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<span class="kw">let </span><font color="Maroon" title="c1">k</font> be   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">h</font> being   <a href="valued_0.html#V1" title="VALUED_0:attr.1">complex-valued</a>  <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a> holds  (<font color="Olive" title="b1">h</font>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>) <a href="flexary1.html#K1" title="FLEXARY1:func.1">+...+</a> (<font color="Olive" title="b1">h</font>,<font color="Maroon" title="c1">k</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> (<font color="Olive" title="b1">h</font>,1) <a href="flexary1.html#K1" title="FLEXARY1:func.1">+...+</a> (<font color="Olive" title="b1">h</font>,<font color="Maroon" title="c1">k</font>)</span><br/><span class="kw">let </span><font color="Maroon" title="c2">h</font> be   <a href="valued_0.html#V1" title="VALUED_0:attr.1">complex-valued</a>  <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (<font color="Maroon" title="c2">h</font>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>) <a href="flexary1.html#K1" title="FLEXARY1:func.1">+...+</a> (<font color="Maroon" title="c2">h</font>,<font color="Maroon" title="c1">k</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> (<font color="Maroon" title="c2">h</font>,1) <a href="flexary1.html#K1" title="FLEXARY1:func.1">+...+</a> (<font color="Maroon" title="c2">h</font>,<font color="Maroon" title="c1">k</font>)</span><br/>



<a NAME="E1:19"/>
 not  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c2">h</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_3.html#T25" onmouseover="rs('finseq_3/T25')" onmouseout="rh()">FINSEQ_3:25</a></span>;<br/>
<a NAME="E2:19"/><span class="kw">then </span><span class="lab"><font color="Green" title="E15">A1</font></span>: 
<font color="Maroon" title="c2">h</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_1.html#D2" onmouseover="rs('funct_1/D2')" onmouseout="rh()">FUNCT_1:def 2</a></span>;<br/>
<a NAME="E3:19"/>
(<font color="Maroon" title="c2">h</font>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>) <a href="flexary1.html#K1" title="FLEXARY1:func.1">+...+</a> (<font color="Maroon" title="c2">h</font>,<font color="Maroon" title="c1">k</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">h</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c2">h</font>,<span class="p2">(<span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>) <a href="flexary1.html#K1" title="FLEXARY1:func.1">+...+</a> (<font color="Maroon" title="c2">h</font>,<font color="Maroon" title="c1">k</font>)</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="flexary1.html#T13" target="_self" onmouseover="rs('flexary1/T13')" onmouseout="rh()">Th13</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:19"/>
(<font color="Maroon" title="c2">h</font>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>) <a href="flexary1.html#K1" title="FLEXARY1:func.1">+...+</a> (<font color="Maroon" title="c2">h</font>,<font color="Maroon" title="c1">k</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> (<font color="Maroon" title="c2">h</font>,1) <a href="flexary1.html#K1" title="FLEXARY1:func.1">+...+</a> (<font color="Maroon" title="c2">h</font>,<font color="Maroon" title="c1">k</font>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:19"><span class="lab"><font color="Green" title="E15">A1</font></span></a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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