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<b>let </b><font color="Maroon" title="c1">p1</font>, <font color="Maroon" title="c2">p2</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>;<br/>



<b>assume </b><a NAME="E1:34"/>
( <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> or <font color="Maroon" title="c1">p1</font> <a href="euclid.html#K20" title="EUCLID:func.20">-</a> <font color="Maroon" title="c2">p2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="euclid.html#K16" title="EUCLID:func.16">0.REAL</a> 2 )
 ;<br/>

<a NAME="E2:34"/><b>then </b><i><font color="Green" title="E23">A1</font></i>: 
<font color="Maroon" title="c1">p1</font> <a href="euclid.html#K20" title="EUCLID:func.20">-</a> <font color="Maroon" title="c2">p2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="euclid.html#K16" title="EUCLID:func.16">0.REAL</a> 2
 
<b>by </b><i><a class="ref" href="euclid.html#T47" title="EUCLID:th.47">EUCLID:47</a></i>;<br/>
<a NAME="E3:34"/>
 <a href="euclid.html#K19" title="EUCLID:func.19">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">p1</font> <a href="euclid.html#K20" title="EUCLID:func.20">-</a> <font color="Maroon" title="c2">p2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">p2</font> <a href="euclid.html#K20" title="EUCLID:func.20">-</a> <font color="Maroon" title="c1">p1</font>
 
<b>by </b><i><a class="ref" href="euclid.html#T48" title="EUCLID:th.48">EUCLID:48</a></i>;<br/>
<b>hence </b><a NAME="E4:34"/>
(  <a href="euclid_3.html#K3" title="EUCLID_3:func.3">Arg</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">p1</font> <a href="euclid.html#K20" title="EUCLID:func.20">-</a> <font color="Maroon" title="c2">p2</font></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a>  <a href="sin_cos.html#K35" title="SIN_COS:func.35">PI</a>  iff  <a href="euclid_3.html#K3" title="EUCLID_3:func.3">Arg</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p2</font> <a href="euclid.html#K20" title="EUCLID:func.20">-</a> <font color="Maroon" title="c1">p1</font></span>)</span> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a>  <a href="sin_cos.html#K35" title="SIN_COS:func.35">PI</a>  )
 <b>by </b><i><a class="txt" href="euclid_3.html#E2:34"><i><font color="Green" title="E23">A1</font></i></a>, <a class="ref" href="euclid_3.html#T38" target="_self" title="EUCLID_3:th.38">Th38</a></i>;<br/>


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