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<b>let </b><font color="Maroon" title="c1">r</font> be  <a href="xreal_0.html#V1" title="XREAL_0:attr.1">real</a>  <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a> <font color="Maroon" title="c1">r</font> &amp; <font color="Maroon" title="c1">r</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a> 2 <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <a href="sin_cos.html#K35" title="SIN_COS:func.35">PI</a>  implies  <a href="sin_cos.html#K23" title="SIN_COS:func.23">cos</a> <font color="Maroon" title="c1">r</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a> 1 )</span><br/>

<b>assume </b><b>that </b><br/><a NAME="E1:36"/><i><font color="Green" title="E53">A1</font></i>: 
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a> <font color="Maroon" title="c1">r</font>
 <b>and </b><br/><a NAME="E2:36"/><i><font color="Green" title="E54">A2</font></i>: 
<font color="Maroon" title="c1">r</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a> 2 <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <a href="sin_cos.html#K35" title="SIN_COS:func.35">PI</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="sin_cos.html#K23" title="SIN_COS:func.23">cos</a> <font color="Maroon" title="c1">r</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a> 1</span><br/>

<a NAME="E3:36"/><i><font color="Green" title="E55">A3</font></i>: 
 <a href="sin_cos.html#K23" title="SIN_COS:func.23">cos</a> <font color="Maroon" title="c1">r</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 1
 
<b>by </b><i><a class="ref" href="sin_cos6.html#T6" target="_self" title="SIN_COS6:th.6">Th6</a></i>;<br/>
<a NAME="E4:36"/>
 <a href="sin_cos.html#K23" title="SIN_COS:func.23">cos</a> <font color="Maroon" title="c1">r</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 1
 
<b>by </b><i><a class="txt" href="sin_cos6.html#E1:36"><i><font color="Green" title="E53">A1</font></i></a>, <a class="txt" href="sin_cos6.html#E2:36"><i><font color="Green" title="E54">A2</font></i></a>, <a class="ref" href="comptrig.html#T79" title="COMPTRIG:th.79">COMPTRIG:79</a></i>;<br/>
<b>hence </b><a NAME="E5:36"/>
 <a href="sin_cos.html#K23" title="SIN_COS:func.23">cos</a> <font color="Maroon" title="c1">r</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a> 1
 <b>by </b><i><a class="txt" href="sin_cos6.html#E3:36"><i><font color="Green" title="E55">A3</font></i></a>, <a class="ref" href="real_1.html#D5" title="REAL_1:def.5">REAL_1:def 5</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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