<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon" title="c1">C</font> be  <a href="connsp_1.html#V2" title="CONNSP_1:attr.2">connected</a> <a href="compts_1.html#V6" title="COMPTS_1:attr.6">compact</a> non <a href="sppol_1.html#V1" title="SPPOL_1:attr.1">horizontal</a> non <a href="sppol_1.html#V2" title="SPPOL_1:attr.2">vertical</a> <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>;<br/>

<a NAME="E1:25"/>
for <font color="Olive" title="b1">P</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> holds <br/> ( <font color="Olive" title="b1">P</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="jordan10.html#K4" title="JORDAN10:func.4">BDD-Family</a> <font color="Maroon" title="c1">C</font> iff <font color="Olive" title="b1">P</font> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="jordan10.html#K3" title="JORDAN10:func.3">UBD-Family</a> <font color="Maroon" title="c1">C</font> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="25_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c2">P</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>;<br/>

<b>thus </b><a NAME="E1:25_1"/>
( <font color="Maroon" title="c2">P</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="jordan10.html#K4" title="JORDAN10:func.4">BDD-Family</a> <font color="Maroon" title="c1">C</font> implies <font color="Maroon" title="c2">P</font> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="jordan10.html#K3" title="JORDAN10:func.3">UBD-Family</a> <font color="Maroon" title="c1">C</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="25_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:25_1_1"/>
<font color="Maroon" title="c2">P</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="jordan10.html#K4" title="JORDAN10:func.4">BDD-Family</a> <font color="Maroon" title="c1">C</font>
 ;<br/>

<b>then consider </b><font color="Maroon" title="c3">k</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> <b> such that </b><br/><a NAME="E3:25_1_1"/><i><font color="Green" title="E21">A1</font></i>: 
<font color="Maroon" title="c2">P</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <span class="p1">(<span class="default"><a href="jordan2c.html#K1" title="JORDAN2C:func.1">BDD</a> <span class="p2">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> <font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c3">k</font></span>)</span></span>)</span></span>)</span>
 ;<br/>
<a NAME="E4:25_1_1"/>
<font color="Maroon" title="c2">P</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <span class="p1">(<span class="default"><a href="goboard9.html#K3" title="GOBOARD9:func.3">RightComp</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> <font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c3">k</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="jordan10.html#E3:25_1_1"><i><font color="Green" title="E21">A1</font></i></a>, <a class="ref" href="gobrd14.html#T47" title="GOBRD14:th.47">GOBRD14:47</a></i>;<br/>
<a NAME="E5:25_1_1"/><b>then </b><i><font color="Green" title="E22">A2</font></i>: 
<font color="Maroon" title="c2">P</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="goboard9.html#K3" title="GOBOARD9:func.3">RightComp</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> <font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c3">k</font></span>)</span></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> <font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c3">k</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="gobrd14.html#T31" title="GOBRD14:th.31">GOBRD14:31</a></i>;<br/>
<a NAME="E6:25_1_1"/><i><font color="Green" title="E23">A3</font></i>: 
 <a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> <font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c3">k</font></span>)</span> <a href="subset_1.html#R1" title="SUBSET_1:pred.1">misses</a>  <a href="goboard9.html#K2" title="GOBOARD9:func.2">LeftComp</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> <font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c3">k</font></span>)</span>
 
<b>by </b><i><a class="ref" href="sprect_3.html#T43" title="SPRECT_3:th.43">SPRECT_3:43</a></i>;<br/>
<a NAME="E7:25_1_1"/>
 <a href="goboard9.html#K3" title="GOBOARD9:func.3">RightComp</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> <font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c3">k</font></span>)</span> <a href="subset_1.html#R1" title="SUBSET_1:pred.1">misses</a>  <a href="goboard9.html#K2" title="GOBOARD9:func.2">LeftComp</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> <font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c3">k</font></span>)</span>
 
<b>by </b><i><a class="ref" href="gobrd14.html#T24" title="GOBRD14:th.24">GOBRD14:24</a></i>;<br/>
<a NAME="E8:25_1_1"/><b>then </b><i><font color="Green" title="E24">A4</font></i>: 
<font color="Maroon" title="c2">P</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="goboard9.html#K2" title="GOBOARD9:func.2">LeftComp</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> <font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c3">k</font></span>)</span>
 
