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<b>let </b><font color="Maroon">p1</font> be   <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span>;<br/><b>let </b><font color="Maroon">p2</font> be   <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span>;<br/>



<b>assume </b><a NAME="E1:47"/><i><font color="Green">E41</font></i>: 
( <font color="Maroon">p1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="euclid.html#K16">0.REAL</a> 2 &amp; <font color="Maroon">p2</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="euclid.html#K16">0.REAL</a> 2 )
 ;<br/>

<a NAME="E2:47"/><b>then </b><i><font color="Green">E49</font></i>: 
 <a href="euclid_3.html#K2" target="_self">euc2cpx</a> <font color="Maroon">p1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="complex1.html#K5">0c</a> 
 
<b>by </b><i>, </i>;<br/>
<a NAME="E3:47"/><i><font color="Green">E50</font></i>: 
 <a href="euclid_3.html#K2" target="_self">euc2cpx</a> <font color="Maroon">p2</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="complex1.html#K5">0c</a> 
 
<b>by </b><i>, , </i>;<br/>
<a NAME="E4:47"/><i><font color="Green">E62</font></i>: 
( <font color="Maroon">p1</font> <a href="euclid.html#K21">`1</a>  <a href="hidden.html#R1">=</a>  <a href="complex1.html#K3">Re</a> <span class="p1">(<span class="default"><a href="euclid_3.html#K2" target="_self">euc2cpx</a> <font color="Maroon">p1</font></span>)</span> &amp; <font color="Maroon">p1</font> <a href="euclid.html#K22">`2</a>  <a href="hidden.html#R1">=</a>  <a href="complex1.html#K4">Im</a> <span class="p1">(<span class="default"><a href="euclid_3.html#K2" target="_self">euc2cpx</a> <font color="Maroon">p1</font></span>)</span> )
 
<b>by </b><i/>;<br/>
<a NAME="E5:47"/>
( <font color="Maroon">p2</font> <a href="euclid.html#K21">`1</a>  <a href="hidden.html#R1">=</a>  <a href="complex1.html#K3">Re</a> <span class="p1">(<span class="default"><a href="euclid_3.html#K2" target="_self">euc2cpx</a> <font color="Maroon">p2</font></span>)</span> &amp; <font color="Maroon">p2</font> <a href="euclid.html#K22">`2</a>  <a href="hidden.html#R1">=</a>  <a href="complex1.html#K4">Im</a> <span class="p1">(<span class="default"><a href="euclid_3.html#K2" target="_self">euc2cpx</a> <font color="Maroon">p2</font></span>)</span> )
 
<b>by </b><i/>;<br/>
<a NAME="E6:47"/><b>then </b><i><font color="Green">E71</font></i>: 
 <a href="complex1.html#K4">Im</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid_3.html#K2" target="_self">euc2cpx</a> <font color="Maroon">p1</font></span>)</span> <a href="complex2.html#K1">.|.</a> <span class="p2">(<span class="default"><a href="euclid_3.html#K2" target="_self">euc2cpx</a> <font color="Maroon">p2</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p1</font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><font color="Maroon">p2</font> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p1</font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><font color="Maroon">p2</font> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span>
 
<b>by </b><i>, </i>;<br/>
<a NAME="E7:47"/><i><font color="Green">E72</font></i>: 
<span class="p1"><a href="complex1.html#K17">|.</a><span class="default"><span class="p2">(<span class="default"><a href="euclid_3.html#K2" target="_self">euc2cpx</a> <font color="Maroon">p1</font></span>)</span></span><a href="complex1.html#K17">.|</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="toprns_1.html#K5">|.</a><span class="default"><font color="Maroon">p1</font></span><a href="toprns_1.html#K5">.|</a></span>
 
<b>by </b><i/>;<br/>
<a NAME="E8:47"/><i><font color="Green">E73</font></i>: 
<span class="p1"><a href="complex1.html#K17">|.</a><span class="default"><span class="p2">(<span class="default"><a href="euclid_3.html#K2" target="_self">euc2cpx</a> <font color="Maroon">p2</font></span>)</span></span><a href="complex1.html#K17">.|</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="toprns_1.html#K5">|.</a><span class="default"><font color="Maroon">p2</font></span><a href="toprns_1.html#K5">.|</a></span>
 
