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<span class="kw">let </span><font color="Maroon" title="c1">H</font> be   <a href="modelc_2.html#NM1" title="MODELC_2:NM.1">LTL-formula</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">r</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="modelc_2.html#K25" title="MODELC_2:func.25">Inf_seq</a> <a href="modelc_2.html#K43" title="MODELC_2:func.43">AtomicFamily</a><br/>  for <font color="Olive" title="b2">W</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <a href="modelc_2.html#K9" title="MODELC_2:func.9">LTL_WFF</a>  st <font color="Maroon" title="c1">H</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b2">W</font> &amp;  <a href="modelc_2.html#K3" title="MODELC_2:func.3">'not'</a> <font color="Maroon" title="c1">H</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b2">W</font> holds <br/><font color="Olive" title="b1">r</font> <a href="modelc_2.html#NR11" title="MODELC_2:NR.11">|/=</a> <font color="Olive" title="b2">W</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">r</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="modelc_2.html#K25" title="MODELC_2:func.25">Inf_seq</a> <a href="modelc_2.html#K43" title="MODELC_2:func.43">AtomicFamily</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">W</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <a href="modelc_2.html#K9" title="MODELC_2:func.9">LTL_WFF</a>  st <font color="Maroon" title="c1">H</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b1">W</font> &amp;  <a href="modelc_2.html#K3" title="MODELC_2:func.3">'not'</a> <font color="Maroon" title="c1">H</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b1">W</font> holds <br/><font color="Maroon" title="c2">r</font> <a href="modelc_2.html#NR11" title="MODELC_2:NR.11">|/=</a> <font color="Olive" title="b1">W</font></span><br/><span class="kw">let </span><font color="Maroon" title="c3">W</font> be   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <a href="modelc_2.html#K9" title="MODELC_2:func.9">LTL_WFF</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">H</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c3">W</font> &amp;  <a href="modelc_2.html#K3" title="MODELC_2:func.3">'not'</a> <font color="Maroon" title="c1">H</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c3">W</font> implies <font color="Maroon" title="c2">r</font> <a href="modelc_2.html#NR11" title="MODELC_2:NR.11">|/=</a> <font color="Maroon" title="c3">W</font> )</span><br/>





<span class="kw">assume </span><a NAME="E1:177"/><span class="lab"><font color="Green" title="E123">A1</font></span>: 
( <font color="Maroon" title="c1">H</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c3">W</font> &amp;  <a href="modelc_2.html#K3" title="MODELC_2:func.3">'not'</a> <font color="Maroon" title="c1">H</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c3">W</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">r</font> <a href="modelc_2.html#NR11" title="MODELC_2:NR.11">|/=</a> <font color="Maroon" title="c3">W</font></span><br/>

<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="177_1"><span class="kw">now </span> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  not <font color="Maroon" title="c2">r</font> <a href="modelc_2.html#R8" title="MODELC_2:pred.8">|=</a> <font color="Maroon" title="c3">W</font></span></a><div class="add"><span class="kw">assume </span><a NAME="E1:177_1"/>
<font color="Maroon" title="c2">r</font> <a href="modelc_2.html#R8" title="MODELC_2:pred.8">|=</a> <font color="Maroon" title="c3">W</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><a NAME="E2:177_1"/><span class="kw">then </span>
( <font color="Maroon" title="c2">r</font> <a href="modelc_2.html#R7" title="MODELC_2:pred.7">|=</a> <font color="Maroon" title="c1">H</font> &amp; <font color="Maroon" title="c2">r</font> <a href="modelc_2.html#R7" title="MODELC_2:pred.7">|=</a>  <a href="modelc_2.html#K3" title="MODELC_2:func.3">'not'</a> <font color="Maroon" title="c1">H</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:177"><span class="lab"><font color="Green" title="E123">A1</font></span></a></span>;<br/><span class="kw">hence </span><a NAME="E3:177_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="ref" href="modelc_2.html#T64" target="_self" onmouseover="rs('modelc_2/T64')" onmouseout="rh()">Th64</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">hence </span><a NAME="E3:177"/>
<font color="Maroon" title="c2">r</font> <a href="modelc_2.html#NR11" title="MODELC_2:NR.11">|/=</a> <font color="Maroon" title="c3">W</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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