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<b>let </b><font color="Maroon">c<sub>1</sub></font> be  non <a href="struct_0.html#V3">empty</a>  <a href="lang1.html#L1" target="_self">DTConstrStr</a> ;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="lang1.html#NM1">Symbol</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be   <a href="lang1.html#NM2">String</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>





<b>given </b><font color="Maroon">c<sub>4</sub></font>, <font color="Maroon">c<sub>5</sub></font>, <font color="Maroon">c<sub>6</sub></font> being   <a href="lang1.html#NM2">String</a> of <font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>7</sub></font> being   <a href="lang1.html#NM1">Symbol</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><a NAME="E1:16"/><i><font color="Green">E4</font></i>: 
( <span class="p1"><a href="lang1.html#K3" target="_self">&lt;*</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="lang1.html#K3" target="_self">*&gt;</a></span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="lang1.html#K1" target="_self">^</a> <span class="p2"><a href="lang1.html#K3" target="_self">&lt;*</a><span class="default"><font color="Maroon">c<sub>7</sub></font></span><a href="lang1.html#K3" target="_self">*&gt;</a></span></span>)</span> <a href="lang1.html#K1" target="_self">^</a> <font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="lang1.html#K1" target="_self">^</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="lang1.html#K1" target="_self">^</a> <font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>7</sub></font> <a href="lang1.html#R1" target="_self">==&gt;</a> <font color="Maroon">c<sub>6</sub></font> )
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="lang1.html#D4" target="_self">LANG1:def 4</a><br/>

<a NAME="E2:16"/>
(  <a href="finseq_1.html#K3">len</a> <span class="p1"><a href="lang1.html#K3" target="_self">&lt;*</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="lang1.html#K3" target="_self">*&gt;</a></span> <a href="hidden.html#R1">=</a> 1 &amp;  <a href="finseq_1.html#K3">len</a> <span class="p1"><a href="lang1.html#K3" target="_self">&lt;*</a><span class="default"><font color="Maroon">c<sub>7</sub></font></span><a href="lang1.html#K3" target="_self">*&gt;</a></span> <a href="hidden.html#R1">=</a> 1 &amp;  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="lang1.html#K1" target="_self">^</a> <span class="p2"><a href="lang1.html#K3" target="_self">&lt;*</a><span class="default"><font color="Maroon">c<sub>7</sub></font></span><a href="lang1.html#K3" target="_self">*&gt;</a></span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2"><a href="lang1.html#K3" target="_self">&lt;*</a><span class="default"><font color="Maroon">c<sub>7</sub></font></span><a href="lang1.html#K3" target="_self">*&gt;</a></span></span>)</span> &amp;  <a href="finseq_1.html#K3">len</a> <span class="p1"><a href="lang1.html#K3" target="_self">&lt;*</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="lang1.html#K3" target="_self">*&gt;</a></span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="lang1.html#K1" target="_self">^</a> <span class="p3"><a href="lang1.html#K3" target="_self">&lt;*</a><span class="default"><font color="Maroon">c<sub>7</sub></font></span><a href="lang1.html#K3" target="_self">*&gt;</a></span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> )
 
<b>by </b><i><a class="txt" href="lang1.html#E1:16"><i><font color="Green">E4</font></i></a>, <a class="ref" href="finseq_1.html#T35">FINSEQ_1:35</a>, <a class="ref" href="finseq_1.html#T57">FINSEQ_1:57</a></i>;<br/>
<a NAME="E3:16"/><b>then </b>
1 <a href="nat_1.html#K1">+</a> 0 <a href="hidden.html#R1">=</a> 1 <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span>
 
;<br/>
<a NAME="E4:16"/><b>then </b>
<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="hidden.html#R1">=</a> 0
 
;<br/>
<a NAME="E5:16"/><b>then </b>
(  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> 0 &amp;  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 0 )
 
<b>by </b><i><a class="ref" href="nat_1.html#T23">NAT_1:23</a></i>;<br/>
<a NAME="E6:16"/><b>then </b>
( <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  &amp; <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  &amp; <a href="xboole_0.html#K1">{}</a>  <a href="finseq_1.html#K7">^</a> <span class="p1"><a href="lang1.html#K3" target="_self">&lt;*</a><span class="default"><font color="Maroon">c<sub>7</sub></font></span><a href="lang1.html#K3" target="_self">*&gt;</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="lang1.html#K3" target="_self">&lt;*</a><span class="default"><font color="Maroon">c<sub>7</sub></font></span><a href="lang1.html#K3" target="_self">*&gt;</a></span> &amp; <span class="p1"><a href="lang1.html#K3" target="_self">&lt;*</a><span class="default"><font color="Maroon">c<sub>7</sub></font></span><a href="lang1.html#K3" target="_self">*&gt;</a></span> <a href="finseq_1.html#K7">^</a> <a href="xboole_0.html#K1">{}</a>  <a href="hidden.html#R1">=</a> <span class="p1"><a href="lang1.html#K3" target="_self">&lt;*</a><span class="default"><font color="Maroon">c<sub>7</sub></font></span><a href="lang1.html#K3" target="_self">*&gt;</a></span> &amp; <a href="xboole_0.html#K1">{}</a>  <a href="finseq_1.html#K7">^</a> <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="finseq_1.html#K7">^</a> <a href="xboole_0.html#K1">{}</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font> &amp; <span class="p1"><a href="lang1.html#K3" target="_self">&lt;*</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="lang1.html#K3" target="_self">*&gt;</a></span> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> &amp; <span class="p1"><a href="lang1.html#K3" target="_self">&lt;*</a><span class="default"><font color="Maroon">c<sub>7</sub></font></span><a href="lang1.html#K3" target="_self">*&gt;</a></span> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font> )
 
<b>by </b><i><a class="ref" href="finseq_1.html#T25">FINSEQ_1:25</a>, <a class="ref" href="finseq_1.html#T47">FINSEQ_1:47</a>, <a class="ref" href="finseq_1.html#T57">FINSEQ_1:57</a></i>;<br/>
<b>hence </b><a NAME="E7:16"/>
<font color="Maroon">c<sub>2</sub></font> <a href="lang1.html#R1" target="_self">==&gt;</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="lang1.html#E1:16"><i><font color="Green">E4</font></i></a></i>;<br/>


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