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<b>let </b><font color="Maroon">i</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>let </b><font color="Maroon">j</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>let </b><font color="Maroon">R1</font> be    <a href="finseq_2.html#M2">Element</a> of <font color="Maroon">i</font> <a href="finseq_2.html#K4">-tuples_on</a> <a href="numbers.html#K2">COMPLEX</a> ;<br/><b>let </b><font color="Maroon">R2</font> be    <a href="finseq_2.html#M2">Element</a> of <font color="Maroon">i</font> <a href="finseq_2.html#K4">-tuples_on</a> <a href="numbers.html#K2">COMPLEX</a> ;<br/>







<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="25_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:25_1"/>
(  not <font color="Maroon">j</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">i</font> or <font color="Maroon">j</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">i</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="25_1_1"><b>suppose </b></a><a NAME="E1:25_1_1"/><i><font color="Green">E32</font></i>: 
not <font color="Maroon">j</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">i</font>
 ;<br/><div class="add"><a NAME="E2:25_1_1"/><b>then </b><i><font color="Green">E33</font></i>: 
not <font color="Maroon">j</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">R1</font>
 <b>by </b><i><a class="ref" href="finseq_2.html#T144">FINSEQ_2:144</a></i>;<br/><a NAME="E3:25_1_1"/><i><font color="Green">E36</font></i>: 
not <font color="Maroon">j</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">R2</font>
 <b>by </b><i>, <a class="ref" href="finseq_2.html#T144">FINSEQ_2:144</a></i>;<br/><a NAME="E4:25_1_1"/>
not <font color="Maroon">j</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">R1</font> <a href="complsp2.html#K2" target="_self">-</a> <font color="Maroon">R2</font></span>)</span>
 <b>by </b><i>, <a class="ref" href="finseq_2.html#T144">FINSEQ_2:144</a></i>;<br/><b>hence </b><span class="p1">(<span class="default"><font color="Maroon">R1</font> <a href="complsp2.html#K2" target="_self">-</a> <font color="Maroon">R2</font></span>)</span> <a href="matrix_5.html#K9">.</a> <font color="Maroon">j</font> = 
0 <a href="binop_2.html#K10">-</a> 0
<b>by </b><i><a class="ref" href="funct_1.html#D4">FUNCT_1:def 4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">R1</font> <a href="matrix_5.html#K9">.</a> <font color="Maroon">j</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> 0
<b>by </b><i>, <a class="ref" href="funct_1.html#D4">FUNCT_1:def 4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">R1</font> <a href="matrix_5.html#K9">.</a> <font color="Maroon">j</font></span>)</span> <a href="binop_2.html#K4">-</a> <span class="p1">(<span class="default"><font color="Maroon">R2</font> <a href="matrix_5.html#K9">.</a> <font color="Maroon">j</font></span>)</span>
<b>by </b><i>, <a class="ref" href="funct_1.html#D4">FUNCT_1:def 4</a></i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="25_1_2"><b>suppose </b></a><a NAME="E1:25_1_2"/>
<font color="Maroon">j</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">i</font>
 ;<br/><div class="add"><a NAME="E2:25_1_2"/><b>then </b>
<font color="Maroon">j</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">R1</font> <a href="complsp2.html#K2" target="_self">-</a> <font color="Maroon">R2</font></span>)</span>
 <b>by </b><i><a class="ref" href="finseq_2.html#T144">FINSEQ_2:144</a></i>;<br/><b>hence </b><a NAME="E3:25_1_2"/>
<span class="p1">(<span class="default"><font color="Maroon">R1</font> <a href="complsp2.html#K2" target="_self">-</a> <font color="Maroon">R2</font></span>)</span> <a href="matrix_5.html#K9">.</a> <font color="Maroon">j</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">R1</font> <a href="matrix_5.html#K9">.</a> <font color="Maroon">j</font></span>)</span> <a href="binop_2.html#K4">-</a> <span class="p1">(<span class="default"><font color="Maroon">R2</font> <a href="matrix_5.html#K9">.</a> <font color="Maroon">j</font></span>)</span>
 <b>by </b><i/>;<br/></div><b>end;</b></div></div><b>end;</b></div>

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