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<span class="kw">let </span><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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <span class="p1">(<span class="default"><a href="sin_cos.html#K25" title="SIN_COS:func.25">exp_R</a> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> 1</span>)</span> <a href="prepower.html#K9" title="PREPOWER:func.9">#R</a> <font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="sin_cos.html#K25" title="SIN_COS:func.25">exp_R</a> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c1">x</font> &amp; <span class="p1">(<span class="default"><a href="sin_cos.html#K25" title="SIN_COS:func.25">exp_R</a> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> 1</span>)</span> <a href="power.html#K3" title="POWER:func.3">to_power</a> <font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="sin_cos.html#K25" title="SIN_COS:func.25">exp_R</a> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c1">x</font> &amp; <a href="power.html#K8" title="POWER:func.8">number_e</a> <a href="power.html#K3" title="POWER:func.3">to_power</a> <font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="sin_cos.html#K25" title="SIN_COS:func.25">exp_R</a> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c1">x</font> &amp; <a href="power.html#K8" title="POWER:func.8">number_e</a> <a href="prepower.html#K9" title="PREPOWER:func.9">#R</a> <font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="sin_cos.html#K25" title="SIN_COS:func.25">exp_R</a> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c1">x</font> )</span><br/>

<span class="kw">thus </span><span class="p1">(<span class="default"><a href="sin_cos.html#K25" title="SIN_COS:func.25">exp_R</a> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> 1</span>)</span> <a href="prepower.html#K9" title="PREPOWER:func.9">#R</a> <font color="Maroon" title="c1">x</font> = 
<span class="p1">(<span class="default"><a href="sin_cos.html#K27" title="SIN_COS:func.27">exp_R</a> 1</span>)</span> <a href="prepower.html#K9" title="PREPOWER:func.9">#R</a> <font color="Maroon" title="c1">x</font>
<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/>.= 
 <a href="sin_cos.html#K26" title="SIN_COS:func.26">exp_R</a> <font color="Maroon" title="c1">x</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="taylor_1.html#T9" target="_self" title="TAYLOR_1:th.9">Th9</a></span>
<br/>.= 
<a href="sin_cos.html#K25" title="SIN_COS:func.25">exp_R</a> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c1">x</font>
<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>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <span class="p1">(<span class="default"><a href="sin_cos.html#K25" title="SIN_COS:func.25">exp_R</a> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> 1</span>)</span> <a href="power.html#K3" title="POWER:func.3">to_power</a> <font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="sin_cos.html#K25" title="SIN_COS:func.25">exp_R</a> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c1">x</font> &amp; <a href="power.html#K8" title="POWER:func.8">number_e</a> <a href="power.html#K3" title="POWER:func.3">to_power</a> <font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="sin_cos.html#K25" title="SIN_COS:func.25">exp_R</a> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c1">x</font> &amp; <a href="power.html#K8" title="POWER:func.8">number_e</a> <a href="prepower.html#K9" title="PREPOWER:func.9">#R</a> <font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="sin_cos.html#K25" title="SIN_COS:func.25">exp_R</a> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c1">x</font> )</span><br/>

<span class="kw">thus </span><span class="p1">(<span class="default"><a href="sin_cos.html#K25" title="SIN_COS:func.25">exp_R</a> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> 1</span>)</span> <a href="power.html#K3" title="POWER:func.3">to_power</a> <font color="Maroon" title="c1">x</font> = 
<span class="p1">(<span class="default"><a href="sin_cos.html#K27" title="SIN_COS:func.27">exp_R</a> 1</span>)</span> <a href="power.html#K3" title="POWER:func.3">to_power</a> <font color="Maroon" title="c1">x</font>
<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/>.= 
 <a href="sin_cos.html#K26" title="SIN_COS:func.26">exp_R</a> <font color="Maroon" title="c1">x</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="taylor_1.html#T9" target="_self" title="TAYLOR_1:th.9">Th9</a></span>
<br/>.= 
<a href="sin_cos.html#K25" title="SIN_COS:func.25">exp_R</a> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c1">x</font>
<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>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <a href="power.html#K8" title="POWER:func.8">number_e</a> <a href="power.html#K3" title="POWER:func.3">to_power</a> <font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="sin_cos.html#K25" title="SIN_COS:func.25">exp_R</a> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c1">x</font> &amp; <a href="power.html#K8" title="POWER:func.8">number_e</a> <a href="prepower.html#K9" title="PREPOWER:func.9">#R</a> <font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="sin_cos.html#K25" title="SIN_COS:func.25">exp_R</a> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c1">x</font> )</span><br/>

<span class="kw">thus </span><a href="power.html#K8" title="POWER:func.8">number_e</a> <a href="power.html#K3" title="POWER:func.3">to_power</a> <font color="Maroon" title="c1">x</font> = 
 <a href="sin_cos.html#K26" title="SIN_COS:func.26">exp_R</a> <font color="Maroon" title="c1">x</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="taylor_1.html#T9" target="_self" title="TAYLOR_1:th.9">Th9</a></span>
<br/>.= 
<a href="sin_cos.html#K25" title="SIN_COS:func.25">exp_R</a> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c1">x</font>
<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>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <a href="power.html#K8" title="POWER:func.8">number_e</a> <a href="prepower.html#K9" title="PREPOWER:func.9">#R</a> <font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="sin_cos.html#K25" title="SIN_COS:func.25">exp_R</a> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c1">x</font></span><br/>

<span class="kw">thus </span><a href="power.html#K8" title="POWER:func.8">number_e</a> <a href="prepower.html#K9" title="PREPOWER:func.9">#R</a> <font color="Maroon" title="c1">x</font> = 
 <a href="sin_cos.html#K26" title="SIN_COS:func.26">exp_R</a> <font color="Maroon" title="c1">x</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="taylor_1.html#T9" target="_self" title="TAYLOR_1:th.9">Th9</a></span>
<br/>.= 
<a href="sin_cos.html#K25" title="SIN_COS:func.25">exp_R</a> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c1">x</font>
<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>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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