span class="lab"><font color="Green" title="E27">A19</font></span></a>, <a class="ref" href="modelc_1.html#D12" target="_self" title="MODELC_1:def.12">Def12</a></span>;<br/><span class="kw">hence </span><a NAME="E7:21_5"/>
<font color="Maroon" title="c2">p</font> <a href="modelc_1.html#K12" title="MODELC_1:func.12">EU</a> <font color="Maroon" title="c3">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <a href="modelc_1.html#K13" title="MODELC_1:func.13">CTL_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 class="kw">by</span> <span class="lab"><a class="txt" href="#E5:21_5"><span class="lab"><font color="Green" title="E28">A20</font></span></a>, <a class="ref" href="xboole_0.html#D5" title="XBOOLE_0:def.5">XBOOLE_0:def 5</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<div><span class="lab"><font color="Green" title="E26">A21</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="21_6"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c2">n</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="modelc_1.html#K7" title="MODELC_1:func.7">atom.</a> <font color="Maroon" title="c2">n</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <a href="modelc_1.html#K13" title="MODELC_1:func.13">CTL_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="E1:21_6"/>
 <a href="modelc_1.html#K7" title="MODELC_1:func.7">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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:21"><span class="lab"><font color="Green" title="E19">A2</font></span></a>, <a class="ref" href="modelc_1.html#D14" target="_self" title="MODELC_1:def.14">Def14</a></span>;<br/><a NAME="E2:21_6"/><span class="kw">then </span><span class="lab"><font color="Green" title="E27">A22</font></span>: 
not  <a href="modelc_1.html#K7" title="MODELC_1:func.7">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>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/><a NAME="E3:21_6"/>
 <a href="modelc_1.html#K7" title="MODELC_1:func.7">atom.</a> <font color="Maroon" title="c2">n</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_1.html#K13" title="MODELC_1:func.13">CTL_WFF</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="modelc_1.html#D12" target="_self" title="MODELC_1:def.12">Def12</a></span>;<br/><span class="kw">hence </span><a NAME="E4:21_6"/>
 <a href="modelc_1.html#K7" title="MODELC_1:func.7">atom.</a> <font color="Maroon" title="c2">n</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <a href="modelc_1.html#K13" title="MODELC_1:func.13">CTL_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 class="kw">by</span> <span class="lab"><a class="txt" href="#E2:21_6"><span class="lab"><font color="Green" title="E27">A22</font></span></a>, <a class="ref" href="xboole_0.html#D5" title="XBOOLE_0:def.5">XBOOLE_0:def 5</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<a NAME="E11:21"/>
 <a href="modelc_1.html#K7" title="MODELC_1:func.7">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_1.html#K13" title="MODELC_1:func.13">CTL_WFF</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="modelc_1.html#D12" target="_self" title="MODELC_1:def.12">Def12</a></span>;<br/>
<a NAME="E12:21"/><span class="kw">then </span><span class="lab"><font color="Green" title="E27">A23</font></span>: 
not <a href="modelc_1.html#K13" title="MODELC_1:func.13">CTL_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> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:21"><span class="lab"><font color="Green" title="E20">A3</font></span></a>, <a class="ref" href="xboole_0.html#D5" title="XBOOLE_0:def.5">XBOOLE_0:def 5</a></span>;<br/>
<a NAME="E13:21"/>
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_1.html#K13" title="MODELC_1:func.13">CTL_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> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="modelc_1.html#D12" target="_self" title="MODELC_1:def.12">Def12</a></span>;<br/>
<a NAME="E14:21"/><span class="kw">then </span>
 <a href="modelc_1.html#K13" title="MODELC_1:func.13">CTL_WFF</a>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <a href="modelc_1.html#K13" title="MODELC_1:func.13">CTL_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 class="kw">by</span> <span class="lab"><a class="txt" href="#E12:21"><span class="lab"><font color="Green" title="E27">A23</font></span></a>, <a class="txt" href="#E10:21"><span class="lab"><font color="Green" title="E26">A21</font></span></a>, <a class="txt" href="#E8:21"><span class="lab"><font color="Green" title="E24">A14</font></span></a>, <a class="txt" href="#E7:21"><span class="lab"><font color="Green" title="E23">A10</font></span></a>, <a class="txt" href="#E6:21"><span class="lab"><font color="Green" title="E22">A7</font></span></a>, <a class="txt" href="#E5:21"><span class="lab"><font color="Green" title="E21">A4</font></span></a>, <a class="txt" href="#E9:21"><span class="lab"><font color="Green" title="E25">A17</font></span></a>, <a class="ref" href="modelc_1.html#D12" target="_self" title="MODELC_1:def.12">Def12</a></span>;<br/>
<a NAME="E15:21"/><span class="kw">then </span>
<font color="Maroon" title="c1">H</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <a href="modelc_1.html#K13" title="MODELC_1:func.13">CTL_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 class="kw">by</span> <span class="lab"><a class="txt" href="#E1:21"><span class="lab"><font color="Green" title="E18">A1</font></span></a>, <a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a></span>;<br/>
<a NAME="E16:21"/><span class="kw">then </span>
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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_0.html#D5" title="XBOOLE_0:def.5">XBOOLE_0:def 5</a></span>;<br/>
<span class="kw">hence </span><a NAME="E17:21"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
