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<span class="kw">let </span><font color="Maroon" title="c1">F</font>, <font color="Maroon" title="c2">G</font>, <font color="Maroon" title="c3">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"> ( <font color="Maroon" title="c1">F</font> <a href="modelc_2.html#R3" title="MODELC_2:pred.3">is_proper_subformula_of</a> <font color="Maroon" title="c2">G</font> &amp; <font color="Maroon" title="c2">G</font> <a href="modelc_2.html#R3" title="MODELC_2:pred.3">is_proper_subformula_of</a> <font color="Maroon" title="c3">H</font> implies <font color="Maroon" title="c1">F</font> <a href="modelc_2.html#R3" title="MODELC_2:pred.3">is_proper_subformula_of</a> <font color="Maroon" title="c3">H</font> )</span><br/>





<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:66"/><span class="lab"><font color="Green" title="E55">A1</font></span>: 
<font color="Maroon" title="c1">F</font> <a href="modelc_2.html#R2" title="MODELC_2:pred.2">is_subformula_of</a> <font color="Maroon" title="c2">G</font>
 <span class="kw">and </span><br/><a NAME="E2:66"/><span class="lab"><font color="Green" title="E56">A2</font></span>: 
<font color="Maroon" title="c1">F</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">G</font>
 <span class="kw">and </span><br/><a NAME="E3:66"/><span class="lab"><font color="Green" title="E57">A3</font></span>: 
<font color="Maroon" title="c2">G</font> <a href="modelc_2.html#R2" title="MODELC_2:pred.2">is_subformula_of</a> <font color="Maroon" title="c3">H</font>
 <span class="kw">and </span><br/><a NAME="E4:66"/><span class="lab"><font color="Green" title="E58">A4</font></span>: 
<font color="Maroon" title="c2">G</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">H</font>
 ; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="modelc_2.html#D23" target="_self" onmouseover="rs('modelc_2/D23')" onmouseout="rh()">MODELC_2:def 23</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">F</font> <a href="modelc_2.html#R3" title="MODELC_2:pred.3">is_proper_subformula_of</a> <font color="Maroon" title="c3">H</font></span><br/>

<span class="kw">consider </span><font color="Maroon" title="c4">m</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>, <font color="Maroon" title="c5">L9</font> being   <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a><span class="kw"> such that </span><br/><a NAME="E6:66"/><span class="lab"><font color="Green" title="E59">A5</font></span>: 
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c4">m</font>
 <span class="kw">and </span><br/><a NAME="E7:66"/><span class="lab"><font color="Green" title="E60">A6</font></span>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c5">L9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">m</font>
 <span class="kw">and </span><br/><a NAME="E8:66"/><span class="lab"><font color="Green" title="E61">A7</font></span>: 
<font color="Maroon" title="c5">L9</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">G</font>
 <span class="kw">and </span><br/><a NAME="E9:66"/><span class="lab"><font color="Green" title="E62">A8</font></span>: 
<font color="Maroon" title="c5">L9</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">H</font>
 <span class="kw">and </span><br/><a NAME="E10:66"/><span class="lab"><font color="Green" title="E63">A9</font></span>: 
 for <font color="Olive" title="b1">k</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b1">k</font> &amp; <font color="Olive" title="b1">k</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c4">m</font> holds <br/> ex <font color="Olive" title="b2">H1</font>, <font color="Olive" title="b3">F1</font> being   <a href="modelc_2.html#NM1" title="MODELC_2:NM.1">LTL-formula</a> st <br/>( <font color="Maroon" title="c5">L9</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">H1</font> &amp; <font color="Maroon" title="c5">L9</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">F1</font> &amp; <font color="Olive" title="b2">H1</font> <a href="modelc_2.html#R1" title="MODELC_2:pred.1">is_immediate_constituent_of</a> <font color="Olive" title="b3">F1</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:66"><span class="lab"><font color="Green" title="E57">A3</font></span></a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c6">n</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>, <font color="Maroon" title="c7">L</font> being   <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a><span class="kw"> such that </span><br/><a NAME="E12:66"/><span class="lab"><font color="Green" title="E64">A10</font></span>: 
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c6">n</font>
 <span class="kw">and </span><br/><a NAME="E13:66"/><span class="lab"><font color="Green" title="E65">A11</font></span>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c7">L</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">n</font>
 <span class="kw">and </span><br/><a NAME="E14:66"/><span class="lab"><font color="Green" title="E66">A12</font></span>: 
<font color="Maroon" title="c7">L</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">F</font>
 <span class="kw">and </span><br/><a NAME="E15:66"/><span class="lab"><font color="Green" title="E67">A13</font></span>: 
<font color="Maroon" title="c7">L</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">G</font>
 <span class="kw">and </span><br/><a NAME="E16:66"/><span class="lab"><font color="Green" title="E68">A14</font></span>: 
 for <font color="Olive" title="b1">k</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b1">k</font> &amp; <font color="Olive" title="b1">k</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c6">n</font> holds <br/> ex <font color="Olive" title="b2">H1</font>, <font color="Olive" title="b3">F1</font> being   <a href="modelc_2.html#NM1" title="MODELC_2:NM.1">LTL-formula</a> st <br/>( <font color="Maroon" title="c7">L</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">H1</font> &amp; <font color="Maroon" title="c7">L</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">F1</font> &amp; <font color="Olive" title="b2">H1</font> <a href="modelc_2.html#R1" title="MODELC_2:pred.1">is_immediate_constituent_of</a> <font color="Olive" title="b3">F1</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:66"><span class="lab"><font color="Green" title="E55">A1</font></span></a></span>;<br/>
<a NAME="E17:66"/>
1 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c6">n</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:66"><span class="lab"><font color="Green" title="E56">A2</font></span></a>, <a class="txt" href="#E12:66"><span class="lab"><font color="Green" title="E64">A10</font></span></a>, <a class="txt" href="#E14:66"><span class="lab"><font color="Green" title="E66">A12</font></span></a>, <a class="txt" href="#E15:66"><span class="lab"><font color="Green" title="E67">A13</font></span></a>, <a class="ref" href="xxreal_0.html#T1" onmouseover="rs('xxreal_0/T1')" onmouseout="rh()">XXREAL_0:1</a></span>;<br/>
<a NAME="E18:66"/><span class="kw">then </span>
