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<span class="kw">let </span><font color="Maroon" title="c1">v</font> be   <a href="modelc_2.html#NM1" title="MODELC_2:NM.1">LTL-formula</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">N2</font>, <font color="Olive" title="b2">N1</font> being  <a href="modelc_3.html#V1" title="MODELC_3:attr.1">strict</a>   <a href="modelc_3.html#L1" title="MODELC_3:struct.1">LTLnode</a> of <font color="Maroon" title="c1">v</font>  st <font color="Olive" title="b1">N2</font> <a href="modelc_3.html#R2" title="MODELC_3:pred.2">is_succ1_of</a> <font color="Olive" title="b2">N1</font> holds <br/> <a href="modelc_3.html#K18" title="MODELC_3:func.18">len</a> the <a href="modelc_3.html#U2" title="MODELC_3:sel.2">LTLnew</a> of <font color="Olive" title="b1">N2</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K18" title="MODELC_3:func.18">len</a> the <a href="modelc_3.html#U2" title="MODELC_3:sel.2">LTLnew</a> of <font color="Olive" title="b2">N1</font></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> 1</span><br/><span class="kw">let </span><font color="Maroon" title="c2">N2</font>, <font color="Maroon" title="c3">N1</font> be   <a href="modelc_3.html#V1" title="MODELC_3:attr.1">strict</a>   <a href="modelc_3.html#L1" title="MODELC_3:struct.1">LTLnode</a> of <font color="Maroon" title="c1">v</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">N2</font> <a href="modelc_3.html#R2" title="MODELC_3:pred.2">is_succ1_of</a> <font color="Maroon" title="c3">N1</font> implies  <a href="modelc_3.html#K18" title="MODELC_3:func.18">len</a> the <a href="modelc_3.html#U2" title="MODELC_3:sel.2">LTLnew</a> of <font color="Maroon" title="c2">N2</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K18" title="MODELC_3:func.18">len</a> the <a href="modelc_3.html#U2" title="MODELC_3:sel.2">LTLnew</a> of <font color="Maroon" title="c3">N1</font></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> 1 )</span><br/>





<span class="kw">set </span><font color="Maroon" title="c4">NN1</font> = the <a href="modelc_3.html#U2" title="MODELC_3:sel.2">LTLnew</a> of <font color="Maroon" title="c3">N1</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c5">NN2</font> = the <a href="modelc_3.html#U2" title="MODELC_3:sel.2">LTLnew</a> of <font color="Maroon" title="c2">N2</font>;<br/>
<span class="kw">assume </span><a NAME="E1:73"/>
<font color="Maroon" title="c2">N2</font> <a href="modelc_3.html#R2" title="MODELC_3:pred.2">is_succ1_of</a> <font color="Maroon" title="c3">N1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="modelc_3.html#K18" title="MODELC_3:func.18">len</a> the <a href="modelc_3.html#U2" title="MODELC_3:sel.2">LTLnew</a> of <font color="Maroon" title="c2">N2</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K18" title="MODELC_3:func.18">len</a> the <a href="modelc_3.html#U2" title="MODELC_3:sel.2">LTLnew</a> of <font color="Maroon" title="c3">N1</font></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> 1</span><br/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c6">H</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="E3:73"/><span class="lab"><font color="Green" title="E64">A1</font></span>: 
<font color="Maroon" title="c6">H</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="modelc_3.html#U2" title="MODELC_3:sel.2">LTLnew</a> of <font color="Maroon" title="c3">N1</font>
 <span class="kw">and </span><br/><a NAME="E4:73"/><span class="lab"><font color="Green" title="E65">A2</font></span>: 
<font color="Maroon" title="c2">N2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="modelc_3.html#K5" title="MODELC_3:func.5">SuccNode1</a> <font color="Maroon" title="c6">H</font>,<font color="Maroon" title="c3">N1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="modelc_3.html#D7" target="_self" title="MODELC_3:def.7">Def7</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c7">M1</font> = the <a href="modelc_3.html#U2" title="MODELC_3:sel.2">LTLnew</a> of <font color="Maroon" title="c3">N1</font> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c6">H</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c8">New1</font> =  <a href="modelc_3.html#K19" title="MODELC_3:func.19">LTLNew1</a> <font color="Maroon" title="c6">H</font>,<font color="Maroon" title="c1">v</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c9">M2</font> = <span class="p1">(<span class="default"><a href="modelc_3.html#K19" title="MODELC_3:func.19">LTLNew1</a> <font color="Maroon" title="c6">H</font>,<font color="Maroon" title="c1">v</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c3">N1</font>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c10">M1</font> = the <a href="modelc_3.html#U2" title="MODELC_3:sel.2">LTLnew</a> of <font color="Maroon" title="c3">N1</font> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c6">H</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> as   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="modelc_3.html#K1" title="MODELC_3:func.1">Subformulae</a> <font color="Maroon" title="c1">v</font></span>)</span> ;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c11">M2</font> = <span class="p1">(<span class="default"><a href="modelc_3.html#K19" title="MODELC_3:func.19">LTLNew1</a> <font color="Maroon" title="c6">H</font>,<font color="Maroon" title="c1">v</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c3">N1</font> as   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="modelc_3.html#K1" title="MODELC_3:func.1">Subformulae</a> <font color="Maroon" title="c1">v</font></span>)</span> ;<br/>
<a NAME="E7:73"/>
