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

<b>assume </b><a NAME="E1:78"/><i><font color="Green">E22</font></i>: 
(  <a href="real_1.html#K1">-</a> 1 <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">r</font> &amp; <font color="Maroon">r</font> <a href="xxreal_0.html#R1">&lt;</a> 1 )
 ;<br/>

<a NAME="E2:78"/><b>then </b>
(  <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><a href="sin_cos.html#K35">PI</a>  <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="sin_cos6.html#K3" target="_self">arcsin</a> <font color="Maroon">r</font> &amp;  <a href="sin_cos6.html#K3" target="_self">arcsin</a> <font color="Maroon">r</font> <a href="xxreal_0.html#R1">&lt;=</a> <a href="sin_cos.html#K35">PI</a>  <a href="real_1.html#K6">/</a> 2 )
 
<b>by </b><i><a class="ref" href="sin_cos6.html#T24" target="_self">Th24</a></i>;<br/>
<a NAME="E3:78"/><b>then </b>
( (  <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><a href="sin_cos.html#K35">PI</a>  <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="xxreal_0.html#R1">&lt;</a>  <a href="sin_cos6.html#K3" target="_self">arcsin</a> <font color="Maroon">r</font> &amp;  <a href="sin_cos6.html#K3" target="_self">arcsin</a> <font color="Maroon">r</font> <a href="xxreal_0.html#R1">&lt;</a> <a href="sin_cos.html#K35">PI</a>  <a href="real_1.html#K6">/</a> 2 ) or  <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><a href="sin_cos.html#K35">PI</a>  <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="hidden.html#R1">=</a>  <a href="sin_cos6.html#K3" target="_self">arcsin</a> <font color="Maroon">r</font> or  <a href="sin_cos6.html#K3" target="_self">arcsin</a> <font color="Maroon">r</font> <a href="hidden.html#R1">=</a> <a href="sin_cos.html#K35">PI</a>  <a href="real_1.html#K6">/</a> 2 )
 
<b>by </b><i><a class="ref" href="real_1.html#D5">REAL_1:def 5</a></i>;<br/>
<b>hence </b><a NAME="E4:78"/>
(  <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><a href="sin_cos.html#K35">PI</a>  <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="xxreal_0.html#R1">&lt;</a>  <a href="sin_cos6.html#K3" target="_self">arcsin</a> <font color="Maroon">r</font> &amp;  <a href="sin_cos6.html#K3" target="_self">arcsin</a> <font color="Maroon">r</font> <a href="xxreal_0.html#R1">&lt;</a> <a href="sin_cos.html#K35">PI</a>  <a href="real_1.html#K6">/</a> 2 )
 <b>by </b><i><a class="ref" href="sin_cos6.html#T26" target="_self">Th26</a>, <a class="ref" href="sin_cos6.html#T6" target="_self">Th6</a>, <a class="ref" href="sin_cos6.html#T23" target="_self">Th23</a>, <a class="ref" href="sin_cos.html#T82">SIN_COS:82</a></i>;<br/>


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