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<span class="kw">let </span><font color="Maroon" title="c1">seq</font> be   <a href="comseq_1.html#NM1" title="COMSEQ_1:NM.1">Complex_Sequence</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">seq</font> is  <a href="comseq_1.html#NV1" title="COMSEQ_1:NV.1">non-zero</a>  implies <font color="Maroon" title="c1">seq</font> <a href="valued_1.html#K36" title="VALUED_1:func.36">"</a>  is  <a href="comseq_1.html#NV1" title="COMSEQ_1:NV.1">non-zero</a>  )</span><br/>

<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:29"/><span class="lab"><font color="Green" title="E15">A1</font></span>: 
<font color="Maroon" title="c1">seq</font> is  <a href="comseq_1.html#NV1" title="COMSEQ_1:NV.1">non-zero</a> 
 <span class="kw">and </span><br/><a NAME="E2:29"/><span class="lab"><font color="Green" title="E16">A2</font></span>: 
not <font color="Maroon" title="c1">seq</font> <a href="valued_1.html#K36" title="VALUED_1:func.36">"</a>  is  <a href="comseq_1.html#NV1" title="COMSEQ_1:NV.1">non-zero</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<span class="kw">consider </span><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> <span class="kw"> such that </span><br/><a NAME="E4:29"/><span class="lab"><font color="Green" title="E17">A3</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">seq</font> <a href="valued_1.html#K36" title="VALUED_1:func.36">"</a> </span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</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> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:29"><span class="lab"><font color="Green" title="E16">A2</font></span></a>, <a class="ref" href="comseq_1.html#T4" target="_self" title="COMSEQ_1:th.4">Th4</a></span>;<br/>
<a NAME="E5:29"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c1">seq</font> <a href="nat_1.html#K6" title="NAT_1:func.6">.</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="valued_1.html#K36" title="VALUED_1:func.36">"</a> </span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c2">n1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="valued_1.html#T10" title="VALUED_1:th.10">VALUED_1:10</a></span>;<br/>
<span class="kw">hence </span><a NAME="E6:29"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:29"><span class="lab"><font color="Green" title="E15">A1</font></span></a>, <a class="txt" href="#E4:29"><span class="lab"><font color="Green" title="E17">A3</font></span></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></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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