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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="partfun1.html#NM1">PartFunc</a> of  <a href="numbers.html#K1">REAL</a> , <a href="numbers.html#K1">REAL</a> ;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be  <a href="integra1.html#V1">closed-interval</a> <a href="subset_1.html#NM2">Subset</a> of <a href="numbers.html#K1">REAL</a> ;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font> be   <a href="real_1.html#NM1">Real</a>;<br/>







<b>assume </b><a NAME="E1:25"/><i><font color="Green">E21</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="rcomp_1.html#K1">[.</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span><a href="rcomp_1.html#K1">.]</a></span>
 ;<br/>

<b>consider </b><font color="Maroon">c<sub>5</sub></font>, <font color="Maroon">c<sub>6</sub></font> being   <a href="real_1.html#NM1">Real</a><b> such that </b><br/><a NAME="E3:25"/><i><font color="Green">E22</font></i>: 
( <font color="Maroon">c<sub>5</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="rcomp_1.html#K1">[.</a><span class="default"><font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span><a href="rcomp_1.html#K1">.]</a></span> )
 <b>by </b><i><a class="ref" href="integra1.html#D1">INTEGRA1:def 1</a></i>;<br/>
<a NAME="E4:25"/><i><font color="Green">E23</font></i>: 
( <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> )
 
<b>by </b><i><a class="txt" href="integra5.html#E1:25"><i><font color="Green">E21</font></i></a>, <a class="txt" href="integra5.html#E3:25"><i><font color="Green">E22</font></i></a>, <a class="ref" href="integra1.html#T6">INTEGRA1:6</a></i>;<br/>
<a NAME="E5:25"/><b>then </b>
 <a href="integra5.html#K4" target="_self">integral</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a>  <a href="integra5.html#K2" target="_self">integral</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p1"><a href="integra5.html#K3" target="_self">['</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span><a href="integra5.html#K3" target="_self">']</a></span>
 
<b>by </b><i><a class="txt" href="integra5.html#E3:25"><i><font color="Green">E22</font></i></a>, <a class="ref" href="integra5.html#D5" target="_self">Def5</a></i>;<br/>
<b>hence </b><a NAME="E6:25"/>
 <a href="integra5.html#K2" target="_self">integral</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="integra5.html#K4" target="_self">integral</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="txt" href="integra5.html#E3:25"><i><font color="Green">E22</font></i></a>, <a class="txt" href="integra5.html#E4:25"><i><font color="Green">E23</font></i></a>, <a class="ref" href="integra5.html#D4" target="_self">Def4</a></i>;<br/>


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