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<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ] <b>means </b> ex <font color="Olive" title="b1">F</font> being  <a href="modelc_2.html#NM2" title="MODELC_2:NM.2">LTL-formula</a> st <br/>( <font color="Olive" title="b1">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> $1 &amp; <font color="Olive" title="b1">F</font> <a href="modelc_2.html#R2" title="MODELC_2:pred.2">is_subformula_of</a> <font color="Maroon" title="c1">H</font> );<br/>
<b>consider </b><font color="Maroon" title="c2">X</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E2:81_1_1"/><i><font color="Green" title="E70">A1</font></i>: 
for <font color="Olive" title="b1">a</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  holds <br/> ( <font color="Olive" title="b1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">X</font> iff ( <font color="Olive" title="b1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  <a href="finseq_1.html#K13" title="FINSEQ_1:func.13">*</a>  &amp; <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">a</font>] ) )
 <b>from </b><i><a class="ref" href="xboole_0.html#S1" title="XBOOLE_0:sch.1">XBOOLE_0:sch 1</a>();<br/></i>
<b>take </b>
<font color="Maroon" title="c2">X</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">a</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  holds <br/> ( <font color="Olive" title="b1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">X</font> iff  ex <font color="Olive" title="b2">F</font> being  <a href="modelc_2.html#NM2" title="MODELC_2:NM.2">LTL-formula</a> st <br/>( <font color="Olive" title="b2">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> &amp; <font color="Olive" title="b2">F</font> <a href="modelc_2.html#R2" title="MODELC_2:pred.2">is_subformula_of</a> <font color="Maroon" title="c1">H</font> ) )</span><br/>

<b>let </b><font color="Maroon" title="c3">a</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c3">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">X</font> iff  ex <font color="Olive" title="b1">F</font> being  <a href="modelc_2.html#NM2" title="MODELC_2:NM.2">LTL-formula</a> st <br/>( <font color="Olive" title="b1">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> &amp; <font color="Olive" title="b1">F</font> <a href="modelc_2.html#R2" title="MODELC_2:pred.2">is_subformula_of</a> <font color="Maroon" title="c1">H</font> ) )</span><br/>

<b>thus </b><a NAME="E3:81_1_1"/>
( <font color="Maroon" title="c3">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">X</font> implies  ex <font color="Olive" title="b1">F</font> being  <a href="modelc_2.html#NM2" title="MODELC_2:NM.2">LTL-formula</a> st <br/>( <font color="Olive" title="b1">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> &amp; <font color="Olive" title="b1">F</font> <a href="modelc_2.html#R2" title="MODELC_2:pred.2">is_subformula_of</a> <font color="Maroon" title="c1">H</font> ) )
 <b>by </b><i><a class="txt" href="modelc_2.html#E2:81_1_1"><i><font color="Green" title="E70">A1</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  ex <font color="Olive" title="b1">F</font> being  <a href="modelc_2.html#NM2" title="MODELC_2:NM.2">LTL-formula</a> st <br/>( <font color="Olive" title="b1">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> &amp; <font color="Olive" title="b1">F</font> <a href="modelc_2.html#R2" title="MODELC_2:pred.2">is_subformula_of</a> <font color="Maroon" title="c1">H</font> ) implies <font color="Maroon" title="c3">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">X</font> )</span><br/>

<b>given </b><font color="Maroon" title="c4">F</font> being   <a href="modelc_2.html#NM2" title="MODELC_2:NM.2">LTL-formula</a><b> such that </b><a NAME="E5:81_1_1"/><i><font color="Green" title="E71">A2</font></i>: 
( <font color="Maroon" title="c4">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> &amp; <font color="Maroon" title="c4">F</font> <a href="modelc_2.html#R2" title="MODELC_2:pred.2">is_subformula_of</a> <font color="Maroon" title="c1">H</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c3">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">X</font></span><br/>

<a NAME="E6:81_1_1"/>
<font color="Maroon" title="c4">F</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  <a href="finseq_1.html#K13" title="FINSEQ_1:func.13">*</a> 
 
<b>by </b><i><a class="ref" href="finseq_1.html#D11" title="FINSEQ_1:def.11">FINSEQ_1:def 11</a></i>;<br/>
<b>hence </b><a NAME="E7:81_1_1"/>
<font color="Maroon" title="c3">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">X</font>
 <b>by </b><i><a class="txt" href="modelc_2.html#E2:81_1_1"><i><font color="Green" title="E70">A1</font></i></a>, <a class="txt" href="modelc_2.html#E5:81_1_1"><i><font color="Green" title="E71">A2</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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