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<b>let </b><font color="Maroon">c<sub>1</sub></font> be  <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:33"/><i><font color="Green">E60</font></i>: 
0 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>1</sub></font>
 <b>and </b><br/><a NAME="E2:33"/><i><font color="Green">E61</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#R1">&lt;</a> <span class="p1">(<span class="default">3 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="real_1.html#K4">*</a> <a href="sin_cos.html#K33">PI</a> 
 <b>and </b><br/><a NAME="E3:33"/><i><font color="Green">E62</font></i>: 
 <a href="sin_cos.html#K20">sin</a> <font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="real_1.html#K1">-</a> 1
 ;<br/>

<a NAME="E4:33"/>
 <a href="sin_cos.html#K20">sin</a> <font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a>  <a href="real_1.html#K1">-</a> 1
 
<b>by </b><i><a class="ref" href="sin_cos6.html#T3" target="_self">Th3</a></i>;<br/>
<a NAME="E5:33"/><b>then </b><i><font color="Green">E63</font></i>: 
 <a href="sin_cos.html#K20">sin</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="real_1.html#K1">-</a> 1
 
<b>by </b><i><a class="txt" href="sin_cos6.html#E3:33"><i><font color="Green">E62</font></i></a>, <a class="ref" href="xxreal_0.html#T1">XXREAL_0:1</a></i>;<br/>
<a NAME="E6:33"/>
<font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> 2 <a href="real_1.html#K4">*</a> <a href="sin_cos.html#K33">PI</a> 
 
<b>by </b><i><a class="txt" href="sin_cos6.html#E2:33"><i><font color="Green">E61</font></i></a>, <a class="txt" href="sin_cos6.html#E19"><i><font color="Green">Lemma19</font></i></a>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/>
<b>hence </b><a NAME="E7:33"/>
contradiction
 <b>by </b><i><a class="txt" href="sin_cos6.html#E1:33"><i><font color="Green">E60</font></i></a>, <a class="txt" href="sin_cos6.html#E2:33"><i><font color="Green">E61</font></i></a>, <a class="txt" href="sin_cos6.html#E5:33"><i><font color="Green">E63</font></i></a>, <a class="ref" href="sin_cos6.html#T27" target="_self">Th27</a></i>;<br/>


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