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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/>

<b>assume </b><a NAME="E1:136"/><i><font color="Green">E115</font></i>: 
2 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/>

<b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font> be   <a href="struct_0.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E2:136"/><i><font color="Green">E116</font></i>: 
<font color="Maroon">c<sub>4</sub></font> is <a href="jordan2c.html#V1" target="_self">Bounded</a>
 <b>and </b><br/><a NAME="E3:136"/><i><font color="Green">E117</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> <a href="jordan2c.html#R2" target="_self">is_outside_component_of</a> <font color="Maroon">c<sub>4</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="jordan2c.html#R2" target="_self">is_outside_component_of</a> <font color="Maroon">c<sub>4</sub></font> )
 ;<br/>

<b>consider </b><font color="Maroon">c<sub>5</sub></font> being   <a href="struct_0.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> <font color="Maroon">c<sub>1</sub></font></span>)</span><b> such that </b><br/><a NAME="E5:136"/><i><font color="Green">E118</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="jordan2c.html#R2" target="_self">is_outside_component_of</a> <font color="Maroon">c<sub>4</sub></font>
 <b>and </b><br/><a NAME="E6:136"/><i><font color="Green">E119</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a>  <a href="jordan2c.html#K2" target="_self">UBD</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="txt" href="jordan2c.html#E1:136"><i><font color="Green">E115</font></i></a>, <a class="txt" href="jordan2c.html#E2:136"><i><font color="Green">E116</font></i></a>, <a class="ref" href="jordan2c.html#T76" target="_self">Th76</a></i>;<br/>
<a NAME="E7:136"/><i><font color="Green">E120</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> <a href="connsp_1.html#R4">is_a_component_of</a> <font color="Maroon">c<sub>4</sub></font> <a href="subset_1.html#K3">`</a>  &amp; <font color="Maroon">c<sub>3</sub></font> <a href="connsp_1.html#R4">is_a_component_of</a> <font color="Maroon">c<sub>4</sub></font> <a href="subset_1.html#K3">`</a>  )
 
<b>by </b><i><a class="txt" href="jordan2c.html#E3:136"><i><font color="Green">E117</font></i></a>, <a class="ref" href="jordan2c.html#D4" target="_self">Def4</a></i>;<br/>
<a NAME="E8:136"/>
1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="txt" href="jordan2c.html#E1:136"><i><font color="Green">E115</font></i></a>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/>
<a NAME="E9:136"/><b>then </b>
not <font color="Maroon">c<sub>4</sub></font> <a href="subset_1.html#K3">`</a>  is <a href="xboole_0.html#V1">empty</a>
 
<b>by </b><i><a class="txt" href="jordan2c.html#E2:136"><i><font color="Green">E116</font></i></a>, <a class="ref" href="jordan2c.html#T74" target="_self">Th74</a></i>;<br/>
<a NAME="E10:136"/><b>then </b><i><font color="Green">E121</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  &amp; <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  )
 
<b>by </b><i><a class="txt" href="jordan2c.html#E7:136"><i><font color="Green">E120</font></i></a>, <a class="ref" href="sprect_1.html#T6">SPRECT_1:6</a></i>;<br/>
<a NAME="E11:136"/><i><font color="Green">E122</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="connsp_1.html#R4">is_a_component_of</a> <font color="Maroon">c<sub>4</sub></font> <a href="subset_1.html#K3">`</a> 
 
<b>by </b><i><a class="txt" href="jordan2c.html#E5:136"><i><font color="Green">E118</font></i></a>, <a class="ref" href="jordan2c.html#D4" target="_self">Def4</a></i>;<br/>
<a NAME="E12:136"/>
( <font color="Maroon">c<sub>2</sub></font> <a href="tarski.html#R1">c=</a>  <a href="jordan2c.html#K2" target="_self">UBD</a> <font color="Maroon">c<sub>4</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="tarski.html#R1">c=</a>  <a href="jordan2c.html#K2" target="_self">UBD</a> <font color="Maroon">c<sub>4</sub></font> )
 
<b>by </b><i><a class="txt" href="jordan2c.html#E3:136"><i><font color="Green">E117</font></i></a>, <a class="ref" href="jordan2c.html#T27" target="_self">Th27</a></i>;<br/>
<a NAME="E13:136"/><b>then </b>
( <font color="Maroon">c<sub>2</sub></font> <a href="xboole_0.html#NR5" target="_self">meets</a> <font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="xboole_0.html#NR5" target="_self">meets</a> <font color="Maroon">c<sub>5</sub></font> )
 
<b>by </b><i><a class="txt" href="jordan2c.html#E6:136"><i><font color="Green">E119</font></i></a>, <a class="txt" href="jordan2c.html#E10:136"><i><font color="Green">E121</font></i></a>, <a class="ref" href="xboole_1.html#T69">XBOOLE_1:69</a></i>;<br/>
<a NAME="E14:136"/><b>then </b>
( <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> )
 
<b>by </b><i><a class="txt" href="jordan2c.html#E7:136"><i><font color="Green">E120</font></i></a>, <a class="txt" href="jordan2c.html#E11:136"><i><font color="Green">E122</font></i></a>, <a class="ref" href="goboard9.html#T3">GOBOARD9:3</a></i>;<br/>
<b>hence </b><a NAME="E15:136"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/>


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