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<b>let </b><font color="Maroon" title="c2">A</font> be   <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>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c2">A</font> is <a href="sppol_1.html#V2" title="SPPOL_1:attr.2">vertical</a> &amp; not <font color="Maroon" title="c2">A</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; <font color="Maroon" title="c2">A</font> is <a href="compts_1.html#V2" title="COMPTS_1:attr.2">compact</a> implies <font color="Maroon" title="c2">A</font> is <a href="jordan21.html#V1" title="JORDAN21:attr.1">with_the_max_arc</a> )</span><br/>

<b>assume </b><a NAME="E1:15_1_1"/><i><font color="Green" title="E8">A1</font></i>: 
( <font color="Maroon" title="c2">A</font> is <a href="sppol_1.html#V2" title="SPPOL_1:attr.2">vertical</a> &amp; not <font color="Maroon" title="c2">A</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; <font color="Maroon" title="c2">A</font> is <a href="compts_1.html#V2" title="COMPTS_1:attr.2">compact</a> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">A</font> is <a href="jordan21.html#V1" title="JORDAN21:attr.1">with_the_max_arc</a></span><br/>

<a NAME="E2:15_1_1"/><b>then </b><i><font color="Green" title="E9">A2</font></i>: 
 <a href="pscomp_1.html#K11" title="PSCOMP_1:func.11">W-bound</a> <font color="Maroon" title="c2">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pscomp_1.html#K13" title="PSCOMP_1:func.13">E-bound</a> <font color="Maroon" title="c2">A</font>
 
<b>by </b><i><a class="ref" href="sprect_1.html#T17" title="SPRECT_1:th.17">SPRECT_1:17</a></i>;<br/>
<a NAME="E3:15_1_1"/><i><font color="Green" title="E10">A3</font></i>: 
 <a href="pscomp_1.html#K28" title="PSCOMP_1:func.28">E-min</a> <font color="Maroon" title="c2">A</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">A</font>
 
<b>by </b><i><a class="txt" href="#E1:15_1_1"><i><font color="Green" title="E8">A1</font></i></a>, <a class="ref" href="sprect_1.html#T16" title="SPRECT_1:th.16">SPRECT_1:16</a></i>;<br/>
<a NAME="E4:15_1_1"/>
<span class="p1">(<span class="default"><a href="pscomp_1.html#K28" title="PSCOMP_1:func.28">E-min</a> <font color="Maroon" title="c2">A</font></span>)</span> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pscomp_1.html#K13" title="PSCOMP_1:func.13">E-bound</a> <font color="Maroon" title="c2">A</font>
 
<b>by </b><i><a class="ref" href="euclid.html#T56" title="EUCLID:th.56">EUCLID:56</a></i>;<br/>
<a NAME="E5:15_1_1"/><b>then </b>
 <a href="pscomp_1.html#K28" title="PSCOMP_1:func.28">E-min</a> <font color="Maroon" title="c2">A</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="pscomp_1.html#K11" title="PSCOMP_1:func.11">W-bound</a> <font color="Maroon" title="c2">A</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p3">(<span class="default"><a href="pscomp_1.html#K13" title="PSCOMP_1:func.13">E-bound</a> <font color="Maroon" title="c2">A</font></span>)</span></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span>
 
<b>by </b><i><a class="txt" href="#E2:15_1_1"><i><font color="Green" title="E9">A2</font></i></a>, <a class="ref" href="jordan6.html#T34" title="JORDAN6:th.34">JORDAN6:34</a></i>;<br/>
<b>hence </b><a NAME="E6:15_1_1"/>
<font color="Maroon" title="c2">A</font> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a>  <a href="jordan6.html#K6" title="JORDAN6:func.6">Vertical_Line</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="pscomp_1.html#K11" title="PSCOMP_1:func.11">W-bound</a> <font color="Maroon" title="c2">A</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p3">(<span class="default"><a href="pscomp_1.html#K13" title="PSCOMP_1:func.13">E-bound</a> <font color="Maroon" title="c2">A</font></span>)</span></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span>
 <b>by </b><i><a class="txt" href="#E3:15_1_1"><i><font color="Green" title="E10">A3</font></i></a>, <a class="ref" href="xboole_0.html#T3" title="XBOOLE_0:th.3">XBOOLE_0:3</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="jordan21.html#D1" title="JORDAN21:def.1">JORDAN21:def 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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