1 <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c6">n</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="nat_1.html#T13" onmouseover="rs('nat_1/T13')" onmouseout="rh()">NAT_1:13</a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c8">k</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a><span class="kw"> such that </span><br/><a NAME="E20:66"/><span class="lab"><font color="Green" title="E69">A15</font></span>: 
<font color="Maroon" title="c6">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c8">k</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="nat_1.html#T10" onmouseover="rs('nat_1/T10')" onmouseout="rh()">NAT_1:10</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c9">L1</font> = <font color="Maroon" title="c7">L</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">|</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p2">(<span class="default">1 <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c8">k</font></span>)</span></span>)</span> as   <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a> <span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#T15" onmouseover="rs('finseq_1/T15')" onmouseout="rh()">FINSEQ_1:15</a></span>;<br/>
<span class="kw">thus </span><a NAME="E22:66"/>
<font color="Maroon" title="c1">F</font> <a href="modelc_2.html#R2" title="MODELC_2:pred.2">is_subformula_of</a> <font color="Maroon" title="c3">H</font>
  <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="modelc_2.html#D23" target="_self" onmouseover="rs('modelc_2/D23')" onmouseout="rh()">MODELC_2:def 23</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">F</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">H</font></span><div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="66_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">take </span><font color="Maroon" title="c10">l</font> = <span class="p1">(<span class="default">1 <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c8">k</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c4">m</font>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="modelc_2.html#D22" target="_self" onmouseover="rs('modelc_2/D22')" onmouseout="rh()">MODELC_2:def 22</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">  ex <font color="Olive" title="b1">L</font> being   <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a> st <br/>( 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c10">l</font> &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b1">L</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">l</font> &amp; <font color="Olive" title="b1">L</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">F</font> &amp; <font color="Olive" title="b1">L</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">l</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">H</font> &amp; (  for <font color="Olive" title="b2">k</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b2">k</font> &amp; <font color="Olive" title="b2">k</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c10">l</font> holds <br/> ex <font color="Olive" title="b3">H1</font>, <font color="Olive" title="b4">F1</font> being   <a href="modelc_2.html#NM1" title="MODELC_2:NM.1">LTL-formula</a> st <br/>( <font color="Olive" title="b1">L</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b2">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">H1</font> &amp; <font color="Olive" title="b1">L</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">F1</font> &amp; <font color="Olive" title="b3">H1</font> <a href="modelc_2.html#R1" title="MODELC_2:pred.1">is_immediate_constituent_of</a> <font color="Olive" title="b4">F1</font> ) ) )</span><br/>

<span class="kw">take </span><font color="Maroon" title="c11">K</font> = <font color="Maroon" title="c9">L1</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c5">L9</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"> ( 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c10">l</font> &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c11">K</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">l</font> &amp; <font color="Maroon" title="c11">K</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">F</font> &amp; <font color="Maroon" title="c11">K</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">l</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">H</font> &amp; (  for <font color="Olive" title="b1">k</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b1">k</font> &amp; <font color="Olive" title="b1">k</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c10">l</font> holds <br/> ex <font color="Olive" title="b2">H1</font>, <font color="Olive" title="b3">F1</font> being   <a href="modelc_2.html#NM1" title="MODELC_2:NM.1">LTL-formula</a> st <br/>( <font color="Maroon" title="c11">K</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">H1</font> &amp; <font color="Maroon" title="c11">K</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">F1</font> &amp; <font color="Olive" title="b2">H1</font> <a href="modelc_2.html#R1" title="MODELC_2:pred.1">is_immediate_constituent_of</a> <font color="Olive" title="b3">F1</font> ) ) )</span><br/>

<a NAME="E1:66_1"/><span class="lab"><font color="Green" title="E70">A16</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c8">k</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c4">m</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default">1 <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c8">k</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">m</font>
 
;<br/>
<a NAME="E2:66_1"/>
<font color="Maroon" title="c4">m</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c4">m</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default">1 <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c8">k</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="nat_1.html#T11" onmouseover="rs('nat_1/T11')" onmouseout="rh()">NAT_1:11</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:66_1"/>
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c10">l</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:66"><span class="lab"><font color="Green" title="E59">A5</font></span></a>, <a class="ref" href="xxreal_0.html#T2" onmouseover="rs('xxreal_0/T2')" onmouseout="rh()">XXREAL_0:2</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"> (  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c11">K</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">l</font> &amp; <font color="Maroon" title="c11">K</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">F</font> &amp; <font color="Maroon" title="c11">K</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">l</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">H</font> &amp; (  for <font color="Olive" title="b1">k</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b1">k</font> &amp; <font color="Olive" title="b1">k</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c10">l</font> holds <br/> ex <font color="Olive" title="b2">H1</font>, <font color="Olive" title="b3">F1</font> being   <a href="modelc_2.html#NM1" title="MODELC_2:NM.1">LTL-formula</a> st <br/>( <font color="Maroon" title="c11">K</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">H1</font> &amp; <font color="Maroon" title="c11">K</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">F1</font> &amp; <font color="Olive" title="b2">H1</font> <a href="modelc_2.html#R1" title="MODELC_2:pred.1">is_immediate_constituent_of</a> <font color="Olive" title="b3">F1</font> ) ) )</span><br/>