<b>by </b><i><a class="txt" href="jordan10.html#E5:25_1_1"><i><font color="Green" title="E22">A2</font></i></a>, <a class="txt" href="jordan10.html#E6:25_1_1"><i><font color="Green" title="E23">A3</font></i></a>, <a class="ref" href="xboole_1.html#T70" title="XBOOLE_1:th.70">XBOOLE_1:70</a></i>;<br/>
<span class="p1">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> </span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="goboard9.html#K2" title="GOBOARD9:func.2">LeftComp</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> <font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c3">k</font></span>)</span></span>)</span> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> </span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p2">(<span class="default"><a href="goboard9.html#K2" title="GOBOARD9:func.2">LeftComp</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> <font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c3">k</font></span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> 
<b>by </b><i><a class="ref" href="xboole_1.html#T53" title="XBOOLE_1:th.53">XBOOLE_1:53</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="subset_1.html#K2" title="SUBSET_1:func.2">[#]</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p2">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span></span>)</span> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> 
<b>by </b><i><a class="txt" href="jordan10.html#E5:25_1_1"><i><font color="Green" title="E22">A2</font></i></a>, <a class="ref" href="gobrd14.html#T25" title="GOBRD14:th.25">GOBRD14:25</a></i>
<br/>.= 
 <a href="subset_1.html#K1" title="SUBSET_1:func.1">{}</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span>
<b>by </b><i><a class="ref" href="xboole_1.html#T37" title="XBOOLE_1:th.37">XBOOLE_1:37</a></i>
;<br/>
<a NAME="E10:25_1_1"/><b>then </b>
<font color="Maroon" title="c2">P</font> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a>  <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <span class="p1">(<span class="default"><a href="goboard9.html#K2" title="GOBOARD9:func.2">LeftComp</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> <font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c3">k</font></span>)</span></span>)</span> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> 
 
<b>by </b><i><a class="ref" href="xboole_0.html#D7" title="XBOOLE_0:def.7">XBOOLE_0:def 7</a></i>;<br/>
<a NAME="E11:25_1_1"/><b>then </b>
<font color="Maroon" title="c2">P</font> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="goboard9.html#K2" title="GOBOARD9:func.2">LeftComp</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> <font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c3">k</font></span>)</span>
 
<b>by </b><i><a class="txt" href="jordan10.html#E8:25_1_1"><i><font color="Green" title="E24">A4</font></i></a>, <a class="ref" href="subset_1.html#T46" title="SUBSET_1:th.46">SUBSET_1:46</a></i>;<br/>
<a NAME="E12:25_1_1"/><b>then </b>
<font color="Maroon" title="c2">P</font> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="jordan2c.html#K2" title="JORDAN2C:func.2">UBD</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> <font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c3">k</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="gobrd14.html#T46" title="GOBRD14:th.46">GOBRD14:46</a></i>;<br/>
<b>hence </b><a NAME="E13:25_1_1"/>
<font color="Maroon" title="c2">P</font> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="jordan10.html#K3" title="JORDAN10:func.3">UBD-Family</a> <font color="Maroon" title="c1">C</font>
 ;<br/>


</div><b>end;</b></div>

<b>assume </b><a NAME="E2:25_1"/>
<font color="Maroon" title="c2">P</font> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="jordan10.html#K3" title="JORDAN10:func.3">UBD-Family</a> <font color="Maroon" title="c1">C</font>
 ;<br/>

<b>then consider </b><font color="Maroon" title="c3">k</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> <b> such that </b><br/><a NAME="E4:25_1"/><i><font color="Green" title="E21">A5</font></i>: 
<font color="Maroon" title="c2">P</font> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="jordan2c.html#K2" title="JORDAN2C:func.2">UBD</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> <font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c3">k</font></span>)</span></span>)</span>
 ;<br/>
<a NAME="E5:25_1"/><i><font color="Green" title="E22">A6</font></i>: 
<font color="Maroon" title="c2">P</font> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="goboard9.html#K2" title="GOBOARD9:func.2">LeftComp</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> <font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c3">k</font></span>)</span>
 
<b>by </b><i><a class="txt" href="jordan10.html#E4:25_1"><i><font color="Green" title="E21">A5</font></i></a>, <a class="ref" href="gobrd14.html#T46" title="GOBRD14:th.46">GOBRD14:46</a></i>;<br/>
<a NAME="E6:25_1"/><b>then </b><i><font color="Green" title="E23">A7</font></i>: 
<font color="Maroon" title="c2">P</font> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a>  <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="goboard9.html#K3" title="GOBOARD9:func.3">RightComp</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> <font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c3">k</font></span>)</span>
 
<b>by </b><i><a class="ref" href="gobrd14.html#T24" title="GOBRD14:th.24">GOBRD14:24</a></i>;<br/>
<a NAME="E7:25_1"/>
<font color="Maroon" title="c2">P</font> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a>  <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> <font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c3">k</font></span>)</span>
 
