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<span class="kw">let </span><font color="Maroon" title="c1">a</font>, <font color="Maroon" title="c2">b</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K2" title="NUMBERS:func.2">COMPLEX</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">r</font> being  <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a> holds   <a href="complex2.html#K2" title="COMPLEX2:func.2">Rotate</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <font color="Maroon" title="c2">b</font></span>)</span>,<font color="Olive" title="b1">r</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="complex2.html#K2" title="COMPLEX2:func.2">Rotate</a> <font color="Maroon" title="c1">a</font>,<font color="Olive" title="b1">r</font></span>)</span> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <span class="p1">(<span class="default"><a href="complex2.html#K2" title="COMPLEX2:func.2">Rotate</a> <font color="Maroon" title="c2">b</font>,<font color="Olive" title="b1">r</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c3">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="complex2.html#K2" title="COMPLEX2:func.2">Rotate</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <font color="Maroon" title="c2">b</font></span>)</span>,<font color="Maroon" title="c3">r</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="complex2.html#K2" title="COMPLEX2:func.2">Rotate</a> <font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c3">r</font></span>)</span> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <span class="p1">(<span class="default"><a href="complex2.html#K2" title="COMPLEX2:func.2">Rotate</a> <font color="Maroon" title="c2">b</font>,<font color="Maroon" title="c3">r</font></span>)</span></span><br/>





<span class="kw">thus </span> <a href="complex2.html#K2" title="COMPLEX2:func.2">Rotate</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <font color="Maroon" title="c2">b</font></span>)</span>,<font color="Maroon" title="c3">r</font> = 
<span class="p1">(<span class="default"><a href="complex2.html#K2" title="COMPLEX2:func.2">Rotate</a> <font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c3">r</font></span>)</span> <a href="complex1.html#K8" title="COMPLEX1:func.8">+</a> <span class="p1">(<span class="default"><a href="complex2.html#K2" title="COMPLEX2:func.2">Rotate</a> <span class="p2">(<span class="default"><a href="complex1.html#K10" title="COMPLEX1:func.10">-</a> <font color="Maroon" title="c2">b</font></span>)</span>,<font color="Maroon" title="c3">r</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="complex2.html#T71" target="_self" title="COMPLEX2:th.71">Th71</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="complex2.html#K2" title="COMPLEX2:func.2">Rotate</a> <font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c3">r</font></span>)</span> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <span class="p1">(<span class="default"><a href="complex2.html#K2" title="COMPLEX2:func.2">Rotate</a> <font color="Maroon" title="c2">b</font>,<font color="Maroon" title="c3">r</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="complex2.html#T72" target="_self" title="COMPLEX2:th.72">Th72</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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