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<b>let </b><font color="Maroon" title="c1">p</font>, <font color="Maroon" title="c2">r</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"> <a href="sin_cos2.html#K7" title="SIN_COS2:func.7">tanh</a>  <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c2">r</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sin_cos2.html#K7" title="SIN_COS2:func.7">tanh</a>  <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="binop_2.html#K10" title="BINOP_2:func.10">-</a> <span class="p2">(<span class="default"><a href="sin_cos2.html#K7" title="SIN_COS2:func.7">tanh</a>  <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c2">r</font></span>)</span></span>)</span> <a href="binop_2.html#K12" title="BINOP_2:func.12">/</a> <span class="p1">(<span class="default">1 <a href="binop_2.html#K10" title="BINOP_2:func.10">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="sin_cos2.html#K7" title="SIN_COS2:func.7">tanh</a>  <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="binop_2.html#K11" title="BINOP_2:func.11">*</a> <span class="p3">(<span class="default"><a href="sin_cos2.html#K7" title="SIN_COS2:func.7">tanh</a>  <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c2">r</font></span>)</span></span>)</span></span>)</span></span><br/>



<a href="sin_cos2.html#K7" title="SIN_COS2:func.7">tanh</a>  <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c2">r</font></span>)</span> = 
<a href="sin_cos2.html#K7" title="SIN_COS2:func.7">tanh</a>  <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <font color="Maroon" title="c2">r</font></span>)</span></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sin_cos2.html#K7" title="SIN_COS2:func.7">tanh</a>  <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="binop_2.html#K9" title="BINOP_2:func.9">+</a> <span class="p2">(<span class="default"><a href="sin_cos2.html#K7" title="SIN_COS2:func.7">tanh</a>  <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p3">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <font color="Maroon" title="c2">r</font></span>)</span></span>)</span></span>)</span> <a href="binop_2.html#K12" title="BINOP_2:func.12">/</a> <span class="p1">(<span class="default">1 <a href="binop_2.html#K9" title="BINOP_2:func.9">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="sin_cos2.html#K7" title="SIN_COS2:func.7">tanh</a>  <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="binop_2.html#K11" title="BINOP_2:func.11">*</a> <span class="p3">(<span class="default"><a href="sin_cos2.html#K7" title="SIN_COS2:func.7">tanh</a>  <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p4">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <font color="Maroon" title="c2">r</font></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="sin_cos2.html#E29"><i><font color="Green" title="E16">Lm6</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sin_cos2.html#K7" title="SIN_COS2:func.7">tanh</a>  <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="binop_2.html#K9" title="BINOP_2:func.9">+</a> <span class="p2">(<span class="default"><a href="binop_2.html#K7" title="BINOP_2:func.7">-</a> <span class="p3">(<span class="default"><a href="sin_cos2.html#K7" title="SIN_COS2:func.7">tanh</a>  <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c2">r</font></span>)</span></span>)</span></span>)</span> <a href="binop_2.html#K12" title="BINOP_2:func.12">/</a> <span class="p1">(<span class="default">1 <a href="binop_2.html#K9" title="BINOP_2:func.9">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="sin_cos2.html#K7" title="SIN_COS2:func.7">tanh</a>  <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="binop_2.html#K11" title="BINOP_2:func.11">*</a> <span class="p3">(<span class="default"><a href="sin_cos2.html#K7" title="SIN_COS2:func.7">tanh</a>  <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p4">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <font color="Maroon" title="c2">r</font></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="sin_cos2.html#T19" target="_self" title="SIN_COS2:th.19">Th19</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sin_cos2.html#K7" title="SIN_COS2:func.7">tanh</a>  <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="binop_2.html#K10" title="BINOP_2:func.10">-</a> <span class="p2">(<span class="default"><a href="sin_cos2.html#K7" title="SIN_COS2:func.7">tanh</a>  <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c2">r</font></span>)</span></span>)</span> <a href="binop_2.html#K12" title="BINOP_2:func.12">/</a> <span class="p1">(<span class="default">1 <a href="binop_2.html#K9" title="BINOP_2:func.9">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="sin_cos2.html#K7" title="SIN_COS2:func.7">tanh</a>  <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="binop_2.html#K11" title="BINOP_2:func.11">*</a> <span class="p3">(<span class="default"><a href="binop_2.html#K7" title="BINOP_2:func.7">-</a> <span class="p4">(<span class="default"><a href="sin_cos2.html#K7" title="SIN_COS2:func.7">tanh</a>  <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c2">r</font></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="sin_cos2.html#T19" target="_self" title="SIN_COS2:th.19">Th19</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sin_cos2.html#K7" title="SIN_COS2:func.7">tanh</a>  <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="binop_2.html#K10" title="BINOP_2:func.10">-</a> <span class="p2">(<span class="default"><a href="sin_cos2.html#K7" title="SIN_COS2:func.7">tanh</a>  <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c2">r</font></span>)</span></span>)</span> <a href="binop_2.html#K12" title="BINOP_2:func.12">/</a> <span class="p1">(<span class="default">1 <a href="binop_2.html#K10" title="BINOP_2:func.10">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="sin_cos2.html#K7" title="SIN_COS2:func.7">tanh</a>  <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="binop_2.html#K11" title="BINOP_2:func.11">*</a> <span class="p3">(<span class="default"><a href="sin_cos2.html#K7" title="SIN_COS2:func.7">tanh</a>  <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c2">r</font></span>)</span></span>)</span></span>)</span>

;<br/>
<b>hence </b><a NAME="E2:40"/>
<a href="sin_cos2.html#K7" title="SIN_COS2:func.7">tanh</a>  <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c2">r</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sin_cos2.html#K7" title="SIN_COS2:func.7">tanh</a>  <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="binop_2.html#K10" title="BINOP_2:func.10">-</a> <span class="p2">(<span class="default"><a href="sin_cos2.html#K7" title="SIN_COS2:func.7">tanh</a>  <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c2">r</font></span>)</span></span>)</span> <a href="binop_2.html#K12" title="BINOP_2:func.12">/</a> <span class="p1">(<span class="default">1 <a href="binop_2.html#K10" title="BINOP_2:func.10">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="sin_cos2.html#K7" title="SIN_COS2:func.7">tanh</a>  <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="binop_2.html#K11" title="BINOP_2:func.11">*</a> <span class="p3">(<span class="default"><a href="sin_cos2.html#K7" title="SIN_COS2:func.7">tanh</a>  <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c2">r</font></span>)</span></span>)</span></span>)</span>
 ; <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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