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<span class="kw">let </span><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>; <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#K3" title="EUCLID_3:func.3">Arg</a> <font color="Maroon" title="c1">p1</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="sin_cos.html#K33" title="SIN_COS:func.33">PI</a>  &amp;  <a href="euclid_3.html#K3" title="EUCLID_3:func.3">Arg</a> <font color="Maroon" title="c2">p2</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="sin_cos.html#K33" title="SIN_COS:func.33">PI</a>  implies  <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="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c2">p2</font></span>)</span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="sin_cos.html#K33" title="SIN_COS:func.33">PI</a>  )</span><br/>



<span class="kw">assume </span><a NAME="E1:32"/>
(  <a href="euclid_3.html#K3" title="EUCLID_3:func.3">Arg</a> <font color="Maroon" title="c1">p1</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="sin_cos.html#K33" title="SIN_COS:func.33">PI</a>  &amp;  <a href="euclid_3.html#K3" title="EUCLID_3:func.3">Arg</a> <font color="Maroon" title="c2">p2</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</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">  <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="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c2">p2</font></span>)</span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="sin_cos.html#K33" title="SIN_COS:func.33">PI</a> </span><br/>

<a NAME="E2:32"/><span class="kw">then </span>
 <a href="comptrig.html#K1" title="COMPTRIG:func.1">Arg</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> <font color="Maroon" title="c1">p1</font></span>)</span> <a href="complex1.html#K8" title="COMPLEX1:func.8">+</a> <span class="p2">(<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></span>)</span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="sin_cos.html#K33" title="SIN_COS:func.33">PI</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="complex2.html#T20" title="COMPLEX2:th.20">COMPLEX2:20</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:32"/>
 <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="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c2">p2</font></span>)</span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="sin_cos.html#K33" title="SIN_COS:func.33">PI</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="euclid_3.html#T9" target="_self" title="EUCLID_3:th.9">Th13</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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