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<b>let </b><font color="Maroon">c<sub>1</sub></font> be  non <a href="struct_0.html#V3">empty</a> <a href="pre_topc.html#NM1">TopSpace</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be  non <a href="xboole_0.html#V1">empty</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be  <a href="compts_1.html#V6">compact</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>4</sub></font> be  <a href="pscomp_1.html#V9" target="_self">continuous</a> <a href="pscomp_1.html#NM1">RealMap</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>







<b>assume </b><a NAME="E1:104"/><i><font color="Green">E65</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/>

<b>then reconsider </b><font color="Maroon">c<sub>5</sub></font> = <font color="Maroon">c<sub>3</sub></font> as  non <a href="xboole_0.html#V1">empty</a> <a href="compts_1.html#V6">compact</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font> <b>by </b><i><a class="ref" href="xboole_1.html#T3">XBOOLE_1:3</a></i>;<br/>
<i><font color="Green">E66</font></i>: <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="pscomp_1.html#K12" target="_self">||</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="relset_1.html#K10">.:</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="pre_topc.html#K3">|</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="pscomp_1.html#K12" target="_self">||</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="relset_1.html#K10">.:</a> <font color="Maroon">c<sub>3</sub></font>
<b>by </b><i><a class="ref" href="pre_topc.html#T29">PRE_TOPC:29</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="relset_1.html#K8">|</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="relset_1.html#K10">.:</a> <font color="Maroon">c<sub>3</sub></font>

<br/>.= 
<font color="Maroon">c<sub>4</sub></font> <a href="relset_1.html#K10">.:</a> <font color="Maroon">c<sub>3</sub></font>
<b>by </b><i><a class="ref" href="rfunct_2.html#T5">RFUNCT_2:5</a></i>
;<br/>
<i><font color="Green">E67</font></i>: <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="pscomp_1.html#K12" target="_self">||</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="relset_1.html#K10">.:</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="pre_topc.html#K3">|</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="pscomp_1.html#K12" target="_self">||</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="relset_1.html#K10">.:</a> <font color="Maroon">c<sub>2</sub></font>
<b>by </b><i><a class="ref" href="pre_topc.html#T29">PRE_TOPC:29</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="relset_1.html#K8">|</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="relset_1.html#K10">.:</a> <font color="Maroon">c<sub>2</sub></font>

<br/>.= 
<font color="Maroon">c<sub>4</sub></font> <a href="relset_1.html#K10">.:</a> <font color="Maroon">c<sub>2</sub></font>
<b>by </b><i><a class="ref" href="rfunct_2.html#T5">RFUNCT_2:5</a></i>
;<br/>
<a NAME="E5:104"/><i><font color="Green">E68</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="pscomp_1.html#K12" target="_self">||</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="relset_1.html#K10">.:</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="pre_topc.html#K3">|</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> is <a href="seq_4.html#V2">bounded_below</a>
 
<b>by </b><i><a class="ref" href="pscomp_1.html#D11" target="_self">Def11</a></i>;<br/>
<a NAME="E6:104"/>
<font color="Maroon">c<sub>4</sub></font> <a href="relset_1.html#K10">.:</a> <font color="Maroon">c<sub>2</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>4</sub></font> <a href="relset_1.html#K10">.:</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="txt" href="pscomp_1.html#E1:104"><i><font color="Green">E65</font></i></a>, <a class="ref" href="relat_1.html#T156">RELAT_1:156</a></i>;<br/>
<b>hence </b><a NAME="E7:104"/>
 <a href="pscomp_1.html#K10" target="_self">inf</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="pscomp_1.html#K12" target="_self">||</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="pscomp_1.html#K10" target="_self">inf</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="pscomp_1.html#K12" target="_self">||</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="pscomp_1.html#E3:104"><i><font color="Green">E66</font></i></a>, <a class="txt" href="pscomp_1.html#E4:104"><i><font color="Green">E67</font></i></a>, <a class="txt" href="pscomp_1.html#E5:104"><i><font color="Green">E68</font></i></a>, <a class="ref" href="seq_4.html#T64">SEQ_4:64</a></i>;<br/>


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