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<span class="kw">let </span><font color="Maroon" title="c1">r</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"> (  <a href="real_1.html#K1" title="REAL_1:func.1">-</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c1">r</font> &amp; <font color="Maroon" title="c1">r</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 1 &amp;  <a href="sin_cos9.html#K5" title="SIN_COS9:func.5">arctan</a> <font color="Maroon" title="c1">r</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="sin_cos.html#K36" title="SIN_COS:func.36">PI</a>  <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 4 implies <font color="Maroon" title="c1">r</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 )</span><br/>

<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:64"/><span class="lab"><font color="Green" title="E57">A1</font></span>: 
 <a href="real_1.html#K1" title="REAL_1:func.1">-</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c1">r</font>
 <span class="kw">and </span><br/><a NAME="E2:64"/><span class="lab"><font color="Green" title="E58">A2</font></span>: 
<font color="Maroon" title="c1">r</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 1
 <span class="kw">and </span><br/><a NAME="E3:64"/><span class="lab"><font color="Green" title="E59">A3</font></span>: 
 <a href="sin_cos9.html#K5" title="SIN_COS9:func.5">arctan</a> <font color="Maroon" title="c1">r</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="sin_cos.html#K36" title="SIN_COS:func.36">PI</a>  <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 4
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c1">r</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1</span><br/>

<span class="kw">thus </span><font color="Maroon" title="c1">r</font> = 
 <a href="sin_cos9.html#K7" title="SIN_COS9:func.7">tan</a> <span class="p1">(<span class="default"><a href="sin_cos.html#K36" title="SIN_COS:func.36">PI</a>  <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 4</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:64"><span class="lab"><font color="Green" title="E57">A1</font></span></a>, <a class="txt" href="#E2:64"><span class="lab"><font color="Green" title="E58">A2</font></span></a>, <a class="txt" href="#E3:64"><span class="lab"><font color="Green" title="E59">A3</font></span></a>, <a class="ref" href="sin_cos9.html#T51" target="_self" title="SIN_COS9:th.51">Th51</a></span>
<br/>.= 
<a href="sin_cos.html#K33" title="SIN_COS:func.33">tan</a>  <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p1">(<span class="default"><a href="sin_cos.html#K36" title="SIN_COS:func.36">PI</a>  <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 4</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="sin_cos9.html#E24"><span class="lab"><font color="Green" title="E14">Lm8</font></span></a>, <a class="ref" href="sin_cos9.html#T13" target="_self" title="SIN_COS9:th.13">Th13</a></span>
<br/>.= 
1
<span class="kw">by</span> <span class="lab"><a class="ref" href="sin_cos.html#D32" title="SIN_COS:def.32">SIN_COS:def 32</a></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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