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<b>let </b><font color="Maroon" title="c1">r</font> be   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="real_1.html#K1" title="REAL_1:func.1">-</a> 1 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c1">r</font> &amp; <font color="Maroon" title="c1">r</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> 1 implies ( <a href="sin_cos.html#K36" title="SIN_COS:func.36">PI</a>  <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 4 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="sin_cos9.html#K6" title="SIN_COS9:func.6">arccot</a> <font color="Maroon" title="c1">r</font> &amp;  <a href="sin_cos9.html#K6" title="SIN_COS9:func.6">arccot</a> <font color="Maroon" title="c1">r</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default">3 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 4</span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <a href="sin_cos.html#K36" title="SIN_COS:func.36">PI</a>  ) )</span><br/>

<b>assume </b><a NAME="E1:68"/><i><font color="Green" title="E59">A1</font></i>: 
(  <a href="real_1.html#K1" title="REAL_1:func.1">-</a> 1 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c1">r</font> &amp; <font color="Maroon" title="c1">r</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> 1 )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <a href="sin_cos.html#K36" title="SIN_COS:func.36">PI</a>  <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 4 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="sin_cos9.html#K6" title="SIN_COS9:func.6">arccot</a> <font color="Maroon" title="c1">r</font> &amp;  <a href="sin_cos9.html#K6" title="SIN_COS9:func.6">arccot</a> <font color="Maroon" title="c1">r</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default">3 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 4</span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <a href="sin_cos.html#K36" title="SIN_COS:func.36">PI</a>  )</span><br/>

<a NAME="E2:68"/><b>then </b>
( <a href="sin_cos.html#K36" title="SIN_COS:func.36">PI</a>  <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 4 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="sin_cos9.html#K6" title="SIN_COS9:func.6">arccot</a> <font color="Maroon" title="c1">r</font> &amp;  <a href="sin_cos9.html#K6" title="SIN_COS9:func.6">arccot</a> <font color="Maroon" title="c1">r</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default">3 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 4</span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <a href="sin_cos.html#K36" title="SIN_COS:func.36">PI</a>  )
 
<b>by </b><i><a class="ref" href="sin_cos9.html#T64" target="_self" title="SIN_COS9:th.64">Th62</a></i>;<br/>
<a NAME="E3:68"/><b>then </b><i><font color="Green" title="E60">A2</font></i>: 
( ( <a href="sin_cos.html#K36" title="SIN_COS:func.36">PI</a>  <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 4 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="sin_cos9.html#K6" title="SIN_COS9:func.6">arccot</a> <font color="Maroon" title="c1">r</font> &amp;  <a href="sin_cos9.html#K6" title="SIN_COS9:func.6">arccot</a> <font color="Maroon" title="c1">r</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default">3 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 4</span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <a href="sin_cos.html#K36" title="SIN_COS:func.36">PI</a>  ) or <a href="sin_cos.html#K36" title="SIN_COS:func.36">PI</a>  <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 4 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="sin_cos9.html#K6" title="SIN_COS9:func.6">arccot</a> <font color="Maroon" title="c1">r</font> or  <a href="sin_cos9.html#K6" title="SIN_COS9:func.6">arccot</a> <font color="Maroon" title="c1">r</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> 4</span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <a href="sin_cos.html#K36" title="SIN_COS:func.36">PI</a>  )
 
<b>by </b><i><a class="ref" href="xxreal_0.html#T1" title="XXREAL_0:th.1">XXREAL_0:1</a></i>;<br/>
<b>thus </b><a NAME="E4:68"/>
( <a href="sin_cos.html#K36" title="SIN_COS:func.36">PI</a>  <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 4 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="sin_cos9.html#K6" title="SIN_COS9:func.6">arccot</a> <font color="Maroon" title="c1">r</font> &amp;  <a href="sin_cos9.html#K6" title="SIN_COS9:func.6">arccot</a> <font color="Maroon" title="c1">r</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default">3 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 4</span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <a href="sin_cos.html#K36" title="SIN_COS:func.36">PI</a>  )
 <b>by </b><i><a class="txt" href="#E1:68"><i><font color="Green" title="E59">A1</font></i></a>, <a class="txt" href="#E3:68"><i><font color="Green" title="E60">A2</font></i></a>, <a class="ref" href="sin_cos9.html#T18" target="_self" title="SIN_COS9:th.18">Th16</a>, <a class="ref" href="sin_cos9.html#T52" target="_self" title="SIN_COS9:th.52">Th50</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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