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<span class="kw">let </span><font color="Maroon" title="c1">n</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a> ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">M</font> being   <a href="ltlaxio1.html#NM1" title="LTLAXIO1:NM.1">LTLModel</a> holds  <span class="p1">(<span class="default"><a href="ltlaxio1.html#K11" title="LTLAXIO1:func.11">SAT</a> <font color="Olive" title="b1">M</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c1">n</font>,<a href="ltlaxio1.html#K3" title="LTLAXIO1:func.3">TVERUM</a></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1</span><br/><span class="kw">let </span><font color="Maroon" title="c2">M</font> be   <a href="ltlaxio1.html#NM1" title="LTLAXIO1:NM.1">LTLModel</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="ltlaxio1.html#K11" title="LTLAXIO1:func.11">SAT</a> <font color="Maroon" title="c2">M</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c1">n</font>,<a href="ltlaxio1.html#K3" title="LTLAXIO1:func.3">TVERUM</a></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1</span><br/>



<span class="kw">assume </span><a NAME="E1:21"/>
 not <span class="p1">(<span class="default"><a href="ltlaxio1.html#K11" title="LTLAXIO1:func.11">SAT</a> <font color="Maroon" title="c2">M</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c1">n</font>,<a href="ltlaxio1.html#K3" title="LTLAXIO1:func.3">TVERUM</a></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 ; <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="E2:21"/><span class="kw">then </span>
 not <span class="p1">(<span class="default"><a href="ltlaxio1.html#K11" title="LTLAXIO1:func.11">SAT</a> <font color="Maroon" title="c2">M</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c1">n</font>,<a href="ltlaxio1.html#NK2" title="LTLAXIO1:NK.2">TFALSUM</a></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ordinal1.html#K5" title="ORDINAL1:func.5">0</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="ltlaxio1.html#T5" target="_self" onmouseover="rs('ltlaxio1/T5')" onmouseout="rh()">Th5</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:21"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="ref" href="ltlaxio1.html#D11" target="_self" onmouseover="rs('ltlaxio1/D11')" onmouseout="rh()">Def11</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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