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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>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <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="subset_1.html#K3" title="SUBSET_1:func.3">`</a>  <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span><br/>

<a NAME="E1:6"/>
 <a href="topreal1.html#K3" title="TOPREAL1:func.3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 1,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 1,<span class="p5">(<span class="default"><a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20" title="EUCLID:func.20">-</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 1,<span class="p3">(<span class="default"><a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> 1</span>)</span>,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">f</font>
 
<b>by </b><i><a class="ref" href="goboard8.html#T33" title="GOBOARD8:th.33">GOBOARD8:33</a></i>;<br/>
<a NAME="E2:6"/><b>then </b>
 <a href="topreal1.html#K3" title="TOPREAL1:func.3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 1,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 1,<span class="p5">(<span class="default"><a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20" title="EUCLID:func.20">-</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 1,<span class="p3">(<span class="default"><a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> 1</span>)</span>,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</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="subset_1.html#K3" title="SUBSET_1:func.3">`</a> 
 
<b>by </b><i><a class="ref" href="subset_1.html#T43" title="SUBSET_1:th.43">SUBSET_1:43</a></i>;<br/>
<b>hence </b><a NAME="E3:6"/>
<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="subset_1.html#K3" title="SUBSET_1:func.3">`</a>  <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 ; <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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