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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="seq_1.html#NM1">Real_Sequence</a>;<br/>



<b>assume </b><a NAME="E1:54"/><i><font color="Green">E40</font></i>: 
<font color="Maroon">c<sub>2</sub></font> is <a href="relat_1.html#V2">being_not_0</a>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="54_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>3</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><a NAME="E1:54_1"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="seqm_3.html#K1" target="_self">^\</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> <a href="seq_1.html#K2">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="seqm_3.html#D9" target="_self">Def9</a></i>;<br/><b>hence </b><a NAME="E2:54_1"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="seqm_3.html#K1" target="_self">^\</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="seq_1.html#K2">.</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="txt" href="seqm_3.html#E1:54"><i><font color="Green">E40</font></i></a>, <a class="ref" href="seq_1.html#T7">SEQ_1:7</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:54"/>
<font color="Maroon">c<sub>2</sub></font> <a href="seqm_3.html#K1" target="_self">^\</a> <font color="Maroon">c<sub>1</sub></font> is <a href="relat_1.html#V2">being_not_0</a>
 <b>by </b><i><a class="ref" href="seq_1.html#T7">SEQ_1:7</a></i>;<br/>


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