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<span class="kw">let </span><font color="Maroon" title="c1">x</font> be   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> 2 <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sin_cos.html#K20" title="SIN_COS:func.20">sin</a>  <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span></span>)</span> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p1">(<span class="default"><a href="sin_cos.html#K23" title="SIN_COS:func.23">cos</a>  <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c1">x</font></span>)</span></span><br/>

<span class="p1">(<span class="default"><a href="sin_cos.html#K22" title="SIN_COS:func.22">sin</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span></span>)</span> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a>  = 
<span class="p1">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p2">(<span class="default"><a href="sin_cos.html#K25" title="SIN_COS:func.25">cos</a> <span class="p3">(<span class="default">2 <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2
<span class="kw">by</span> <span class="lab"><a class="ref" href="sin_cos5.html#T20" title="SIN_COS5:th.20">SIN_COS5:20</a></span>
<br/>.= 
<span class="p1">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p2">(<span class="default"><a href="sin_cos.html#K25" title="SIN_COS:func.25">cos</a> <font color="Maroon" title="c1">x</font></span>)</span></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2

;<br/>
<span class="kw">then </span>2 <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sin_cos.html#K20" title="SIN_COS:func.20">sin</a>  <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span></span>)</span> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> </span>)</span> = 
2 <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p3">(<span class="default"><a href="sin_cos.html#K25" title="SIN_COS:func.25">cos</a> <font color="Maroon" title="c1">x</font></span>)</span></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="sin_cos.html#D21" title="SIN_COS:def.21">SIN_COS:def 21</a></span>
<br/>.= 
1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p1">(<span class="default"><a href="sin_cos.html#K23" title="SIN_COS:func.23">cos</a>  <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c1">x</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="sin_cos.html#D23" title="SIN_COS:def.23">SIN_COS:def 23</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E3:5"/>
2 <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sin_cos.html#K20" title="SIN_COS:func.20">sin</a>  <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span></span>)</span> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p1">(<span class="default"><a href="sin_cos.html#K23" title="SIN_COS:func.23">cos</a>  <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c1">x</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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