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<span class="kw">let </span><font color="Maroon" title="c3">A</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ltlaxio1.html#NK1" title="LTLAXIO1:NK.1">LTLB_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"> (  <a href="subset_1.html#K1" title="SUBSET_1:func.1">{}</a> <a href="ltlaxio1.html#NK1" title="LTLAXIO1:NK.1">LTLB_WFF</a> <a href="ltlaxio1.html#R3" title="LTLAXIO1:pred.3">|=</a> <font color="Maroon" title="c3">A</font> iff  not  <a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <font color="Maroon" title="c3">A</font> is  <a href="ltlaxio4.html#V1" title="LTLAXIO4:attr.1">satisfiable</a>  )</span><br/>

<div><span class="kw">hereby </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  <a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <font color="Maroon" title="c3">A</font> is  <a href="ltlaxio4.html#V1" title="LTLAXIO4:attr.1">satisfiable</a>  implies  <a href="subset_1.html#K1" title="SUBSET_1:func.1">{}</a> <a href="ltlaxio1.html#NK1" title="LTLAXIO1:NK.1">LTLB_WFF</a> <a href="ltlaxio1.html#R3" title="LTLAXIO1:pred.3">|=</a> <font color="Maroon" title="c3">A</font> )</span>
<div class="add"><span class="kw">assume </span><a NAME="E1:10_1"/><span class="lab"><font color="Green" title="E5">A1</font></span>: 
 <a href="subset_1.html#K1" title="SUBSET_1:func.1">{}</a> <a href="ltlaxio1.html#NK1" title="LTLAXIO1:NK.1">LTLB_WFF</a> <a href="ltlaxio1.html#R3" title="LTLAXIO1:pred.3">|=</a> <font color="Maroon" title="c3">A</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">  not  <a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <font color="Maroon" title="c3">A</font> is  <a href="ltlaxio4.html#V1" title="LTLAXIO4:attr.1">satisfiable</a> </span><br/><span class="kw">assume </span><a NAME="E2:10_1"/>
 <a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <font color="Maroon" title="c3">A</font> is  <a href="ltlaxio4.html#V1" title="LTLAXIO4:attr.1">satisfiable</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"> contradiction</span><br/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c4">M</font> being   <a href="ltlaxio1.html#NM1" title="LTLAXIO1:NM.1">LTLModel</a>, <font color="Maroon" title="c5">n</font> being    <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> <span class="kw"> such that </span><br/><a NAME="E4:10_1"/><span class="lab"><font color="Green" title="E6">A2</font></span>: 
<span class="p1">(<span class="default"><a href="ltlaxio1.html#K11" title="LTLAXIO1:func.11">SAT</a> <font color="Maroon" title="c4">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="c5">n</font>,<span class="p2">(<span class="default"><a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <font color="Maroon" title="c3">A</font></span>)</span></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
 ;<br/><a NAME="E5:10_1"/><span class="lab"><font color="Green" title="E7">A3</font></span>: 
<font color="Maroon" title="c4">M</font> <a href="ltlaxio1.html#R2" title="LTLAXIO1:pred.2">|=</a>  <a href="subset_1.html#K1" title="SUBSET_1:func.1">{}</a> <a href="ltlaxio1.html#NK1" title="LTLAXIO1:NK.1">LTLB_WFF</a>
 ;<br/><a NAME="E6:10_1"/>
<span class="p1">(<span class="default"><a href="ltlaxio1.html#K11" title="LTLAXIO1:func.11">SAT</a> <font color="Maroon" title="c4">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="c5">n</font>,<font color="Maroon" title="c3">A</font></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="numbers.html#K5" title="NUMBERS:func.5">0</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:10_1"><span class="lab"><font color="Green" title="E6">A2</font></span></a>, <a class="ref" href="ltlaxio1.html#T5" onmouseover="rs('ltlaxio1/T5')" onmouseout="rh()">LTLAXIO1:5</a></span>;<br/><span class="kw">hence </span><a NAME="E7:10_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:10_1"><span class="lab"><font color="Green" title="E7">A3</font></span></a>, <a class="txt" href="#E1:10_1"><span class="lab"><font color="Green" title="E5">A1</font></span></a>, <a class="ref" href="ltlaxio1.html#D12" onmouseover="rs('ltlaxio1/D12')" onmouseout="rh()">LTLAXIO1:def 12</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">assume </span><a NAME="E2:10"/><span class="lab"><font color="Green" title="E5">A4</font></span>: 
