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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="struct_0.html#L2">ZeroStr</a> ;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="algseq_1.html#NM1">AlgSequence</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>



<a NAME="E1:27"/><i><font color="Green">E20</font></i>: 
0 <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a> 1
 
;<br/>
<b>assume </b><a NAME="E2:27"/>
<font color="Maroon">c<sub>2</sub></font> <a href="funct_2.html#R2">=</a> <span class="p1"><a href="algseq_1.html#K5" target="_self">&lt;%</a><span class="default"><span class="p2">(<span class="default"><a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span><a href="algseq_1.html#K5" target="_self">%&gt;</a></span>
 ;<br/>

<a NAME="E3:27"/><b>then </b>
(  <a href="algseq_1.html#K3" target="_self">len</a> <font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> 1 &amp; <font color="Maroon">c<sub>2</sub></font> <a href="funct_2.html#K3">.</a> 0 <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>1</sub></font> )
 
<b>by </b><i><a class="ref" href="algseq_1.html#D6" target="_self">Def6</a></i>;<br/>
<a NAME="E4:27"/><b>then </b>
(  <a href="algseq_1.html#K3" target="_self">len</a> <font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> 1 &amp;  <a href="algseq_1.html#K3" target="_self">len</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 1 )
 
<b>by </b><i><a class="txt" href="algseq_1.html#E1:27"><i><font color="Green">E20</font></i></a>, <a class="ref" href="algseq_1.html#T25" target="_self">Th25</a></i>;<br/>
<a NAME="E5:27"/><b>then </b>
 <a href="algseq_1.html#K3" target="_self">len</a> <font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 1
 
<b>by </b><i><a class="ref" href="real_1.html#D5">REAL_1:def 5</a></i>;<br/>
<b>hence </b><a NAME="E6:27"/>
 <a href="algseq_1.html#K3" target="_self">len</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> 0
 <b>by </b><i><a class="ref" href="nat_1.html#T39">NAT_1:39</a></i>;<br/>


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