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<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font> be   <a href="zf_lang.html#NM2">ZF-formula</a>;<br/>







<b>assume </b><a NAME="E1:45"/><i><font color="Green">E32</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="zf_lang.html#K7" target="_self">'&amp;'</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="zf_lang.html#K7" target="_self">'&amp;'</a> <font color="Maroon">c<sub>4</sub></font>
 ;<br/>

<a NAME="E2:45"/>
( <font color="Maroon">c<sub>1</sub></font> <a href="zf_lang.html#K7" target="_self">'&amp;'</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K12">&lt;*</a><span class="default">3</span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="finseq_1.html#K8">^</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="finseq_1.html#K8">^</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="zf_lang.html#K7" target="_self">'&amp;'</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K12">&lt;*</a><span class="default">3</span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="finseq_1.html#K8">^</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="finseq_1.html#K8">^</a> <font color="Maroon">c<sub>4</sub></font> &amp; <span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K12">&lt;*</a><span class="default">3</span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="finseq_1.html#K8">^</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="finseq_1.html#K8">^</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default">3</span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="finseq_1.html#K8">^</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="finseq_1.html#K8">^</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> &amp; <span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K12">&lt;*</a><span class="default">3</span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="finseq_1.html#K8">^</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="finseq_1.html#K8">^</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default">3</span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="finseq_1.html#K8">^</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="finseq_1.html#K8">^</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> )
 
<b>by </b><i><a class="ref" href="finseq_1.html#T45">FINSEQ_1:45</a></i>;<br/>
<a NAME="E3:45"/><b>then </b>
<font color="Maroon">c<sub>1</sub></font> <a href="finseq_1.html#K8">^</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="finseq_1.html#K8">^</a> <font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="txt" href="zf_lang.html#E1:45"><i><font color="Green">E32</font></i></a>, <a class="ref" href="finseq_1.html#T46">FINSEQ_1:46</a></i>;<br/>
<a NAME="E4:45"/><b>then </b><i><font color="Green">E33</font></i>: 
( (  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>3</sub></font> or  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>3</sub></font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>1</sub></font> ) &amp; (  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>3</sub></font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>1</sub></font> implies ex <font color="Olive">b<sub>1</sub></font> being  <a href="finseq_1.html#NM1">FinSequence</a> st <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="finseq_1.html#K7">^</a> <font color="Olive">b<sub>1</sub></font> ) &amp; (  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>3</sub></font> implies ex <font color="Olive">b<sub>1</sub></font> being  <a href="finseq_1.html#NM1">FinSequence</a> st <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> <a href="finseq_1.html#K7">^</a> <font color="Olive">b<sub>1</sub></font> ) )
 
<b>by </b><i><a class="ref" href="finseq_1.html#T64">FINSEQ_1:64</a></i>;<br/>
<a NAME="E5:45"/><i><font color="Green">E34</font></i>: 
( ex <font color="Olive">b<sub>1</sub></font> being  <a href="finseq_1.html#NM1">FinSequence</a> st <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> <a href="finseq_1.html#K7">^</a> <font color="Olive">b<sub>1</sub></font> implies <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> )
 
<b>by </b><i><a class="ref" href="zf_lang.html#T46" target="_self">Th46</a></i>;<br/>
<b>thus </b><a NAME="E6:45"/>
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="zf_lang.html#E4:45"><i><font color="Green">E33</font></i></a>, <a class="ref" href="zf_lang.html#T46" target="_self">Th46</a></i>;<br/>

<b>thus </b><a NAME="E7:45"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="txt" href="zf_lang.html#E1:45"><i><font color="Green">E32</font></i></a>, <a class="txt" href="zf_lang.html#E4:45"><i><font color="Green">E33</font></i></a>, <a class="txt" href="zf_lang.html#E5:45"><i><font color="Green">E34</font></i></a>, <a class="ref" href="zf_lang.html#T46" target="_self">Th46</a>, <a class="ref" href="finseq_1.html#T46">FINSEQ_1:46</a></i>;<br/>


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