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<b>let </b><font color="Maroon">N</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>let </b><font color="Maroon">seq</font> be   <a href="toprns_1.html#NM1">Real_Sequence</a> of <font color="Maroon">N</font>;<br/>



<b>thus </b><a NAME="E1:5"/>
( <font color="Maroon">seq</font> is <a href="toprns_1.html#V1" target="_self">non-zero</a> implies for <font color="Olive">n</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>   holds <font color="Maroon">seq</font> <a href="normsp_1.html#K2">.</a> <font color="Olive">n</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="euclid.html#K16">0.REAL</a> <font color="Maroon">N</font> )
 <b>by </b><i/>;<br/>

<b>assume </b><a NAME="E2:5"/>
for <font color="Olive">n</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>   holds <font color="Maroon">seq</font> <a href="normsp_1.html#K2">.</a> <font color="Olive">n</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="euclid.html#K16">0.REAL</a> <font color="Maroon">N</font>
 ;<br/>

<a NAME="E3:5"/><b>then </b>
for <font color="Olive">x</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">x</font> <a href="hidden.html#R2">in</a>  <a href="numbers.html#K5">NAT</a>  holds <br/><font color="Maroon">seq</font> <a href="funct_1.html#K1">.</a> <font color="Olive">x</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="euclid.html#K16">0.REAL</a> <font color="Maroon">N</font>
 
;<br/>
<b>hence </b><a NAME="E4:5"/>
<font color="Maroon">seq</font> is <a href="toprns_1.html#V1" target="_self">non-zero</a>
 <b>by </b><i/>;<br/>


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