 <a href="modelc_3.html#K19" title="MODELC_3:func.19">LTLNew1</a> <font color="Maroon" title="c6">H</font>,<font color="Maroon" title="c1">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="modelc_3.html#K2" title="MODELC_3:func.2">LTLNew1</a> <font color="Maroon" title="c6">H</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:73"><span class="lab"><font color="Green" title="E64">A1</font></span></a>, <a class="ref" href="modelc_3.html#D27" target="_self" title="MODELC_3:def.27">Def27</a></span>;<br/>
<a NAME="E8:73"/><span class="kw">then </span>
the <a href="modelc_3.html#U2" title="MODELC_3:sel.2">LTLnew</a> of <font color="Maroon" title="c2">N2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">M1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c11">M2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:73"><span class="lab"><font color="Green" title="E64">A1</font></span></a>, <a class="txt" href="#E4:73"><span class="lab"><font color="Green" title="E65">A2</font></span></a>, <a class="ref" href="modelc_3.html#D4" target="_self" title="MODELC_3:def.4">Def4</a></span>;<br/>
<a NAME="E9:73"/><span class="kw">then </span><span class="lab"><font color="Green" title="E66">A3</font></span>: 
 <a href="modelc_3.html#K18" title="MODELC_3:func.18">len</a> the <a href="modelc_3.html#U2" title="MODELC_3:sel.2">LTLnew</a> of <font color="Maroon" title="c2">N2</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K18" title="MODELC_3:func.18">len</a> <font color="Maroon" title="c10">M1</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K18" title="MODELC_3:func.18">len</a> <font color="Maroon" title="c11">M2</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="modelc_3.html#T18" target="_self" title="MODELC_3:th.18">Th18</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c12">NN1</font> = the <a href="modelc_3.html#U2" title="MODELC_3:sel.2">LTLnew</a> of <font color="Maroon" title="c3">N1</font> as   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="modelc_3.html#K1" title="MODELC_3:func.1">Subformulae</a> <font color="Maroon" title="c1">v</font></span>)</span> ;<br/>
<a NAME="E11:73"/><span class="lab"><font color="Green" title="E67">A4</font></span>: 
 <a href="modelc_3.html#K18" title="MODELC_3:func.18">len</a> <font color="Maroon" title="c11">M2</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="modelc_3.html#K18" title="MODELC_3:func.18">len</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K19" title="MODELC_3:func.19">LTLNew1</a> <font color="Maroon" title="c6">H</font>,<font color="Maroon" title="c1">v</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="modelc_3.html#T15" target="_self" title="MODELC_3:th.15">Th15</a>, <a class="ref" href="xboole_1.html#T36" title="XBOOLE_1:th.36">XBOOLE_1:36</a></span>;<br/>
<a NAME="E12:73"/>
 <a href="modelc_3.html#K18" title="MODELC_3:func.18">len</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K19" title="MODELC_3:func.19">LTLNew1</a> <font color="Maroon" title="c6">H</font>,<font color="Maroon" title="c1">v</font></span>)</span> <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="c6">H</font></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:73"><span class="lab"><font color="Green" title="E64">A1</font></span></a>, <a class="txt" href="modelc_3.html#E74"><span class="lab"><font color="Green" title="E61">Lm28</font></span></a></span>;<br/>
<a NAME="E13:73"/><span class="kw">then </span>
 <a href="modelc_3.html#K18" title="MODELC_3:func.18">len</a> <font color="Maroon" title="c11">M2</font> <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="c6">H</font></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:73"><span class="lab"><font color="Green" title="E67">A4</font></span></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></span>;<br/>
<a NAME="E14:73"/><span class="kw">then </span><span class="lab"><font color="Green" title="E68">A5</font></span>: 
<span class="p1">(<span class="default"><a href="modelc_3.html#K18" title="MODELC_3:func.18">len</a> <font color="Maroon" title="c10">M1</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K18" title="MODELC_3:func.18">len</a> <font color="Maroon" title="c11">M2</font></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K18" title="MODELC_3:func.18">len</a> <font color="Maroon" title="c10">M1</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">H</font></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> 1</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xreal_1.html#T8" title="XREAL_1:th.8">XREAL_1:8</a></span>;<br/>
<a NAME="E15:73"/>
 <a href="modelc_3.html#K18" title="MODELC_3:func.18">len</a> <font color="Maroon" title="c10">M1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K18" title="MODELC_3:func.18">len</a> <font color="Maroon" title="c12">NN1</font></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">H</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:73"><span class="lab"><font color="Green" title="E64">A1</font></span></a>, <a class="ref" href="modelc_3.html#T10" target="_self" title="MODELC_3:th.10">Th10</a></span>;<br/>
<span class="kw">hence </span><a NAME="E16:73"/>
 <a href="modelc_3.html#K18" title="MODELC_3:func.18">len</a> the <a href="modelc_3.html#U2" title="MODELC_3:sel.2">LTLnew</a> of <font color="Maroon" title="c2">N2</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K18" title="MODELC_3:func.18">len</a> the <a href="modelc_3.html#U2" title="MODELC_3:sel.2">LTLnew</a> of <font color="Maroon" title="c3">N1</font></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> 1
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:73"><span class="lab"><font color="Green" title="E68">A5</font></span></a>, <a class="txt" href="#E9:73"><span class="lab"><font color="Green" title="E66">A3</font></span></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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