<b>by </b><i><a class="txt" href="jordan10.html#E5:25_1"><i><font color="Green" title="E22">A6</font></i></a>, <a class="ref" href="sprect_3.html#T43" title="SPRECT_3:th.43">SPRECT_3:43</a></i>;<br/>
<a NAME="E8:25_1"/><b>then </b>
<font color="Maroon" title="c2">P</font> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a>  <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <span class="p1">(<span class="default"><a href="goboard9.html#K3" title="GOBOARD9:func.3">RightComp</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> <font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c3">k</font></span>)</span></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> <font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c3">k</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="jordan10.html#E6:25_1"><i><font color="Green" title="E23">A7</font></i></a>, <a class="ref" href="xboole_1.html#T70" title="XBOOLE_1:th.70">XBOOLE_1:70</a></i>;<br/>
<a NAME="E9:25_1"/><b>then </b><i><font color="Green" title="E24">A8</font></i>: 
<font color="Maroon" title="c2">P</font> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a>  <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <span class="p1">(<span class="default"><a href="goboard9.html#K3" title="GOBOARD9:func.3">RightComp</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> <font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c3">k</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="gobrd14.html#T31" title="GOBRD14:th.31">GOBRD14:31</a></i>;<br/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> </span>)</span> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> </span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <span class="p3">(<span class="default"><a href="goboard9.html#K3" title="GOBOARD9:func.3">RightComp</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> <font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c3">k</font></span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> </span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> </span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p2">(<span class="default"><a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <span class="p3">(<span class="default"><a href="goboard9.html#K3" title="GOBOARD9:func.3">RightComp</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> <font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c3">k</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> 
<b>by </b><i><a class="ref" href="xboole_1.html#T53" title="XBOOLE_1:th.53">XBOOLE_1:53</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> </span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="goboard9.html#K3" title="GOBOARD9:func.3">RightComp</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> <font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c3">k</font></span>)</span></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p3">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> <font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c3">k</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> 
<b>by </b><i><a class="ref" href="gobrd14.html#T31" title="GOBRD14:th.31">GOBRD14:31</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="subset_1.html#K2" title="SUBSET_1:func.2">[#]</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p2">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span></span>)</span> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> 
<b>by </b><i><a class="txt" href="jordan10.html#E5:25_1"><i><font color="Green" title="E22">A6</font></i></a>, <a class="ref" href="gobrd14.html#T25" title="GOBRD14:th.25">GOBRD14:25</a></i>
<br/>.= 
 <a href="subset_1.html#K1" title="SUBSET_1:func.1">{}</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span>
<b>by </b><i><a class="ref" href="xboole_1.html#T37" title="XBOOLE_1:th.37">XBOOLE_1:37</a></i>
;<br/>
<a NAME="E11:25_1"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> </span>)</span> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a>  <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <span class="p1">(<span class="default"><a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <span class="p2">(<span class="default"><a href="goboard9.html#K3" title="GOBOARD9:func.3">RightComp</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> <font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c3">k</font></span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> 
 
<b>by </b><i><a class="ref" href="xboole_0.html#D7" title="XBOOLE_0:def.7">XBOOLE_0:def 7</a></i>;<br/>
<a NAME="E12:25_1"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> </span>)</span> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <span class="p1">(<span class="default"><a href="goboard9.html#K3" title="GOBOARD9:func.3">RightComp</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> <font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c3">k</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="jordan10.html#E9:25_1"><i><font color="Green" title="E24">A8</font></i></a>, <a class="ref" href="subset_1.html#T46" title="SUBSET_1:th.46">SUBSET_1:46</a></i>;<br/>
<a NAME="E13:25_1"/><b>then </b>
<font color="Maroon" title="c2">P</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <span class="p1">(<span class="default"><a href="jordan2c.html#K1" title="JORDAN2C:func.1">BDD</a> <span class="p2">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> <font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c3">k</font></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="gobrd14.html#T47" title="GOBRD14:th.47">GOBRD14:47</a></i>;<br/>
<b>hence </b><a NAME="E14:25_1"/>
<font color="Maroon" title="c2">P</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="jordan10.html#K4" title="JORDAN10:func.4">BDD-Family</a> <font color="Maroon" title="c1">C</font>
 ;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E2:25"/>
 <a href="setfam_1.html#K7" title="SETFAM_1:func.7">COMPLEMENT</a> <span class="p1">(<span class="default"><a href="jordan10.html#K3" title="JORDAN10:func.3">UBD-Family</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="jordan10.html#K4" title="JORDAN10:func.4">BDD-Family</a> <font color="Maroon" title="c1">C</font>
 <b>by </b><i><a class="ref" href="setfam_1.html#D8" title="SETFAM_1:def.8">SETFAM_1:def 8</a></i>;<br/>


</div>
