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<b>let </b><font color="Maroon" title="c1">x</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"> <span class="p1">(<span class="default"><a href="sin_cos.html#K20" title="SIN_COS:func.20">sin</a> <font color="Maroon" title="c1">x</font></span>)</span> <a href="newton.html#K2" title="NEWTON:func.2">|^</a> 3 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">3 <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p3">(<span class="default"><a href="sin_cos.html#K20" title="SIN_COS:func.20">sin</a> <font color="Maroon" title="c1">x</font></span>)</span></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p2">(<span class="default"><a href="sin_cos.html#K21" title="SIN_COS:func.21">sin</a> <span class="p3">(<span class="default">3 <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c1">x</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 4</span><br/>

<span class="p1">(<span class="default"><span class="p2">(<span class="default">3 <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p3">(<span class="default"><a href="sin_cos.html#K20" title="SIN_COS:func.20">sin</a> <font color="Maroon" title="c1">x</font></span>)</span></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p2">(<span class="default"><a href="sin_cos.html#K21" title="SIN_COS:func.21">sin</a> <span class="p3">(<span class="default">3 <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c1">x</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 4 = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">3 <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p3">(<span class="default"><a href="sin_cos.html#K20" title="SIN_COS:func.20">sin</a> <font color="Maroon" title="c1">x</font></span>)</span></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p4">(<span class="default">4 <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="sin_cos.html#K20" title="SIN_COS:func.20">sin</a> <font color="Maroon" title="c1">x</font></span>)</span> <a href="newton.html#K2" title="NEWTON:func.2">|^</a> 3</span>)</span></span>)</span></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p3">(<span class="default">3 <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p4">(<span class="default"><a href="sin_cos.html#K20" title="SIN_COS:func.20">sin</a> <font color="Maroon" title="c1">x</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 4
<b>by </b><i><a class="ref" href="sin_cos5.html#T16" target="_self" title="SIN_COS5:th.16">Th16</a></i>
<br/>.= 
<span class="p1">(<span class="default">4 <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="sin_cos.html#K20" title="SIN_COS:func.20">sin</a> <font color="Maroon" title="c1">x</font></span>)</span> <a href="newton.html#K2" title="NEWTON:func.2">|^</a> 3</span>)</span></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 4

;<br/>
<b>hence </b><a NAME="E2:21"/>
<span class="p1">(<span class="default"><a href="sin_cos.html#K20" title="SIN_COS:func.20">sin</a> <font color="Maroon" title="c1">x</font></span>)</span> <a href="newton.html#K2" title="NEWTON:func.2">|^</a> 3 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">3 <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p3">(<span class="default"><a href="sin_cos.html#K20" title="SIN_COS:func.20">sin</a> <font color="Maroon" title="c1">x</font></span>)</span></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p2">(<span class="default"><a href="sin_cos.html#K21" title="SIN_COS:func.21">sin</a> <span class="p3">(<span class="default">3 <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c1">x</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 4
 ; <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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