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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E40">Th25</font></span>: <a NAME="T25"><span class="comment"><font color="firebrick">:: JGRAPH_3:25</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">Kb</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span>  st <font color="Olive" title="b1">Kb</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"> { <span class="default"> <font color="Olive" title="b2">q</font> where <font color="Olive" title="b2">q</font> is   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span> : ( (  <a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">q</font> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a>  &amp;  <a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b2">q</font> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a>  &amp; <font color="Olive" title="b2">q</font> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 1 ) or ( <font color="Olive" title="b2">q</font> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 &amp;  <a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b2">q</font> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a>  &amp; <font color="Olive" title="b2">q</font> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 1 ) or (  <a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">q</font> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a>  &amp;  <a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b2">q</font> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a>  &amp; <font color="Olive" title="b2">q</font> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 1 ) or ( 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">q</font> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a>  &amp;  <a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b2">q</font> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a>  &amp; <font color="Olive" title="b2">q</font> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 1 ) ) </span> } </span>  holds <br/>( <font color="Olive" title="b1">Kb</font> is  <a href="topreal2.html#V1" title="TOPREAL2:attr.1">being_simple_closed_curve</a>  &amp; <font color="Olive" title="b1">Kb</font> is  <a href="compts_1.html#V2" title="COMPTS_1:attr.2">compact</a>  )</div></div>
