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<span class="kw">let </span><font color="Maroon" title="c1">p1</font>, <font color="Maroon" title="c2">p2</font>, <font color="Maroon" title="c3">p3</font> be   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">p1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">p2</font> &amp; <font color="Maroon" title="c3">p3</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">p2</font> implies ( <span class="p1"><a href="rvsum_1.html#K23" title="RVSUM_1:func.23">|(</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">p1</font> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <font color="Maroon" title="c2">p2</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">p3</font> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <font color="Maroon" title="c2">p2</font></span>)</span></span><a href="rvsum_1.html#K23" title="RVSUM_1:func.23">)|</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  iff (  <a href="euclid_3.html#K4" title="EUCLID_3:func.4">angle</a> (<font color="Maroon" title="c1">p1</font>,<font color="Maroon" title="c2">p2</font>,<font color="Maroon" title="c3">p3</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="sin_cos.html#K33" title="SIN_COS:func.33">PI</a> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2 or  <a href="euclid_3.html#K4" title="EUCLID_3:func.4">angle</a> (<font color="Maroon" title="c1">p1</font>,<font color="Maroon" title="c2">p2</font>,<font color="Maroon" title="c3">p3</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">3 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <a href="sin_cos.html#K33" title="SIN_COS:func.33">PI</a> ) ) )</span><br/>





<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:44"/><span class="lab"><font color="Green" title="E23">A1</font></span>: 
<font color="Maroon" title="c1">p1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">p2</font>
 <span class="kw">and </span><br/><a NAME="E2:44"/><span class="lab"><font color="Green" title="E24">A2</font></span>: 
<font color="Maroon" title="c3">p3</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">p2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <span class="p1"><a href="rvsum_1.html#K23" title="RVSUM_1:func.23">|(</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">p1</font> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <font color="Maroon" title="c2">p2</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">p3</font> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <font color="Maroon" title="c2">p2</font></span>)</span></span><a href="rvsum_1.html#K23" title="RVSUM_1:func.23">)|</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  iff (  <a href="euclid_3.html#K4" title="EUCLID_3:func.4">angle</a> (<font color="Maroon" title="c1">p1</font>,<font color="Maroon" title="c2">p2</font>,<font color="Maroon" title="c3">p3</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="sin_cos.html#K33" title="SIN_COS:func.33">PI</a> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2 or  <a href="euclid_3.html#K4" title="EUCLID_3:func.4">angle</a> (<font color="Maroon" title="c1">p1</font>,<font color="Maroon" title="c2">p2</font>,<font color="Maroon" title="c3">p3</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">3 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <a href="sin_cos.html#K33" title="SIN_COS:func.33">PI</a> ) )</span><br/>

<a NAME="E3:44"/>
<font color="Maroon" title="c1">p1</font> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <font color="Maroon" title="c2">p2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:44"><span class="lab"><font color="Green" title="E23">A1</font></span></a>, <a class="ref" href="euclid.html#T43" title="EUCLID:th.43">EUCLID:43</a></span>;<br/>
<a NAME="E4:44"/><span class="kw">then </span><span class="lab"><font color="Green" title="E25">A3</font></span>: 
 <a href="euclid_3.html#K2" title="EUCLID_3:func.2">euc2cpx</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">p1</font> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <font color="Maroon" title="c2">p2</font></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="complex1.html#K5" title="COMPLEX1:func.5">0c</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="euclid_3.html#T2" target="_self" title="EUCLID_3:th.2">Th2</a>, <a class="ref" href="euclid_3.html#T16" target="_self" title="EUCLID_3:th.16">Th20</a></span>;<br/>
<a NAME="E5:44"/>
<font color="Maroon" title="c3">p3</font> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <font color="Maroon" title="c2">p2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:44"><span class="lab"><font color="Green" title="E24">A2</font></span></a>, <a class="ref" href="euclid.html#T43" title="EUCLID:th.43">EUCLID:43</a></span>;<br/>