 not  <a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <font color="Maroon" title="c3">A</font> is  <a href="ltlaxio4.html#V1" title="LTLAXIO4:attr.1">satisfiable</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">  <a href="subset_1.html#K1" title="SUBSET_1:func.1">{}</a> <a href="ltlaxio1.html#NK1" title="LTLAXIO1:NK.1">LTLB_WFF</a> <a href="ltlaxio1.html#R3" title="LTLAXIO1:pred.3">|=</a> <font color="Maroon" title="c3">A</font></span><br/>

<span class="kw">assume </span><a NAME="E3:10"/>
 not  <a href="subset_1.html#K1" title="SUBSET_1:func.1">{}</a> <a href="ltlaxio1.html#NK1" title="LTLAXIO1:NK.1">LTLB_WFF</a> <a href="ltlaxio1.html#R3" title="LTLAXIO1:pred.3">|=</a> <font color="Maroon" title="c3">A</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/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c4">M</font> being   <a href="ltlaxio1.html#NM1" title="LTLAXIO1:NM.1">LTLModel</a><span class="kw"> such that </span><br/><a NAME="E5:10"/>
<font color="Maroon" title="c4">M</font> <a href="ltlaxio1.html#R2" title="LTLAXIO1:pred.2">|=</a>  <a href="subset_1.html#K1" title="SUBSET_1:func.1">{}</a> <a href="ltlaxio1.html#NK1" title="LTLAXIO1:NK.1">LTLB_WFF</a>
 <span class="kw">and </span><br/><a NAME="E6:10"/><span class="lab"><font color="Green" title="E6">A5</font></span>: 
 not <font color="Maroon" title="c4">M</font> <a href="ltlaxio1.html#R1" title="LTLAXIO1:pred.1">|=</a> <font color="Maroon" title="c3">A</font>
 ;<br/>
<span class="kw">consider </span><font color="Maroon" title="c5">n</font> being    <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> <span class="kw"> such that </span><br/><a NAME="E8:10"/><span class="lab"><font color="Green" title="E7">A6</font></span>: 
 not <span class="p1">(<span class="default"><a href="ltlaxio1.html#K11" title="LTLAXIO1:func.11">SAT</a> <font color="Maroon" title="c4">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="c5">n</font>,<font color="Maroon" title="c3">A</font></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 class="kw">by</span> <span class="lab"><a class="txt" href="#E6:10"><span class="lab"><font color="Green" title="E6">A5</font></span></a></span>;<br/>
<a NAME="E9:10"/>
<span class="p1">(<span class="default"><a href="ltlaxio1.html#K11" title="LTLAXIO1:func.11">SAT</a> <font color="Maroon" title="c4">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="c5">n</font>,<span class="p2">(<span class="default"><a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <font color="Maroon" title="c3">A</font></span>)</span></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 class="kw">by</span> <span class="lab"><a class="txt" href="#E8:10"><span class="lab"><font color="Green" title="E7">A6</font></span></a>, <a class="ref" href="xboolean.html#D3" onmouseover="rs('xboolean/D3')" onmouseout="rh()">XBOOLEAN:def 3</a>, <a class="ref" href="ltlaxio1.html#T5" onmouseover="rs('ltlaxio1/T5')" onmouseout="rh()">LTLAXIO1:5</a></span>;<br/>
<span class="kw">hence </span><a NAME="E10:10"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:10"><span class="lab"><font color="Green" title="E5">A4</font></span></a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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