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<span class="kw">let </span><font color="Maroon" title="c1">p</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" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  <a href="euclid_3.html#K3" title="EUCLID_3:func.3">Arg</a> <font color="Maroon" title="c1">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="rcomp_1.html#K2" title="RCOMP_1:func.2">].</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<a href="sin_cos.html#K28" title="SIN_COS:func.28">PI</a></span><a href="rcomp_1.html#K2" title="RCOMP_1:func.2">.[</a></span> iff <font color="Maroon" title="c1">p</font> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a>  <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  )</span><br/>

<a NAME="E1:31"/>
 <a href="complex1.html#K4" title="COMPLEX1:func.4">Im</a> <span class="p1">(<span class="default"><a href="euclid_3.html#K2" title="EUCLID_3:func.2">euc2cpx</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">p</font> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="complex1.html#T12" onmouseover="rs('complex1/T12')" onmouseout="rh()">COMPLEX1:12</a></span>;<br/>
<span class="kw">hence </span><a NAME="E2:31"/>
(  <a href="euclid_3.html#K3" title="EUCLID_3:func.3">Arg</a> <font color="Maroon" title="c1">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="rcomp_1.html#K2" title="RCOMP_1:func.2">].</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<a href="sin_cos.html#K28" title="SIN_COS:func.28">PI</a></span><a href="rcomp_1.html#K2" title="RCOMP_1:func.2">.[</a></span> iff <font color="Maroon" title="c1">p</font> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a>  <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="complex2.html#T18" onmouseover="rs('complex2/T18')" onmouseout="rh()">COMPLEX2:18</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" 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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