<a NAME="E6:44"/><span class="kw">then </span><span class="lab"><font color="Green" title="E26">A4</font></span>: 
 <a href="euclid_3.html#K2" title="EUCLID_3:func.2">euc2cpx</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">p3</font> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <font color="Maroon" title="c2">p2</font></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="complex1.html#K5" title="COMPLEX1:func.5">0c</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="euclid_3.html#T2" target="_self" title="EUCLID_3:th.2">Th2</a>, <a class="ref" href="euclid_3.html#T16" target="_self" title="EUCLID_3:th.16">Th20</a></span>;<br/>
<a NAME="E7:44"/><span class="lab"><font color="Green" title="E27">A5</font></span>: 
( <span class="p1">(<span class="default"><a href="euclid_3.html#K2" title="EUCLID_3:func.2">euc2cpx</a> <font color="Maroon" title="c1">p1</font></span>)</span> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <span class="p1">(<span class="default"><a href="euclid_3.html#K2" title="EUCLID_3:func.2">euc2cpx</a> <font color="Maroon" title="c2">p2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="euclid_3.html#K2" title="EUCLID_3:func.2">euc2cpx</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">p1</font> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <font color="Maroon" title="c2">p2</font></span>)</span> &amp; <span class="p1">(<span class="default"><a href="euclid_3.html#K2" title="EUCLID_3:func.2">euc2cpx</a> <font color="Maroon" title="c3">p3</font></span>)</span> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <span class="p1">(<span class="default"><a href="euclid_3.html#K2" title="EUCLID_3:func.2">euc2cpx</a> <font color="Maroon" title="c2">p2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="euclid_3.html#K2" title="EUCLID_3:func.2">euc2cpx</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">p3</font> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <font color="Maroon" title="c2">p2</font></span>)</span> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="euclid_3.html#T15" target="_self" title="EUCLID_3:th.15">Th19</a></span>;<br/>
<div><span class="kw">hereby </span> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( (  <a href="euclid_3.html#K4" title="EUCLID_3:func.4">angle</a> (<font color="Maroon" title="c1">p1</font>,<font color="Maroon" title="c2">p2</font>,<font color="Maroon" title="c3">p3</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="sin_cos.html#K33" title="SIN_COS:func.33">PI</a> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2 or  <a href="euclid_3.html#K4" title="EUCLID_3:func.4">angle</a> (<font color="Maroon" title="c1">p1</font>,<font color="Maroon" title="c2">p2</font>,<font color="Maroon" title="c3">p3</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">3 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <a href="sin_cos.html#K33" title="SIN_COS:func.33">PI</a> ) implies <span class="p1"><a href="rvsum_1.html#K23" title="RVSUM_1:func.23">|(</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">p1</font> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <font color="Maroon" title="c2">p2</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">p3</font> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <font color="Maroon" title="c2">p2</font></span>)</span></span><a href="rvsum_1.html#K23" title="RVSUM_1:func.23">)|</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  )</span>
<div class="add"><span class="kw">assume </span><a NAME="E1:44_1"/>
<span class="p1"><a href="rvsum_1.html#K23" title="RVSUM_1:func.23">|(</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">p1</font> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <font color="Maroon" title="c2">p2</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">p3</font> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <font color="Maroon" title="c2">p2</font></span>)</span></span><a href="rvsum_1.html#K23" title="RVSUM_1:func.23">)|</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  <a href="euclid_3.html#K4" title="EUCLID_3:func.4">angle</a> (<font color="Maroon" title="c1">p1</font>,<font color="Maroon" title="c2">p2</font>,<font color="Maroon" title="c3">p3</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="sin_cos.html#K33" title="SIN_COS:func.33">PI</a> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2 or  <a href="euclid_3.html#K4" title="EUCLID_3:func.4">angle</a> (<font color="Maroon" title="c1">p1</font>,<font color="Maroon" title="c2">p2</font>,<font color="Maroon" title="c3">p3</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">3 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <a href="sin_cos.html#K33" title="SIN_COS:func.33">PI</a> )</span><br/><a NAME="E2:44_1"/><span class="kw">then </span>
