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<b>let </b><font color="Maroon" title="c1">n</font> be    <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> ;<br/>

<b>assume </b><a NAME="E1:135"/><i><font color="Green" title="E111">A1</font></i>: 
2 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c1">n</font>
 ;<br/>

<b>let </b><font color="Maroon" title="c2">A</font>, <font color="Maroon" title="c3">B</font>, <font color="Maroon" title="c4">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> <font color="Maroon" title="c1">n</font></span>)</span>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E2:135"/><i><font color="Green" title="E112">A2</font></i>: 
<font color="Maroon" title="c4">P</font> is <a href="jordan2c.html#V1" title="JORDAN2C:attr.1">Bounded</a>
 <b>and </b><br/><a NAME="E3:135"/><i><font color="Green" title="E113">A3</font></i>: 
( <font color="Maroon" title="c2">A</font> <a href="jordan2c.html#R2" title="JORDAN2C:pred.2">is_outside_component_of</a> <font color="Maroon" title="c4">P</font> &amp; <font color="Maroon" title="c3">B</font> <a href="jordan2c.html#R2" title="JORDAN2C:pred.2">is_outside_component_of</a> <font color="Maroon" title="c4">P</font> )
 ;<br/>

<a NAME="E4:135"/><i><font color="Green" title="E114">A4</font></i>: 
 <a href="jordan2c.html#K2" title="JORDAN2C:func.2">UBD</a> <font color="Maroon" title="c4">P</font> <a href="jordan2c.html#R2" title="JORDAN2C:pred.2">is_outside_component_of</a> <font color="Maroon" title="c4">P</font>
 
<b>by </b><i><a class="txt" href="jordan2c.html#E1:135"><i><font color="Green" title="E111">A1</font></i></a>, <a class="txt" href="jordan2c.html#E2:135"><i><font color="Green" title="E112">A2</font></i></a>, <a class="ref" href="jordan2c.html#T76" target="_self" title="JORDAN2C:th.76">Th76</a></i>;<br/>
<a NAME="E5:135"/><i><font color="Green" title="E115">A5</font></i>: 
( <font color="Maroon" title="c2">A</font> <a href="connsp_1.html#R4" title="CONNSP_1:pred.4">is_a_component_of</a> <font color="Maroon" title="c4">P</font> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a>  &amp; <font color="Maroon" title="c3">B</font> <a href="connsp_1.html#R4" title="CONNSP_1:pred.4">is_a_component_of</a> <font color="Maroon" title="c4">P</font> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a>  )
 
<b>by </b><i><a class="txt" href="jordan2c.html#E3:135"><i><font color="Green" title="E113">A3</font></i></a>, <a class="ref" href="jordan2c.html#D4" target="_self" title="JORDAN2C:def.4">Def4</a></i>;<br/>
<a NAME="E6:135"/>
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c1">n</font>
 
<b>by </b><i><a class="txt" href="jordan2c.html#E1:135"><i><font color="Green" title="E111">A1</font></i></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></i>;<br/>
<a NAME="E7:135"/><b>then </b>
not <font color="Maroon" title="c4">P</font> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a>  is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>
 
<b>by </b><i><a class="txt" href="jordan2c.html#E2:135"><i><font color="Green" title="E112">A2</font></i></a>, <a class="ref" href="jordan2c.html#T74" target="_self" title="JORDAN2C:th.74">Th74</a></i>;<br/>
<a NAME="E8:135"/><b>then </b><i><font color="Green" title="E116">A6</font></i>: 
( <font color="Maroon" title="c2">A</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Maroon" title="c3">B</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  )
 
<b>by </b><i><a class="txt" href="jordan2c.html#E5:135"><i><font color="Green" title="E115">A5</font></i></a>, <a class="ref" href="sprect_1.html#T6" title="SPRECT_1:th.6">SPRECT_1:6</a></i>;<br/>
<a NAME="E9:135"/><i><font color="Green" title="E117">A7</font></i>: 
 <a href="jordan2c.html#K2" title="JORDAN2C:func.2">UBD</a> <font color="Maroon" title="c4">P</font> <a href="connsp_1.html#R4" title="CONNSP_1:pred.4">is_a_component_of</a> <font color="Maroon" title="c4">P</font> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> 
 
<b>by </b><i><a class="txt" href="jordan2c.html#E4:135"><i><font color="Green" title="E114">A4</font></i></a>, <a class="ref" href="jordan2c.html#D4" target="_self" title="JORDAN2C:def.4">Def4</a></i>;<br/>
<a NAME="E10:135"/>
( <font color="Maroon" title="c2">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="jordan2c.html#K2" title="JORDAN2C:func.2">UBD</a> <font color="Maroon" title="c4">P</font> &amp; <font color="Maroon" title="c3">B</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="jordan2c.html#K2" title="JORDAN2C:func.2">UBD</a> <font color="Maroon" title="c4">P</font> )
 
<b>by </b><i><a class="txt" href="jordan2c.html#E3:135"><i><font color="Green" title="E113">A3</font></i></a>, <a class="ref" href="jordan2c.html#T27" target="_self" title="JORDAN2C:th.27">Th27</a></i>;<br/>
<a NAME="E11:135"/><b>then </b>
( <font color="Maroon" title="c2">A</font> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a>  <a href="jordan2c.html#K2" title="JORDAN2C:func.2">UBD</a> <font color="Maroon" title="c4">P</font> &amp; <font color="Maroon" title="c3">B</font> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a>  <a href="jordan2c.html#K2" title="JORDAN2C:func.2">UBD</a> <font color="Maroon" title="c4">P</font> )
 
<b>by </b><i><a class="txt" href="jordan2c.html#E8:135"><i><font color="Green" title="E116">A6</font></i></a>, <a class="ref" href="xboole_1.html#T69" title="XBOOLE_1:th.69">XBOOLE_1:69</a></i>;<br/>
<a NAME="E12:135"/><b>then </b>
( <font color="Maroon" title="c2">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="jordan2c.html#K2" title="JORDAN2C:func.2">UBD</a> <font color="Maroon" title="c4">P</font> &amp; <font color="Maroon" title="c3">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="jordan2c.html#K2" title="JORDAN2C:func.2">UBD</a> <font color="Maroon" title="c4">P</font> )
 
<b>by </b><i><a class="txt" href="jordan2c.html#E5:135"><i><font color="Green" title="E115">A5</font></i></a>, <a class="txt" href="jordan2c.html#E9:135"><i><font color="Green" title="E117">A7</font></i></a>, <a class="ref" href="goboard9.html#T3" title="GOBOARD9:th.3">GOBOARD9:3</a></i>;<br/>
<b>hence </b><a NAME="E13:135"/>
<font color="Maroon" title="c2">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">B</font>
 ;<br/>


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