<a NAME="E4:66_1"/>
<span class="p1">(<span class="default">1 <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c8">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">1 <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c8">k</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1
 
;<br/>
<a NAME="E5:66_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E71">A17</font></span>: 
1 <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c8">k</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c6">n</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E20:66"><span class="lab"><font color="Green" title="E69">A15</font></span></a>, <a class="ref" href="nat_1.html#T11" onmouseover="rs('nat_1/T11')" onmouseout="rh()">NAT_1:11</a></span>;<br/>
<a NAME="E6:66_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E72">A18</font></span>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c9">L1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c8">k</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:66"><span class="lab"><font color="Green" title="E65">A11</font></span></a>, <a class="ref" href="finseq_1.html#T17" onmouseover="rs('finseq_1/T17')" onmouseout="rh()">FINSEQ_1:17</a></span>;<br/>
<span class="kw">hence </span><a NAME="E7:66_1"/><span class="lab"><font color="Green" title="E73">A19</font></span>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c11">K</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">l</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:66"><span class="lab"><font color="Green" title="E60">A6</font></span></a>, <a class="ref" href="finseq_1.html#T22" onmouseover="rs('finseq_1/T22')" onmouseout="rh()">FINSEQ_1:22</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"> ( <font color="Maroon" title="c11">K</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">F</font> &amp; <font color="Maroon" title="c11">K</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">l</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">H</font> &amp; (  for <font color="Olive" title="b1">k</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b1">k</font> &amp; <font color="Olive" title="b1">k</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c10">l</font> holds <br/> ex <font color="Olive" title="b2">H1</font>, <font color="Olive" title="b3">F1</font> being   <a href="modelc_2.html#NM1" title="MODELC_2:NM.1">LTL-formula</a> st <br/>( <font color="Maroon" title="c11">K</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">H1</font> &amp; <font color="Maroon" title="c11">K</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">F1</font> &amp; <font color="Olive" title="b2">H1</font> <a href="modelc_2.html#R1" title="MODELC_2:pred.1">is_immediate_constituent_of</a> <font color="Olive" title="b3">F1</font> ) ) )</span><br/>

<div><span class="lab"><font color="Green" title="E74">A20</font></span>: <a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="66_1_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">  for <font color="Olive" title="b1">j</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b1">j</font> &amp; <font color="Olive" title="b1">j</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 1 <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c8">k</font> holds <br/><font color="Maroon" title="c11">K</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">L</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">j</font></span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c12">j</font> be   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">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"> ( 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c12">j</font> &amp; <font color="Maroon" title="c12">j</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 1 <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c8">k</font> implies <font color="Maroon" title="c11">K</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c12">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">L</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c12">j</font> )</span><br/><span class="kw">assume </span><a NAME="E1:66_1_1"/>
( 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c12">j</font> &amp; <font color="Maroon" title="c12">j</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 1 <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c8">k</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="c11">K</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c12">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">L</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c12">j</font></span><br/><a NAME="E2:66_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E75">A21</font></span>: 
<font color="Maroon" title="c12">j</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default">1 <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c8">k</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#T1" onmouseover="rs('finseq_1/T1')" onmouseout="rh()">FINSEQ_1:1</a></span>;<br/><a NAME="E3:66_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c12">j</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c9">L1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:66"><span class="lab"><font color="Green" title="E65">A11</font></span></a>, <a class="txt" href="#E5:66_1"><span class="lab"><font color="Green" title="E71">A17</font></span></a>, <a class="ref" href="finseq_1.html#T17" onmouseover="rs('finseq_1/T17')" onmouseout="rh()">FINSEQ_1:17</a></span>;<br/><a NAME="E4:66_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c11">K</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c12">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">L1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c12">j</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#D7" onmouseover="rs('finseq_1/D7')" onmouseout="rh()">FINSEQ_1:def 7</a></span>;<br/><span class="kw">hence </span><a NAME="E5:66_1_1"/>
<font color="Maroon" title="c11">K</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c12">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">L</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c12">j</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:66_1_1"><span class="lab"><font color="Green" title="E75">A21</font></span></a>, <a class="ref" href="funct_1.html#T49" onmouseover="rs('funct_1/T49')" onmouseout="rh()">FUNCT_1:49</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>
<a NAME="E9:66_1"/>
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 1 <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c8">k</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="nat_1.html#T11" onmouseover="rs('nat_1/T11')" onmouseout="rh()">NAT_1:11</a></span>;<br/>