 <a href="complex1.html#K3" title="COMPLEX1:func.3">Re</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid_3.html#K2" title="EUCLID_3:func.2">euc2cpx</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">p1</font> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <font color="Maroon" title="c2">p2</font></span>)</span></span>)</span> <a href="complex2.html#K1" title="COMPLEX2:func.1">.|.</a> <span class="p2">(<span class="default"><a href="euclid_3.html#K2" title="EUCLID_3:func.2">euc2cpx</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">p3</font> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <font color="Maroon" title="c2">p2</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="euclid_3.html#T42" target="_self" title="EUCLID_3:th.42">Th51</a></span>;<br/><a NAME="E3:44_1"/><span class="kw">then </span>
(  <a href="complex2.html#K4" title="COMPLEX2:func.4">angle</a> (<span class="p1">(<span class="default"><a href="euclid_3.html#K2" title="EUCLID_3:func.2">euc2cpx</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">p1</font> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <font color="Maroon" title="c2">p2</font></span>)</span></span>)</span>,<a href="complex1.html#K5" title="COMPLEX1:func.5">0c</a>,<span class="p1">(<span class="default"><a href="euclid_3.html#K2" title="EUCLID_3:func.2">euc2cpx</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">p3</font> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <font color="Maroon" title="c2">p2</font></span>)</span></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="sin_cos.html#K33" title="SIN_COS:func.33">PI</a> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2 or  <a href="complex2.html#K4" title="COMPLEX2:func.4">angle</a> (<span class="p1">(<span class="default"><a href="euclid_3.html#K2" title="EUCLID_3:func.2">euc2cpx</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">p1</font> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <font color="Maroon" title="c2">p2</font></span>)</span></span>)</span>,<a href="complex1.html#K5" title="COMPLEX1:func.5">0c</a>,<span class="p1">(<span class="default"><a href="euclid_3.html#K2" title="EUCLID_3:func.2">euc2cpx</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">p3</font> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <font color="Maroon" title="c2">p2</font></span>)</span></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">3 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <a href="sin_cos.html#K33" title="SIN_COS:func.33">PI</a> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:44"><span class="lab"><font color="Green" title="E25">A3</font></span></a>, <a class="txt" href="#E6:44"><span class="lab"><font color="Green" title="E26">A4</font></span></a>, <a class="ref" href="complex2.html#T75" title="COMPLEX2:th.75">COMPLEX2:75</a></span>;<br/><span class="kw">hence </span><a NAME="E4:44_1"/>
(  <a href="euclid_3.html#K4" title="EUCLID_3:func.4">angle</a> (<font color="Maroon" title="c1">p1</font>,<font color="Maroon" title="c2">p2</font>,<font color="Maroon" title="c3">p3</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="sin_cos.html#K33" title="SIN_COS:func.33">PI</a> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2 or  <a href="euclid_3.html#K4" title="EUCLID_3:func.4">angle</a> (<font color="Maroon" title="c1">p1</font>,<font color="Maroon" title="c2">p2</font>,<font color="Maroon" title="c3">p3</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">3 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <a href="sin_cos.html#K33" title="SIN_COS:func.33">PI</a> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:44"><span class="lab"><font color="Green" title="E27">A5</font></span></a>, <a class="ref" href="complex2.html#T71" title="COMPLEX2:th.71">COMPLEX2:71</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div>
<span class="kw">end;</span></div>

<a NAME="E9:44"/><span class="lab"><font color="Green" title="E28">A6</font></span>: 
<span class="p1"><a href="rvsum_1.html#K23" title="RVSUM_1:func.23">|(</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">p1</font> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <font color="Maroon" title="c2">p2</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">p3</font> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <font color="Maroon" title="c2">p2</font></span>)</span></span><a href="rvsum_1.html#K23" title="RVSUM_1:func.23">)|</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="complex1.html#K3" title="COMPLEX1:func.3">Re</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid_3.html#K2" title="EUCLID_3:func.2">euc2cpx</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">p1</font> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <font color="Maroon" title="c2">p2</font></span>)</span></span>)</span> <a href="complex2.html#K1" title="COMPLEX2:func.1">.|.</a> <span class="p2">(<span class="default"><a href="euclid_3.html#K2" title="EUCLID_3:func.2">euc2cpx</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">p3</font> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <font color="Maroon" title="c2">p2</font></span>)</span></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="euclid_3.html#T42" target="_self" title="EUCLID_3:th.42">Th51</a></span>;<br/>
