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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="E1:76"/>
 <a href="int_1.html#K4">frac</a> <font color="Maroon">r</font> <a href="hidden.html#R1">=</a> 1 <a href="real_1.html#K6">/</a> 4
 ;<br/>

<a NAME="E2:76"/><b>then </b><i><font color="Green">E61</font></i>: 
<font color="Maroon">r</font> <a href="xcmplx_0.html#K6">-</a> <span class="p1"><a href="int_1.html#K1">[\</a><span class="default"><font color="Maroon">r</font></span><a href="int_1.html#K1">/]</a></span> <a href="hidden.html#R1">=</a> 1 <a href="real_1.html#K6">/</a> 4
 
<b>by </b><i><a class="ref" href="int_1.html#D6">INT_1:def 6</a></i>;<br/>
<b>thus </b><a href="toprealb.html#K12" target="_self">CircleMap</a>  <a href="funct_1.html#K1">.</a> <font color="Maroon">r</font> = 
<a href="toprealb.html#K12" target="_self">CircleMap</a>  <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">r</font> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p3"><a href="int_1.html#K1">[\</a><span class="default"><font color="Maroon">r</font></span><a href="int_1.html#K1">/]</a></span></span>)</span></span>)</span>
<b>by </b><i/>
<br/>.= 
<span class="p1"><a href="euclid.html#K23">|[</a><span class="default"><span class="p2">(<span class="default"><a href="sin_cos.html#K24">cos</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="real_1.html#K4">*</a> <a href="sin_cos.html#K35">PI</a> </span>)</span> <a href="real_1.html#K4">*</a> <span class="p4">(<span class="default">1 <a href="real_1.html#K6">/</a> 4</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="sin_cos.html#K21">sin</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="real_1.html#K4">*</a> <a href="sin_cos.html#K35">PI</a> </span>)</span> <a href="real_1.html#K4">*</a> <span class="p4">(<span class="default">1 <a href="real_1.html#K6">/</a> 4</span>)</span></span>)</span></span>)</span></span><a href="euclid.html#K23">]|</a></span>
<b>by </b><i><a class="txt" href="toprealb.html#E7"><i><font color="Green">Lemma50</font></i></a>, <a class="txt" href="toprealb.html#E5"><i><font color="Green">Lemma42</font></i></a></i>
<br/>.= 
<span class="p1"><a href="euclid.html#K23">|[</a><span class="default">0,1</span><a href="euclid.html#K23">]|</a></span>
<b>by </b><i><a class="ref" href="sin_cos.html#T82">SIN_COS:82</a></i>
;<br/>


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