<span class="kw">hence </span><a NAME="E10:66_1"/>
<font color="Maroon" title="c11">K</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">F</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:66"><span class="lab"><font color="Green" title="E66">A12</font></span></a>, <a class="txt" href="#E8:66_1"><span class="lab"><font color="Green" title="E74">A20</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"> ( <font color="Maroon" title="c11">K</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">l</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">H</font> &amp; (  for <font color="Olive" title="b1">k</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b1">k</font> &amp; <font color="Olive" title="b1">k</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c10">l</font> holds <br/> ex <font color="Olive" title="b2">H1</font>, <font color="Olive" title="b3">F1</font> being   <a href="modelc_2.html#NM1" title="MODELC_2:NM.1">LTL-formula</a> st <br/>( <font color="Maroon" title="c11">K</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">H1</font> &amp; <font color="Maroon" title="c11">K</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">F1</font> &amp; <font color="Olive" title="b2">H1</font> <a href="modelc_2.html#R1" title="MODELC_2:pred.1">is_immediate_constituent_of</a> <font color="Olive" title="b3">F1</font> ) ) )</span><br/>

<a NAME="E11:66_1"/>
<span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c9">L1</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c9">L1</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c4">m</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:66"><span class="lab"><font color="Green" title="E59">A5</font></span></a>, <a class="ref" href="xreal_1.html#T7" onmouseover="rs('xreal_1/T7')" onmouseout="rh()">XREAL_1:7</a></span>;<br/>
<a NAME="E12:66_1"/><span class="kw">then </span>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c9">L1</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c10">l</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:66_1"><span class="lab"><font color="Green" title="E72">A18</font></span></a>, <a class="ref" href="nat_1.html#T13" onmouseover="rs('nat_1/T13')" onmouseout="rh()">NAT_1:13</a></span>;<br/>
<a NAME="E13:66_1"/><span class="kw">then </span>
<font color="Maroon" title="c11">K</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">l</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">L9</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">l</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c9">L1</font></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:66_1"><span class="lab"><font color="Green" title="E73">A19</font></span></a>, <a class="ref" href="finseq_1.html#T24" onmouseover="rs('finseq_1/T24')" onmouseout="rh()">FINSEQ_1:24</a></span>;<br/>
<span class="kw">hence </span><a NAME="E14:66_1"/>
<font color="Maroon" title="c11">K</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">l</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">H</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:66"><span class="lab"><font color="Green" title="E65">A11</font></span></a>, <a class="txt" href="#E9:66"><span class="lab"><font color="Green" title="E62">A8</font></span></a>, <a class="txt" href="#E5:66_1"><span class="lab"><font color="Green" title="E71">A17</font></span></a>, <a class="txt" href="#E1:66_1"><span class="lab"><font color="Green" title="E70">A16</font></span></a>, <a class="ref" href="finseq_1.html#T17" onmouseover="rs('finseq_1/T17')" onmouseout="rh()">FINSEQ_1:17</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">  for <font color="Olive" title="b1">k</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b1">k</font> &amp; <font color="Olive" title="b1">k</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c10">l</font> holds <br/> ex <font color="Olive" title="b2">H1</font>, <font color="Olive" title="b3">F1</font> being   <a href="modelc_2.html#NM1" title="MODELC_2:NM.1">LTL-formula</a> st <br/>( <font color="Maroon" title="c11">K</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">H1</font> &amp; <font color="Maroon" title="c11">K</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">F1</font> &amp; <font color="Olive" title="b2">H1</font> <a href="modelc_2.html#R1" title="MODELC_2:pred.1">is_immediate_constituent_of</a> <font color="Olive" title="b3">F1</font> )</span><br/>

<span class="kw">let </span><font color="Maroon" title="c12">j</font> be   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">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"> ( 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c12">j</font> &amp; <font color="Maroon" title="c12">j</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c10">l</font> implies  ex <font color="Olive" title="b1">H1</font>, <font color="Olive" title="b2">F1</font> being   <a href="modelc_2.html#NM1" title="MODELC_2:NM.1">LTL-formula</a> st <br/>( <font color="Maroon" title="c11">K</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c12">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">H1</font> &amp; <font color="Maroon" title="c11">K</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">j</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">F1</font> &amp; <font color="Olive" title="b1">H1</font> <a href="modelc_2.html#R1" title="MODELC_2:pred.1">is_immediate_constituent_of</a> <font color="Olive" title="b2">F1</font> ) )</span><br/>

<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E15:66_1"/><span class="lab"><font color="Green" title="E75">A22</font></span>: 
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c12">j</font>
 <span class="kw">and </span><br/><a NAME="E16:66_1"/><span class="lab"><font color="Green" title="E76">A23</font></span>: 
<font color="Maroon" title="c12">j</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c10">l</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">  ex <font color="Olive" title="b1">H1</font>, <font color="Olive" title="b2">F1</font> being   <a href="modelc_2.html#NM1" title="MODELC_2:NM.1">LTL-formula</a> st <br/>( <font color="Maroon" title="c11">K</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c12">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">H1</font> &amp; <font color="Maroon" title="c11">K</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">j</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">F1</font> &amp; <font color="Olive" title="b1">H1</font> <a href="modelc_2.html#R1" title="MODELC_2:pred.1">is_immediate_constituent_of</a> <font color="Olive" title="b2">F1</font> )</span><br/>

<a NAME="E17:66_1"/>
<font color="Maroon" title="c12">j</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c12">j</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xreal_1.html#T7" onmouseover="rs('xreal_1/T7')" onmouseout="rh()">XREAL_1:7</a></span>;<br/>
<a NAME="E18:66_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E77">A24</font></span>: 