<span class="kw">assume </span><a NAME="E10:44"/>
(  <a href="euclid_3.html#K4" title="EUCLID_3:func.4">angle</a> (<font color="Maroon" title="c1">p1</font>,<font color="Maroon" title="c2">p2</font>,<font color="Maroon" title="c3">p3</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="sin_cos.html#K33" title="SIN_COS:func.33">PI</a> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2 or  <a href="euclid_3.html#K4" title="EUCLID_3:func.4">angle</a> (<font color="Maroon" title="c1">p1</font>,<font color="Maroon" title="c2">p2</font>,<font color="Maroon" title="c3">p3</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">3 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <a href="sin_cos.html#K33" title="SIN_COS:func.33">PI</a> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1"><a href="rvsum_1.html#K23" title="RVSUM_1:func.23">|(</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">p1</font> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <font color="Maroon" title="c2">p2</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">p3</font> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <font color="Maroon" title="c2">p2</font></span>)</span></span><a href="rvsum_1.html#K23" title="RVSUM_1:func.23">)|</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><br/>

<a NAME="E11:44"/><span class="kw">then </span>
(  <a href="complex2.html#K4" title="COMPLEX2:func.4">angle</a> (<span class="p1">(<span class="default"><a href="euclid_3.html#K2" title="EUCLID_3:func.2">euc2cpx</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">p1</font> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <font color="Maroon" title="c2">p2</font></span>)</span></span>)</span>,<a href="complex1.html#K5" title="COMPLEX1:func.5">0c</a>,<span class="p1">(<span class="default"><a href="euclid_3.html#K2" title="EUCLID_3:func.2">euc2cpx</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">p3</font> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <font color="Maroon" title="c2">p2</font></span>)</span></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="sin_cos.html#K33" title="SIN_COS:func.33">PI</a> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2 or  <a href="complex2.html#K4" title="COMPLEX2:func.4">angle</a> (<span class="p1">(<span class="default"><a href="euclid_3.html#K2" title="EUCLID_3:func.2">euc2cpx</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">p1</font> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <font color="Maroon" title="c2">p2</font></span>)</span></span>)</span>,<a href="complex1.html#K5" title="COMPLEX1:func.5">0c</a>,<span class="p1">(<span class="default"><a href="euclid_3.html#K2" title="EUCLID_3:func.2">euc2cpx</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">p3</font> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <font color="Maroon" title="c2">p2</font></span>)</span></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">3 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <a href="sin_cos.html#K33" title="SIN_COS:func.33">PI</a> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:44"><span class="lab"><font color="Green" title="E27">A5</font></span></a>, <a class="ref" href="complex2.html#T71" title="COMPLEX2:th.71">COMPLEX2:71</a></span>;<br/>
<span class="kw">hence </span><a NAME="E12:44"/>
<span class="p1"><a href="rvsum_1.html#K23" title="RVSUM_1:func.23">|(</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">p1</font> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <font color="Maroon" title="c2">p2</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">p3</font> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <font color="Maroon" title="c2">p2</font></span>)</span></span><a href="rvsum_1.html#K23" title="RVSUM_1:func.23">)|</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:44"><span class="lab"><font color="Green" title="E28">A6</font></span></a>, <a class="txt" href="#E4:44"><span class="lab"><font color="Green" title="E25">A3</font></span></a>, <a class="txt" href="#E6:44"><span class="lab"><font color="Green" title="E26">A4</font></span></a>, <a class="ref" href="complex2.html#T75" title="COMPLEX2:th.75">COMPLEX2:75</a></span>; <a class="txt" 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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