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<b>let </b><font color="Maroon">a</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K2">COMPLEX</a> , <font color="Maroon">b</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K2">COMPLEX</a> ;<br/><b>let </b><font color="Maroon">x</font> be    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="numbers.html#K2">COMPLEX</a> , <font color="Maroon">y</font> be    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="numbers.html#K2">COMPLEX</a> , <font color="Maroon">z</font> be    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="numbers.html#K2">COMPLEX</a> ;<br/>



<b>assume </b><a NAME="E1:92"/><i><font color="Green">E32</font></i>: 
(  <a href="finseq_1.html#K3">len</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">y</font> &amp;  <a href="finseq_1.html#K3">len</a> <font color="Maroon">y</font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">z</font> )
 ;<br/>

<a NAME="E2:92"/><i><font color="Green">E33</font></i>: 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="complsp1.html#K6">*</a> <font color="Maroon">y</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">y</font>
 
<b>by </b><i/>;<br/>
<a NAME="E3:92"/>
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="complsp1.html#K6">*</a> <font color="Maroon">z</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">z</font>
 
<b>by </b><i/>;<br/>
<b>then </b><span class="p1"><a href="complsp2.html#K8" target="_self">|(</a><span class="default"><font color="Maroon">x</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">a</font> <a href="complsp1.html#K6">*</a> <font color="Maroon">y</font></span>)</span> <a href="complsp1.html#K3">+</a> <span class="p3">(<span class="default"><font color="Maroon">b</font> <a href="complsp1.html#K6">*</a> <font color="Maroon">z</font></span>)</span></span>)</span></span><a href="complsp2.html#K8" target="_self">)|</a></span> = 
<span class="p1"><a href="complsp2.html#K8" target="_self">|(</a><span class="default"><font color="Maroon">x</font>,<span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="complsp1.html#K6">*</a> <font color="Maroon">y</font></span>)</span></span><a href="complsp2.html#K8" target="_self">)|</a></span> <a href="binop_2.html#K3">+</a> <span class="p1"><a href="complsp2.html#K8" target="_self">|(</a><span class="default"><font color="Maroon">x</font>,<span class="p2">(<span class="default"><font color="Maroon">b</font> <a href="complsp1.html#K6">*</a> <font color="Maroon">z</font></span>)</span></span><a href="complsp2.html#K8" target="_self">)|</a></span>
<b>by </b><i><a class="ref" href="complsp2.html#T19" target="_self">Th19</a>, , <a class="ref" href="complsp2.html#T12" target="_self">Th12</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="complex1.html#K15">*'</a> </span>)</span> <a href="binop_2.html#K5">*</a> <span class="p2"><a href="complsp2.html#K8" target="_self">|(</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="complsp2.html#K8" target="_self">)|</a></span></span>)</span> <a href="binop_2.html#K3">+</a> <span class="p1"><a href="complsp2.html#K8" target="_self">|(</a><span class="default"><font color="Maroon">x</font>,<span class="p2">(<span class="default"><font color="Maroon">b</font> <a href="complsp1.html#K6">*</a> <font color="Maroon">z</font></span>)</span></span><a href="complsp2.html#K8" target="_self">)|</a></span>
<b>by </b><i><a class="ref" href="complsp2.html#T19" target="_self">Th19</a>, <a class="ref" href="complsp2.html#T18" target="_self">Th18</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="complex1.html#K15">*'</a> </span>)</span> <a href="binop_2.html#K5">*</a> <span class="p2"><a href="complsp2.html#K8" target="_self">|(</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="complsp2.html#K8" target="_self">)|</a></span></span>)</span> <a href="binop_2.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">b</font> <a href="complex1.html#K15">*'</a> </span>)</span> <a href="binop_2.html#K5">*</a> <span class="p2"><a href="complsp2.html#K8" target="_self">|(</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">z</font></span><a href="complsp2.html#K8" target="_self">)|</a></span></span>)</span>
<b>by </b><i><a class="ref" href="complsp2.html#T19" target="_self">Th19</a>, <a class="ref" href="complsp2.html#T18" target="_self">Th18</a></i>
;<br/>
<b>hence </b><a NAME="E5:92"/>
<span class="p1"><a href="complsp2.html#K8" target="_self">|(</a><span class="default"><font color="Maroon">x</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">a</font> <a href="complsp1.html#K6">*</a> <font color="Maroon">y</font></span>)</span> <a href="complsp1.html#K3">+</a> <span class="p3">(<span class="default"><font color="Maroon">b</font> <a href="complsp1.html#K6">*</a> <font color="Maroon">z</font></span>)</span></span>)</span></span><a href="complsp2.html#K8" target="_self">)|</a></span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="complex1.html#K15">*'</a> </span>)</span> <a href="binop_2.html#K5">*</a> <span class="p2"><a href="complsp2.html#K8" target="_self">|(</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="complsp2.html#K8" target="_self">)|</a></span></span>)</span> <a href="binop_2.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">b</font> <a href="complex1.html#K15">*'</a> </span>)</span> <a href="binop_2.html#K5">*</a> <span class="p2"><a href="complsp2.html#K8" target="_self">|(</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">z</font></span><a href="complsp2.html#K8" target="_self">)|</a></span></span>)</span>
 ;<br/>


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