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c12">j</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E15:66_1"><span class="lab"><font color="Green" title="E75">A22</font></span></a>, <a class="ref" href="xxreal_0.html#T2" onmouseover="rs('xxreal_0/T2')" onmouseout="rh()">XXREAL_0:2</a></span>;<br/>
<div><span class="lab"><font color="Green" title="E78">A25</font></span>: <a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="66_1_2"><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"> ( <font color="Maroon" title="c12">j</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> 1 <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c8">k</font> implies  ex <font color="Olive" title="b1">F1</font>, <font color="Olive" title="b2">G1</font> being   <a href="modelc_2.html#NM1" title="MODELC_2:NM.1">LTL-formula</a> st <br/>( <font color="Maroon" title="c11">K</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c12">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">F1</font> &amp; <font color="Maroon" title="c11">K</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">j</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">G1</font> &amp; <font color="Olive" title="b1">F1</font> <a href="modelc_2.html#R1" title="MODELC_2:pred.1">is_immediate_constituent_of</a> <font color="Olive" title="b2">G1</font> ) )</span></a><div class="add"><span class="kw">assume </span><a NAME="E1:66_1_2"/><span class="lab"><font color="Green" title="E79">A26</font></span>: 
<font color="Maroon" title="c12">j</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> 1 <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c8">k</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">  ex <font color="Olive" title="b1">F1</font>, <font color="Olive" title="b2">G1</font> being   <a href="modelc_2.html#NM1" title="MODELC_2:NM.1">LTL-formula</a> st <br/>( <font color="Maroon" title="c11">K</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c12">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">F1</font> &amp; <font color="Maroon" title="c11">K</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">j</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">G1</font> &amp; <font color="Olive" title="b1">F1</font> <a href="modelc_2.html#R1" title="MODELC_2:pred.1">is_immediate_constituent_of</a> <font color="Olive" title="b2">G1</font> )</span><br/><a NAME="E2:66_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E80">A27</font></span>: 
<font color="Maroon" title="c12">j</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 1 <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c8">k</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="nat_1.html#T13" onmouseover="rs('nat_1/T13')" onmouseout="rh()">NAT_1:13</a></span>;<br/><a NAME="E3:66_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c12">j</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c6">n</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:66_1"><span class="lab"><font color="Green" title="E71">A17</font></span></a>, <a class="ref" href="xxreal_0.html#T2" onmouseover="rs('xxreal_0/T2')" onmouseout="rh()">XXREAL_0:2</a></span>;<br/><a NAME="E4:66_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c12">j</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c6">n</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="nat_1.html#T13" onmouseover="rs('nat_1/T13')" onmouseout="rh()">NAT_1:13</a></span>;<br/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c13">F1</font>, <font color="Maroon" title="c14">G1</font> being   <a href="modelc_2.html#NM1" title="MODELC_2:NM.1">LTL-formula</a><span class="kw"> such that </span><br/><a NAME="E6:66_1_2"/><span class="lab"><font color="Green" title="E81">A28</font></span>: 
( <font color="Maroon" title="c7">L</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c12">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">F1</font> &amp; <font color="Maroon" title="c7">L</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">j</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">G1</font> &amp; <font color="Maroon" title="c13">F1</font> <a href="modelc_2.html#R1" title="MODELC_2:pred.1">is_immediate_constituent_of</a> <font color="Maroon" title="c14">G1</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E16:66"><span class="lab"><font color="Green" title="E68">A14</font></span></a>, <a class="txt" href="#E15:66_1"><span class="lab"><font color="Green" title="E75">A22</font></span></a></span>;<br/><span class="kw">take </span><font color="Maroon" title="c15">F1</font> = <font color="Maroon" title="c13">F1</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">  ex <font color="Olive" title="b1">G1</font> being   <a href="modelc_2.html#NM1" title="MODELC_2:NM.1">LTL-formula</a> st <br/>( <font color="Maroon" title="c11">K</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c12">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">F1</font> &amp; <font color="Maroon" title="c11">K</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">j</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">G1</font> &amp; <font color="Maroon" title="c15">F1</font> <a href="modelc_2.html#R1" title="MODELC_2:pred.1">is_immediate_constituent_of</a> <font color="Olive" title="b1">G1</font> )</span><br/><span class="kw">take </span><font color="Maroon" title="c16">G1</font> = <font color="Maroon" title="c14">G1</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="c11">K</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c12">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">F1</font> &amp; <font color="Maroon" title="c11">K</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">j</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">G1</font> &amp; <font color="Maroon" title="c15">F1</font> <a href="modelc_2.html#R1" title="MODELC_2:pred.1">is_immediate_constituent_of</a> <font color="Maroon" title="c16">G1</font> )</span><br/><span class="kw">thus </span><a NAME="E7:66_1_2"/>
( <font color="Maroon" title="c11">K</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c12">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">F1</font> &amp; <font color="Maroon" title="c11">K</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">j</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">G1</font> &amp; <font color="Maroon" title="c15">F1</font> <a href="modelc_2.html#R1" title="MODELC_2:pred.1">is_immediate_constituent_of</a> <font color="Maroon" title="c16">G1</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:66_1"><span class="lab"><font color="Green" title="E74">A20</font></span></a>, <a class="txt" href="#E15:66_1"><span class="lab"><font color="Green" title="E75">A22</font></span></a>, <a class="txt" href="#E18:66_1"><span class="lab"><font color="Green" title="E77">A24</font></span></a>, <a class="txt" href="#E1:66_1_2"><span class="lab"><font color="Green" title="E79">A26</font></span></a>, <a class="txt" href="#E2:66_1_2"><span class="lab"><font color="Green" title="E80">A27</font></span></a>, <a class="txt" href="#E6:66_1_2"><span class="lab"><font color="Green" title="E81">A28</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/></div><span class="kw">end;</span></div>
