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<span class="kw">let </span><font color="Maroon" title="c1">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" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">F</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <a href="ltlaxio1.html#NK1" title="LTLAXIO1:NK.1">LTLB_WFF</a>  st <font color="Olive" title="b1">F</font> <a href="ltlaxio1.html#R3" title="LTLAXIO1:pred.3">|=</a> <font color="Maroon" title="c1">A</font> holds <br/><font color="Olive" title="b1">F</font> <a href="ltlaxio1.html#R3" title="LTLAXIO1:pred.3">|=</a>  <a href="ltlaxio1.html#K2" title="LTLAXIO1:func.2">'X'</a> <font color="Maroon" title="c1">A</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">F</font> be   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <a href="ltlaxio1.html#NK1" title="LTLAXIO1:NK.1">LTLB_WFF</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">F</font> <a href="ltlaxio1.html#R3" title="LTLAXIO1:pred.3">|=</a> <font color="Maroon" title="c1">A</font> implies <font color="Maroon" title="c2">F</font> <a href="ltlaxio1.html#R3" title="LTLAXIO1:pred.3">|=</a>  <a href="ltlaxio1.html#K2" title="LTLAXIO1:func.2">'X'</a> <font color="Maroon" title="c1">A</font> )</span><br/>



<span class="kw">assume </span><a NAME="E1:43"/><span class="lab"><font color="Green" title="E30">A1</font></span>: 
<font color="Maroon" title="c2">F</font> <a href="ltlaxio1.html#R3" title="LTLAXIO1:pred.3">|=</a> <font color="Maroon" title="c1">A</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">F</font> <a href="ltlaxio1.html#R3" title="LTLAXIO1:pred.3">|=</a>  <a href="ltlaxio1.html#K2" title="LTLAXIO1:func.2">'X'</a> <font color="Maroon" title="c1">A</font></span><br/>

<span class="kw">let </span><font color="Maroon" title="c3">M</font> be   <a href="ltlaxio1.html#NM1" title="LTLAXIO1:NM.1">LTLModel</a>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="ltlaxio1.html#D14" target="_self" title="LTLAXIO1:def.14">LTLAXIO1:def 14</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c3">M</font> <a href="ltlaxio1.html#R2" title="LTLAXIO1:pred.2">|=</a> <font color="Maroon" title="c2">F</font> implies <font color="Maroon" title="c3">M</font> <a href="ltlaxio1.html#R1" title="LTLAXIO1:pred.1">|=</a>  <a href="ltlaxio1.html#K2" title="LTLAXIO1:func.2">'X'</a> <font color="Maroon" title="c1">A</font> )</span><br/>

<span class="kw">assume </span><a NAME="E2:43"/>
<font color="Maroon" title="c3">M</font> <a href="ltlaxio1.html#R2" title="LTLAXIO1:pred.2">|=</a> <font color="Maroon" title="c2">F</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c3">M</font> <a href="ltlaxio1.html#R1" title="LTLAXIO1:pred.1">|=</a>  <a href="ltlaxio1.html#K2" title="LTLAXIO1:func.2">'X'</a> <font color="Maroon" title="c1">A</font></span><br/>

<a NAME="E3:43"/><span class="kw">then </span><span class="lab"><font color="Green" title="E31">A2</font></span>: 
<font color="Maroon" title="c3">M</font> <a href="ltlaxio1.html#R1" title="LTLAXIO1:pred.1">|=</a> <font color="Maroon" title="c1">A</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:43"><span class="lab"><font color="Green" title="E30">A1</font></span></a>, <a class="ref" href="ltlaxio1.html#D14" target="_self" title="LTLAXIO1:def.14">Def15</a></span>;<br/>
<span class="kw">let </span><font color="Maroon" title="c4">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> ; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="ltlaxio1.html#D12" target="_self" title="LTLAXIO1:def.12">LTLAXIO1:def 12</a> <a class="txt" 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="c3">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="c4">n</font>,<span class="p2">(<span class="default"><a href="ltlaxio1.html#K2" title="LTLAXIO1:func.2">'X'</a> <font color="Maroon" title="c1">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><br/>

<span class="kw">thus </span><span class="p1">(<span class="default"><a href="ltlaxio1.html#K11" title="LTLAXIO1:func.11">SAT</a> <font color="Maroon" title="c3">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="c4">n</font>,<span class="p2">(<span class="default"><a href="ltlaxio1.html#K2" title="LTLAXIO1:func.2">'X'</a> <font color="Maroon" title="c1">A</font></span>)</span></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> = 
<span class="p1">(<span class="default"><a href="ltlaxio1.html#K11" title="LTLAXIO1:func.11">SAT</a> <font color="Maroon" title="c3">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"><span class="p2">(<span class="default"><font color="Maroon" title="c4">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<font color="Maroon" title="c1">A</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="ltlaxio1.html#T9" target="_self" title="LTLAXIO1:th.9">Th10</a></span>
<br/>.= 
1
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:43"><span class="lab"><font color="Green" title="E31">A2</font></span></a>, <a class="ref" href="ltlaxio1.html#D12" target="_self" title="LTLAXIO1:def.12">Def13</a></span>
; <a class="txt" 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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