<b>by </b><i/>;<br/>
<b>thus </b><a NAME="E9:47"/>
( <!--HUMANRECFAILED-->( ( not <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p1</font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><font color="Maroon">p2</font> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p1</font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><font color="Maroon">p2</font> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="toprns_1.html#K5">|.</a><span class="default"><font color="Maroon">p1</font></span><a href="toprns_1.html#K5">.|</a></span> <a href="real_1.html#K4">*</a> <span class="p1"><a href="toprns_1.html#K5">|.</a><span class="default"><font color="Maroon">p2</font></span><a href="toprns_1.html#K5">.|</a></span> &amp; not <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p1</font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><font color="Maroon">p2</font> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p1</font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><font color="Maroon">p2</font> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><span class="p2"><a href="toprns_1.html#K5">|.</a><span class="default"><font color="Maroon">p1</font></span><a href="toprns_1.html#K5">.|</a></span> <a href="real_1.html#K4">*</a> <span class="p2"><a href="toprns_1.html#K5">|.</a><span class="default"><font color="Maroon">p2</font></span><a href="toprns_1.html#K5">.|</a></span></span>)</span> ) or  <a href="euclid_3.html#K4" target="_self">angle</a> <font color="Maroon">p1</font>,<span class="p1">(<span class="default"><a href="euclid.html#K16">0.REAL</a> 2</span>)</span>,<font color="Maroon">p2</font> <a href="hidden.html#R1">=</a> <a href="sin_cos.html#K35">PI</a>  <a href="real_1.html#K6">/</a> 2 or  <a href="euclid_3.html#K4" target="_self">angle</a> <font color="Maroon">p1</font>,<span class="p1">(<span class="default"><a href="euclid.html#K16">0.REAL</a> 2</span>)</span>,<font color="Maroon">p2</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default">3 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="real_1.html#K4">*</a> <a href="sin_cos.html#K35">PI</a>  ) &amp; ( ( not  <a href="euclid_3.html#K4" target="_self">angle</a> <font color="Maroon">p1</font>,<span class="p1">(<span class="default"><a href="euclid.html#K16">0.REAL</a> 2</span>)</span>,<font color="Maroon">p2</font> <a href="hidden.html#R1">=</a> <a href="sin_cos.html#K35">PI</a>  <a href="real_1.html#K6">/</a> 2 &amp; not  <a href="euclid_3.html#K4" target="_self">angle</a> <font color="Maroon">p1</font>,<span class="p1">(<span class="default"><a href="euclid.html#K16">0.REAL</a> 2</span>)</span>,<font color="Maroon">p2</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default">3 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="real_1.html#K4">*</a> <a href="sin_cos.html#K35">PI</a>  ) or <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p1</font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><font color="Maroon">p2</font> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p1</font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><font color="Maroon">p2</font> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="toprns_1.html#K5">|.</a><span class="default"><font color="Maroon">p1</font></span><a href="toprns_1.html#K5">.|</a></span> <a href="real_1.html#K4">*</a> <span class="p1"><a href="toprns_1.html#K5">|.</a><span class="default"><font color="Maroon">p2</font></span><a href="toprns_1.html#K5">.|</a></span> or <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p1</font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><font color="Maroon">p2</font> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p1</font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><font color="Maroon">p2</font> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><span class="p2"><a href="toprns_1.html#K5">|.</a><span class="default"><font color="Maroon">p1</font></span><a href="toprns_1.html#K5">.|</a></span> <a href="real_1.html#K4">*</a> <span class="p2"><a href="toprns_1.html#K5">|.</a><span class="default"><font color="Maroon">p2</font></span><a href="toprns_1.html#K5">.|</a></span></span>)</span> ) )
 <b>by </b><i>, , , , , , <a class="ref" href="complex2.html#T90">COMPLEX2:90</a></i>;<br/>


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