<div><span class="lab"><font color="Green" title="E79">A29</font></span>: <a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="66_1_3"><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"> ( 1 <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c8">k</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c12">j</font> implies  ex <font color="Olive" title="b1">F1</font>, <font color="Olive" title="b2">G1</font> being   <a href="modelc_2.html#NM1" title="MODELC_2:NM.1">LTL-formula</a> st <br/>( <font color="Maroon" title="c11">K</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c12">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">F1</font> &amp; <font color="Maroon" title="c11">K</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">j</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">G1</font> &amp; <font color="Olive" title="b1">F1</font> <a href="modelc_2.html#R1" title="MODELC_2:pred.1">is_immediate_constituent_of</a> <font color="Olive" title="b2">G1</font> ) )</span></a><div class="add"><a NAME="E1:66_1_3"/><span class="lab"><font color="Green" title="E80">A30</font></span>: 
<font color="Maroon" title="c12">j</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c10">l</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E16:66_1"><span class="lab"><font color="Green" title="E76">A23</font></span></a>, <a class="ref" href="nat_1.html#T13" onmouseover="rs('nat_1/T13')" onmouseout="rh()">NAT_1:13</a></span>;<br/><span class="kw">assume </span><a NAME="E2:66_1_3"/><span class="lab"><font color="Green" title="E81">A31</font></span>: 
1 <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c8">k</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c12">j</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">  ex <font color="Olive" title="b1">F1</font>, <font color="Olive" title="b2">G1</font> being   <a href="modelc_2.html#NM1" title="MODELC_2:NM.1">LTL-formula</a> st <br/>( <font color="Maroon" title="c11">K</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c12">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">F1</font> &amp; <font color="Maroon" title="c11">K</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">j</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">G1</font> &amp; <font color="Olive" title="b1">F1</font> <a href="modelc_2.html#R1" title="MODELC_2:pred.1">is_immediate_constituent_of</a> <font color="Olive" title="b2">G1</font> )</span><br/><a NAME="E3:66_1_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E82">A32</font></span>: 
1 <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c8">k</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c12">j</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1
 <span class="kw">by</span> <span class="lab"><a class="ref" href="nat_1.html#T13" onmouseover="rs('nat_1/T13')" onmouseout="rh()">NAT_1:13</a></span>;<br/><a NAME="E4:66_1_3"/>
<span class="p1">(<span class="default">1 <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c8">k</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c12">j</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:66_1_3"><span class="lab"><font color="Green" title="E81">A31</font></span></a>, <a class="ref" href="nat_1.html#T13" onmouseover="rs('nat_1/T13')" onmouseout="rh()">NAT_1:13</a></span>;<br/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c13">j1</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a><span class="kw"> such that </span><br/><a NAME="E6:66_1_3"/><span class="lab"><font color="Green" title="E83">A33</font></span>: 
<font color="Maroon" title="c12">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c8">k</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c13">j1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="nat_1.html#T10" onmouseover="rs('nat_1/T10')" onmouseout="rh()">NAT_1:10</a></span>;<br/><a NAME="E7:66_1_3"/>
<font color="Maroon" title="c12">j</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default">1 <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c8">k</font></span>)</span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c10">l</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default">1 <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c8">k</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E16:66_1"><span class="lab"><font color="Green" title="E76">A23</font></span></a>, <a class="ref" href="xreal_1.html#T9" onmouseover="rs('xreal_1/T9')" onmouseout="rh()">XREAL_1:9</a></span>;<br/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c14">F1</font>, <font color="Maroon" title="c15">G1</font> being   <a href="modelc_2.html#NM1" title="MODELC_2:NM.1">LTL-formula</a><span class="kw"> such that </span><br/><a NAME="E9:66_1_3"/><span class="lab"><font color="Green" title="E84">A34</font></span>: 
( <font color="Maroon" title="c5">L9</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default">1 <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c13">j1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">F1</font> &amp; <font color="Maroon" title="c5">L9</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c13">j1</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">G1</font> &amp; <font color="Maroon" title="c14">F1</font> <a href="modelc_2.html#R1" title="MODELC_2:pred.1">is_immediate_constituent_of</a> <font color="Maroon" title="c15">G1</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:66"><span class="lab"><font color="Green" title="E63">A9</font></span></a>, <a class="txt" href="#E6:66_1_3"><span class="lab"><font color="Green" title="E83">A33</font></span></a>, <a class="ref" href="nat_1.html#T11" onmouseover="rs('nat_1/T11')" onmouseout="rh()">NAT_1:11</a></span>;<br/><span class="kw">take </span><font color="Maroon" title="c16">F1</font> = <font color="Maroon" title="c14">F1</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">  ex <font color="Olive" title="b1">G1</font> being   <a href="modelc_2.html#NM1" title="MODELC_2:NM.1">LTL-formula</a> st <br/>( <font color="Maroon" title="c11">K</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c12">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">F1</font> &amp; <font color="Maroon" title="c11">K</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">j</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">G1</font> &amp; <font color="Maroon" title="c16">F1</font> <a href="modelc_2.html#R1" title="MODELC_2:pred.1">is_immediate_constituent_of</a> <font color="Olive" title="b1">G1</font> )</span><br/><span class="kw">take </span><font color="Maroon" title="c17">G1</font> = <font color="Maroon" title="c15">G1</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="c11">K</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c12">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">F1</font> &amp; <font color="Maroon" title="c11">K</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">j</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c17">G1</font> &amp; <font color="Maroon" title="c16">F1</font> <a href="modelc_2.html#R1" title="MODELC_2:pred.1">is_immediate_constituent_of</a> <font color="Maroon" title="c17">G1</font> )</span><br/><a NAME="E10:66_1_3"/><span class="lab"><font color="Green" title="E85">A35</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c13">j1</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default">1 <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c8">k</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default">1 <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c8">k</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c13">j1</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default">1 <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c8">k</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <span class="p2">(<span class="default">1 <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c8">k</font></span>)</span></span>)</span>
