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<b>let </b><font color="Maroon">c<sub>1</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be  non <a href="xboole_0.html#V1">empty</a>  <a href="finseq_1.html#M2">FinSequence</a> of <font color="Maroon">c<sub>2</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>4</sub></font> be    <a href="finseq_1.html#M2">FinSequence</a> of <font color="Maroon">c<sub>2</sub></font>;<br/>







<b>assume </b><a NAME="E1:7"/><i><font color="Green">E6</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="finseq_4.html#K5">..</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/>

<a NAME="E2:7"/>
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 
<b>by </b><i><a class="ref" href="finseq_1.html#T25">FINSEQ_1:25</a></i>;<br/>
<a NAME="E3:7"/><b>then </b><i><font color="Green">E7</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K5">rng</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="txt" href="topreal8.html#E1:7"><i><font color="Green">E6</font></i></a>, <a class="ref" href="topreal8.html#T4" target="_self">Th4</a></i>;<br/>
<a NAME="E4:7"/><b>then </b><i><font color="Green">E8</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="finseq_4.html#K5">..</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> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="txt" href="topreal8.html#E1:7"><i><font color="Green">E6</font></i></a>, <a class="ref" href="finseq_6.html#T8">FINSEQ_6:8</a></i>;<br/>
<a NAME="E5:7"/>
 <a href="relset_1.html#K5">rng</a> <font color="Maroon">c<sub>3</sub></font> <a href="tarski.html#R1">c=</a>  <a href="relset_1.html#K5">rng</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#T42">FINSEQ_1:42</a></i>;<br/>
<b>hence </b><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> <a href="finseq_4.html#K7">|--</a> <font color="Maroon">c<sub>1</sub></font> = 
<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> <a href="rfinseq.html#K1">/^</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="finseq_4.html#K5">..</a> <span class="p2">(<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></span>)</span>
<b>by </b><i><a class="txt" href="topreal8.html#E3:7"><i><font color="Green">E7</font></i></a>, <a class="ref" href="finseq_5.html#T38">FINSEQ_5:38</a></i>
<br/>.= 
<font color="Maroon">c<sub>4</sub></font>
<b>by </b><i><a class="txt" href="topreal8.html#E4:7"><i><font color="Green">E8</font></i></a>, <a class="ref" href="finseq_5.html#T40">FINSEQ_5:40</a></i>
;<br/><br/>


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