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<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></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="E1:34"/>
( <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>2</sub></font> or <font color="Maroon">c<sub>1</sub></font> <a href="euclid.html#K20">-</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="euclid.html#K16">0.REAL</a> 2 )
 ;<br/>

<a NAME="E2:34"/><b>then </b><i><font color="Green">E23</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="euclid.html#K20">-</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="euclid.html#K16">0.REAL</a> 2
 
<b>by </b><i><a class="ref" href="euclid.html#T47">EUCLID:47</a></i>;<br/>
<a NAME="E3:34"/>
 <a href="euclid.html#K19">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="euclid.html#K20">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> <a href="euclid.html#K20">-</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="euclid.html#T48">EUCLID:48</a></i>;<br/>
<b>hence </b><a NAME="E4:34"/>
(  <a href="euclid_3.html#K3" target="_self">Arg</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="euclid.html#K20">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xxreal_0.html#R1">&lt;</a>  <a href="sin_cos.html#K33">PI</a>  iff  <a href="euclid_3.html#K3" target="_self">Arg</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="euclid.html#K20">-</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a>  <a href="sin_cos.html#K33">PI</a>  )
 <b>by </b><i><a class="txt" href="euclid_3.html#E2:34"><i><font color="Green">E23</font></i></a>, <a class="ref" href="euclid_3.html#T38" target="_self">Th38</a></i>;<br/>


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