 ;<br/><span class="p1">(<span class="default"><font color="Maroon" title="c12">j</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c9">L1</font></span>)</span> = 
1 <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">j</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <span class="p3">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c9">L1</font></span>)</span></span>)</span></span>)</span>

<br/>.= 
<span class="p1">(<span class="default">1 <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c13">j1</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:66"><span class="lab"><font color="Green" title="E65">A11</font></span></a>, <a class="txt" href="#E5:66_1"><span class="lab"><font color="Green" title="E71">A17</font></span></a>, <a class="txt" href="#E6:66_1_3"><span class="lab"><font color="Green" title="E83">A33</font></span></a>, <a class="txt" href="#E10:66_1_3"><span class="lab"><font color="Green" title="E85">A35</font></span></a>, <a class="ref" href="finseq_1.html#T17" onmouseover="rs('finseq_1/T17')" onmouseout="rh()">FINSEQ_1:17</a></span>
;<br/><span class="kw">hence </span><a NAME="E12:66_1_3"/>
( <font color="Maroon" title="c11">K</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c12">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">F1</font> &amp; <font color="Maroon" title="c11">K</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">j</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c17">G1</font> &amp; <font color="Maroon" title="c16">F1</font> <a href="modelc_2.html#R1" title="MODELC_2:pred.1">is_immediate_constituent_of</a> <font color="Maroon" title="c17">G1</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:66_1"><span class="lab"><font color="Green" title="E72">A18</font></span></a>, <a class="txt" href="#E7:66_1"><span class="lab"><font color="Green" title="E73">A19</font></span></a>, <a class="txt" href="#E16:66_1"><span class="lab"><font color="Green" title="E76">A23</font></span></a>, <a class="txt" href="#E2:66_1_3"><span class="lab"><font color="Green" title="E81">A31</font></span></a>, <a class="txt" href="#E3:66_1_3"><span class="lab"><font color="Green" title="E82">A32</font></span></a>, <a class="txt" href="#E1:66_1_3"><span class="lab"><font color="Green" title="E80">A30</font></span></a>, <a class="txt" href="#E10:66_1_3"><span class="lab"><font color="Green" title="E85">A35</font></span></a>, <a class="txt" href="#E9:66_1_3"><span class="lab"><font color="Green" title="E84">A34</font></span></a>, <a class="ref" href="finseq_1.html#T24" onmouseover="rs('finseq_1/T24')" onmouseout="rh()">FINSEQ_1:24</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>
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="66_1_4"><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"> ( <font color="Maroon" title="c12">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c8">k</font> implies  ex <font color="Olive" title="b1">F1</font>, <font color="Olive" title="b2">G1</font> being   <a href="modelc_2.html#NM1" title="MODELC_2:NM.1">LTL-formula</a> st <br/>( <font color="Maroon" title="c11">K</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c12">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">F1</font> &amp; <font color="Maroon" title="c11">K</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">j</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">G1</font> &amp; <font color="Olive" title="b1">F1</font> <a href="modelc_2.html#R1" title="MODELC_2:pred.1">is_immediate_constituent_of</a> <font color="Olive" title="b2">G1</font> ) )</span></a><div class="add"><a NAME="E1:66_1_4"/><span class="lab"><font color="Green" title="E80">A36</font></span>: 
( <font color="Maroon" title="c12">j</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c10">l</font> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c12">j</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c12">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">j</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <font color="Maroon" title="c12">j</font></span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E16:66_1"><span class="lab"><font color="Green" title="E76">A23</font></span></a>, <a class="ref" href="nat_1.html#T13" onmouseover="rs('nat_1/T13')" onmouseout="rh()">NAT_1:13</a></span>;<br/><span class="kw">assume </span><a NAME="E2:66_1_4"/><span class="lab"><font color="Green" title="E81">A37</font></span>: 
<font color="Maroon" title="c12">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c8">k</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">  ex <font color="Olive" title="b1">F1</font>, <font color="Olive" title="b2">G1</font> being   <a href="modelc_2.html#NM1" title="MODELC_2:NM.1">LTL-formula</a> st <br/>( <font color="Maroon" title="c11">K</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c12">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">F1</font> &amp; <font color="Maroon" title="c11">K</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">j</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">G1</font> &amp; <font color="Olive" title="b1">F1</font> <a href="modelc_2.html#R1" title="MODELC_2:pred.1">is_immediate_constituent_of</a> <font color="Olive" title="b2">G1</font> )</span><br/><a NAME="E3:66_1_4"/><span class="kw">then </span>
<font color="Maroon" title="c12">j</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default">1 <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c8">k</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1
 <span class="kw">by</span> <span class="lab"><a class="ref" href="nat_1.html#T13" onmouseover="rs('nat_1/T13')" onmouseout="rh()">NAT_1:13</a></span>;<br/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c13">F1</font>, <font color="Maroon" title="c14">G1</font> being   <a href="modelc_2.html#NM1" title="MODELC_2:NM.1">LTL-formula</a><span class="kw"> such that </span><br/><a NAME="E5:66_1_4"/><span class="lab"><font color="Green" title="E82">A38</font></span>: 
