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<span class="kw">let </span><font color="Maroon" title="c1">V</font> be    <a href="modelc_1.html#L2" title="MODELC_1:struct.2">CTLModelStr</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">Kai</font> being  <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <a href="modelc_1.html#K19" title="MODELC_1:func.19">atomic_WFF</a> ,the <a href="modelc_1.html#U6" title="MODELC_1:sel.6">BasicAssign</a> of <font color="Maroon" title="c1">V</font><br/> for <font color="Olive" title="b2">f1</font>, <font color="Olive" title="b3">f2</font> being  <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <a href="modelc_1.html#K13" title="MODELC_1:func.13">CTL_WFF</a> ,the <a href="modelc_1.html#U5" title="MODELC_1:sel.5">Assignations</a> of <font color="Maroon" title="c1">V</font>  st <font color="Olive" title="b2">f1</font> <a href="modelc_1.html#R1" title="MODELC_1:pred.1">is-Evaluation-for</a> <font color="Olive" title="b1">Kai</font> &amp; <font color="Olive" title="b3">f2</font> <a href="modelc_1.html#R1" title="MODELC_1:pred.1">is-Evaluation-for</a> <font color="Olive" title="b1">Kai</font> holds <br/><font color="Olive" title="b2">f1</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Olive" title="b3">f2</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">Kai</font> be   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <a href="modelc_1.html#K19" title="MODELC_1:func.19">atomic_WFF</a> ,the <a href="modelc_1.html#U6" title="MODELC_1:sel.6">BasicAssign</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"> for <font color="Olive" title="b1">f1</font>, <font color="Olive" title="b2">f2</font> being  <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <a href="modelc_1.html#K13" title="MODELC_1:func.13">CTL_WFF</a> ,the <a href="modelc_1.html#U5" title="MODELC_1:sel.5">Assignations</a> of <font color="Maroon" title="c1">V</font>  st <font color="Olive" title="b1">f1</font> <a href="modelc_1.html#R1" title="MODELC_1:pred.1">is-Evaluation-for</a> <font color="Maroon" title="c2">Kai</font> &amp; <font color="Olive" title="b2">f2</font> <a href="modelc_1.html#R1" title="MODELC_1:pred.1">is-Evaluation-for</a> <font color="Maroon" title="c2">Kai</font> holds <br/><font color="Olive" title="b1">f1</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Olive" title="b2">f2</font></span><br/><span class="kw">let </span><font color="Maroon" title="c3">f1</font>, <font color="Maroon" title="c4">f2</font> be   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <a href="modelc_1.html#K13" title="MODELC_1:func.13">CTL_WFF</a> ,the <a href="modelc_1.html#U5" title="MODELC_1:sel.5">Assignations</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="c3">f1</font> <a href="modelc_1.html#R1" title="MODELC_1:pred.1">is-Evaluation-for</a> <font color="Maroon" title="c2">Kai</font> &amp; <font color="Maroon" title="c4">f2</font> <a href="modelc_1.html#R1" title="MODELC_1:pred.1">is-Evaluation-for</a> <font color="Maroon" title="c2">Kai</font> implies <font color="Maroon" title="c3">f1</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c4">f2</font> )</span><br/>







<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:64"/><span class="lab"><font color="Green" title="E57">A1</font></span>: 
<font color="Maroon" title="c3">f1</font> <a href="modelc_1.html#R1" title="MODELC_1:pred.1">is-Evaluation-for</a> <font color="Maroon" title="c2">Kai</font>
 <span class="kw">and </span><br/><a NAME="E2:64"/><span class="lab"><font color="Green" title="E58">A2</font></span>: 
<font color="Maroon" title="c4">f2</font> <a href="modelc_1.html#R1" title="MODELC_1:pred.1">is-Evaluation-for</a> <font color="Maroon" title="c2">Kai</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="c3">f1</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c4">f2</font></span><br/>

<a NAME="E3:64"/>
for <font color="Olive" title="b1">H</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">H</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_1.html#K13" title="MODELC_1:func.13">CTL_WFF</a>  holds <br/><font color="Maroon" title="c3">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">H</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="64_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c5">H</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <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="c5">H</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_1.html#K13" title="MODELC_1:func.13">CTL_WFF</a>  implies <font color="Maroon" title="c3">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">H</font> )</span><br/>

<span class="kw">assume </span><a NAME="E1:64_1"/>
<font color="Maroon" title="c5">H</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_1.html#K13" title="MODELC_1:func.13">CTL_WFF</a> 
 ; <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="c3">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">H</font></span><br/>

<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c6">H</font> = <font color="Maroon" title="c5">H</font> as   <a href="modelc_1.html#NM1" title="MODELC_1:NM.1">CTL-formula</a> <span class="kw">by</span> <span class="lab"><a class="ref" href="modelc_1.html#T1" target="_self" title="MODELC_1:th.1">Th1</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c7">n</font> =  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">H</font>;<br/>
<a NAME="E3:64_1"/><span class="lab"><font color="Green" title="E59">A3</font></span>: 
<font color="Maroon" title="c4">f2</font> <a href="modelc_1.html#R2" title="MODELC_1:pred.2">is-PreEvaluation-for</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">H</font>,<font color="Maroon" title="c2">Kai</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:64"><span class="lab"><font color="Green" title="E58">A2</font></span></a>, <a class="txt" href="modelc_1.html#E56"><span class="lab"><font color="Green" title="E48">Lm26</font></span></a></span>;<br/>
<a NAME="E4:64_1"/>
<font color="Maroon" title="c3">f1</font> <a href="modelc_1.html#R2" title="MODELC_1:pred.2">is-PreEvaluation-for</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">H</font>,<font color="Maroon" title="c2">Kai</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:64"><span class="lab"><font color="Green" title="E57">A1</font></span></a>, <a class="txt" href="modelc_1.html#E56"><span class="lab"><font color="Green" title="E48">Lm26</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:64_1"/>
<font color="Maroon" title="c3">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">H</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:64_1"><span class="lab"><font color="Green" title="E59">A3</font></span></a>, <a class="txt" href="modelc_1.html#E57"><span class="lab"><font color="Green" title="E49">Lm27</font></span></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/>


</div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E4:64"/>
<font color="Maroon" title="c3">f1</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c4">f2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#T18" title="FUNCT_2:th.18">FUNCT_2:18</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/>


</div>
