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<b>let </b><font color="Maroon" title="c1">seq</font> be   <a href="comseq_1.html#NM1" title="COMSEQ_1:NM.1">Complex_Sequence</a>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:43"/><i><font color="Green" title="E31">A1</font></i>: 
<font color="Maroon" title="c1">seq</font> is <a href="comseq_1.html#V1" title="COMSEQ_1:attr.1">non-zero</a>
 <b>and </b><br/><a NAME="E2:43"/><i><font color="Green" title="E32">A2</font></i>: 
not <font color="Maroon" title="c1">seq</font> <a href="comseq_1.html#K7" title="COMSEQ_1:func.7">"</a>  is <a href="comseq_1.html#V1" title="COMSEQ_1:attr.1">non-zero</a>
 ;<br/>

<b>consider </b><font color="Maroon" title="c2">n1</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> <b> such that </b><br/><a NAME="E4:43"/><i><font color="Green" title="E33">A3</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">seq</font> <a href="comseq_1.html#K7" title="COMSEQ_1:func.7">"</a> </span>)</span> <a href="comseq_1.html#K1" title="COMSEQ_1:func.1">.</a> <font color="Maroon" title="c2">n1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="complex1.html#K5" title="COMPLEX1:func.5">0c</a> 
 <b>by </b><i><a class="txt" href="comseq_1.html#E2:43"><i><font color="Green" title="E32">A2</font></i></a>, <a class="ref" href="comseq_1.html#T4" target="_self" title="COMSEQ_1:th.4">Th4</a></i>;<br/>
<a NAME="E5:43"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c1">seq</font> <a href="comseq_1.html#K1" title="COMSEQ_1:func.1">.</a> <font color="Maroon" title="c2">n1</font></span>)</span> <a href="complex1.html#K12" title="COMPLEX1:func.12">"</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">seq</font> <a href="comseq_1.html#K7" title="COMSEQ_1:func.7">"</a> </span>)</span> <a href="comseq_1.html#K1" title="COMSEQ_1:func.1">.</a> <font color="Maroon" title="c2">n1</font>
 
<b>by </b><i><a class="ref" href="comseq_1.html#D11" target="_self" title="COMSEQ_1:def.11">Def11</a></i>;<br/>
<b>hence </b><a NAME="E6:43"/>
contradiction
 <b>by </b><i><a class="txt" href="comseq_1.html#E1:43"><i><font color="Green" title="E31">A1</font></i></a>, <a class="txt" href="comseq_1.html#E4:43"><i><font color="Green" title="E33">A3</font></i></a>, <a class="ref" href="comseq_1.html#T4" target="_self" title="COMSEQ_1:th.4">Th4</a>, <a class="ref" href="xcmplx_1.html#T203" title="XCMPLX_1:th.203">XCMPLX_1:203</a></i>;<br/>


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