( <font color="Maroon" title="c7">L</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c12">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">F1</font> &amp; <font color="Maroon" title="c7">L</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">j</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">G1</font> &amp; <font color="Maroon" title="c13">F1</font> <a href="modelc_2.html#R1" title="MODELC_2:pred.1">is_immediate_constituent_of</a> <font color="Maroon" title="c14">G1</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E16:66"><span class="lab"><font color="Green" title="E68">A14</font></span></a>, <a class="txt" href="#E20:66"><span class="lab"><font color="Green" title="E69">A15</font></span></a>, <a class="txt" href="#E15:66_1"><span class="lab"><font color="Green" title="E75">A22</font></span></a></span>;<br/><span class="kw">take </span><font color="Maroon" title="c15">F1</font> = <font color="Maroon" title="c13">F1</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">  ex <font color="Olive" title="b1">G1</font> being   <a href="modelc_2.html#NM1" title="MODELC_2:NM.1">LTL-formula</a> st <br/>( <font color="Maroon" title="c11">K</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c12">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">F1</font> &amp; <font color="Maroon" title="c11">K</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">j</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">G1</font> &amp; <font color="Maroon" title="c15">F1</font> <a href="modelc_2.html#R1" title="MODELC_2:pred.1">is_immediate_constituent_of</a> <font color="Olive" title="b1">G1</font> )</span><br/><span class="kw">take </span><font color="Maroon" title="c16">G1</font> = <font color="Maroon" title="c14">G1</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="c11">K</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c12">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">F1</font> &amp; <font color="Maroon" title="c11">K</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">j</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">G1</font> &amp; <font color="Maroon" title="c15">F1</font> <a href="modelc_2.html#R1" title="MODELC_2:pred.1">is_immediate_constituent_of</a> <font color="Maroon" title="c16">G1</font> )</span><br/><a NAME="E6:66_1_4"/>
1 <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c8">k</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c12">j</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:66_1_4"><span class="lab"><font color="Green" title="E81">A37</font></span></a>, <a class="ref" href="nat_1.html#T13" onmouseover="rs('nat_1/T13')" onmouseout="rh()">NAT_1:13</a></span>;<br/><span class="kw">hence </span><a NAME="E7:66_1_4"/>
( <font color="Maroon" title="c11">K</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c12">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">F1</font> &amp; <font color="Maroon" title="c11">K</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">j</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">G1</font> &amp; <font color="Maroon" title="c15">F1</font> <a href="modelc_2.html#R1" title="MODELC_2:pred.1">is_immediate_constituent_of</a> <font color="Maroon" title="c16">G1</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E15:66"><span class="lab"><font color="Green" title="E67">A13</font></span></a>, <a class="txt" href="#E8:66"><span class="lab"><font color="Green" title="E61">A7</font></span></a>, <a class="txt" href="#E20:66"><span class="lab"><font color="Green" title="E69">A15</font></span></a>, <a class="txt" href="#E6:66_1"><span class="lab"><font color="Green" title="E72">A18</font></span></a>, <a class="txt" href="#E7:66_1"><span class="lab"><font color="Green" title="E73">A19</font></span></a>, <a class="txt" href="#E8:66_1"><span class="lab"><font color="Green" title="E74">A20</font></span></a>, <a class="txt" href="#E15:66_1"><span class="lab"><font color="Green" title="E75">A22</font></span></a>, <a class="txt" href="#E2:66_1_4"><span class="lab"><font color="Green" title="E81">A37</font></span></a>, <a class="txt" href="#E1:66_1_4"><span class="lab"><font color="Green" title="E80">A36</font></span></a>, <a class="txt" href="#E5:66_1_4"><span class="lab"><font color="Green" title="E82">A38</font></span></a>, <a class="ref" href="finseq_1.html#T24" onmouseover="rs('finseq_1/T24')" onmouseout="rh()">FINSEQ_1:24</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="E22:66_1"/>
 ex <font color="Olive" title="b1">H1</font>, <font color="Olive" title="b2">F1</font> being   <a href="modelc_2.html#NM1" title="MODELC_2:NM.1">LTL-formula</a> st <br/>( <font color="Maroon" title="c11">K</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c12">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">H1</font> &amp; <font color="Maroon" title="c11">K</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">j</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">F1</font> &amp; <font color="Olive" title="b1">H1</font> <a href="modelc_2.html#R1" title="MODELC_2:pred.1">is_immediate_constituent_of</a> <font color="Olive" title="b2">F1</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:66_1"><span class="lab"><font color="Green" title="E78">A25</font></span></a>, <a class="txt" href="#E20:66_1"><span class="lab"><font color="Green" title="E79">A29</font></span></a>, <a class="ref" href="xxreal_0.html#T1" onmouseover="rs('xxreal_0/T1')" onmouseout="rh()">XXREAL_0:1</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="E23:66"/><span class="lab"><font color="Green" title="E70">A39</font></span>: 
<font color="Maroon" title="c1">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">H</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="E24:66"/>
<font color="Maroon" title="c1">F</font> <a href="modelc_2.html#R3" title="MODELC_2:pred.3">is_proper_subformula_of</a> <font color="Maroon" title="c2">G</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:66"><span class="lab"><font color="Green" title="E55">A1</font></span></a>, <a class="txt" href="#E2:66"><span class="lab"><font color="Green" title="E56">A2</font></span></a></span>;<br/>
<a NAME="E25:66"/><span class="kw">then </span><span class="lab"><font color="Green" title="E71">A40</font></span>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c1">F</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">G</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="modelc_2.html#T32" target="_self" onmouseover="rs('modelc_2/T32')" onmouseout="rh()">Th32</a></span>;<br/>
<a NAME="E26:66"/>
<font color="Maroon" title="c2">G</font> <a href="modelc_2.html#R3" title="MODELC_2:pred.3">is_proper_subformula_of</a> <font color="Maroon" title="c3">H</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:66"><span class="lab"><font color="Green" title="E57">A3</font></span></a>, <a class="txt" href="#E4:66"><span class="lab"><font color="Green" title="E58">A4</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E27:66"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E23:66"><span class="lab"><font color="Green" title="E70">A39</font></span></a>, <a class="txt" href="#E25:66"><span class="lab"><font color="Green" title="E71">A40</font></span></a>, <a class="ref" href="modelc_2.html#T32" target="_self" onmouseover="rs('modelc_2/T32')" onmouseout="rh()">Th32</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>
