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<b>let </b><font color="Maroon" title="c1">f</font> be  non <a href="funct_1.html#V3" title="FUNCT_1:attr.3">constant</a> <a href="goboard5.html#V2" title="GOBOARD5:attr.2">standard</a> <a href="goboard5.html#NM1" title="GOBOARD5:NM.1">special_circular_sequence</a>;<br/>

<a NAME="E1:57"/><i><font color="Green" title="E44">A1</font></i>: 
 <a href="pscomp_1.html#K32" title="PSCOMP_1:func.32">E-min</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c1">f</font>
 
<b>by </b><i><a class="ref" href="sprect_2.html#T49" title="SPRECT_2:th.49">SPRECT_2:49</a></i>;<br/>
<a NAME="E2:57"/><i><font color="Green" title="E45">A2</font></i>: 
 <a href="pscomp_1.html#K31" title="PSCOMP_1:func.31">E-max</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c1">f</font>
 
<b>by </b><i><a class="ref" href="sprect_2.html#T50" title="SPRECT_2:th.50">SPRECT_2:50</a></i>;<br/>
<a NAME="E3:57"/>
 <a href="pscomp_1.html#K32" title="PSCOMP_1:func.32">E-min</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="pscomp_1.html#K31" title="PSCOMP_1:func.31">E-max</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">f</font></span>)</span>
 
<b>by </b><i><a class="ref" href="sprect_2.html#T58" title="SPRECT_2:th.58">SPRECT_2:58</a></i>;<br/>
<a NAME="E4:57"/><b>then </b><i><font color="Green" title="E46">A3</font></i>: 
<span class="p1">(<span class="default"><a href="pscomp_1.html#K32" title="PSCOMP_1:func.32">E-min</a> <span class="p2">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span> <a href="finseq_4.html#K5" title="FINSEQ_4:func.5">..</a> <font color="Maroon" title="c1">f</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K31" title="PSCOMP_1:func.31">E-max</a> <span class="p2">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span> <a href="finseq_4.html#K5" title="FINSEQ_4:func.5">..</a> <font color="Maroon" title="c1">f</font>
 
<b>by </b><i><a class="txt" href="sprect_5.html#E1:57"><i><font color="Green" title="E44">A1</font></i></a>, <a class="txt" href="sprect_5.html#E2:57"><i><font color="Green" title="E45">A2</font></i></a>, <a class="ref" href="finseq_5.html#T10" title="FINSEQ_5:th.10">FINSEQ_5:10</a></i>;<br/>
<a NAME="E5:57"/>
<span class="p1">(<span class="default"><a href="pscomp_1.html#K32" title="PSCOMP_1:func.32">E-min</a> <span class="p2">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span> <a href="finseq_4.html#K5" title="FINSEQ_4:func.5">..</a> <font color="Maroon" title="c1">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c1">f</font>
 
<b>by </b><i><a class="txt" href="sprect_5.html#E1:57"><i><font color="Green" title="E44">A1</font></i></a>, <a class="ref" href="finseq_4.html#T30" title="FINSEQ_4:th.30">FINSEQ_4:30</a></i>;<br/>
<a NAME="E6:57"/><b>then </b><i><font color="Green" title="E47">A4</font></i>: 
<span class="p1">(<span class="default"><a href="pscomp_1.html#K32" title="PSCOMP_1:func.32">E-min</a> <span class="p2">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span> <a href="finseq_4.html#K5" title="FINSEQ_4:func.5">..</a> <font color="Maroon" title="c1">f</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 1
 
<b>by </b><i><a class="ref" href="finseq_3.html#T27" title="FINSEQ_3:th.27">FINSEQ_3:27</a></i>;<br/>
<b>assume </b><a NAME="E7:57"/>
<font color="Maroon" title="c1">f</font> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">/.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pscomp_1.html#K31" title="PSCOMP_1:func.31">E-max</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">f</font></span>)</span>
 ;<br/>

<a NAME="E8:57"/><b>then </b>
<span class="p1">(<span class="default"><a href="pscomp_1.html#K31" title="PSCOMP_1:func.31">E-max</a> <span class="p2">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span> <a href="finseq_4.html#K5" title="FINSEQ_4:func.5">..</a> <font color="Maroon" title="c1">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 
<b>by </b><i><a class="ref" href="finseq_6.html#T47" title="FINSEQ_6:th.47">FINSEQ_6:47</a></i>;<br/>
<b>hence </b><a NAME="E9:57"/>
<span class="p1">(<span class="default"><a href="pscomp_1.html#K31" title="PSCOMP_1:func.31">E-max</a> <span class="p2">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span> <a href="finseq_4.html#K5" title="FINSEQ_4:func.5">..</a> <font color="Maroon" title="c1">f</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K32" title="PSCOMP_1:func.32">E-min</a> <span class="p2">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span> <a href="finseq_4.html#K5" title="FINSEQ_4:func.5">..</a> <font color="Maroon" title="c1">f</font>
 <b>by </b><i><a class="txt" href="sprect_5.html#E4:57"><i><font color="Green" title="E46">A3</font></i></a>, <a class="txt" href="sprect_5.html#E6:57"><i><font color="Green" title="E47">A4</font></i></a>, <a class="ref" href="real_1.html#D5" title="REAL_1:def.5">REAL_1:def 5</a></i>;<br/>


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