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<b>let </b><font color="Maroon">c<sub>1</sub></font> be  non <a href="xboole_0.html#V1">zero</a> <a href="nat_1.html#NM1">Nat</a>;<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="finseq_2.html#M2">Element</a> of  <a href="euclid.html#K1">REAL</a> <font color="Maroon">c<sub>1</sub></font>;<br/>







<b>given </b><font color="Maroon">c<sub>5</sub></font> being    <a href="subset_1.html#M1">Element</a> of  <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">c<sub>1</sub></font><b> such that </b><a NAME="E1:43"/><i><font color="Green">E29</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="chain_1.html#K2" target="_self">.</a> <font color="Maroon">c<sub>5</sub></font> <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">c<sub>3</sub></font> <a href="chain_1.html#K2" target="_self">.</a> <font color="Maroon">c<sub>5</sub></font>
 ;<br/>

<a NAME="E2:43"/>
( <font color="Maroon">c<sub>4</sub></font> <a href="chain_1.html#K2" target="_self">.</a> <font color="Maroon">c<sub>5</sub></font> <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">c<sub>3</sub></font> <a href="chain_1.html#K2" target="_self">.</a> <font color="Maroon">c<sub>5</sub></font> or <font color="Maroon">c<sub>2</sub></font> <a href="chain_1.html#K2" target="_self">.</a> <font color="Maroon">c<sub>5</sub></font> <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">c<sub>4</sub></font> <a href="chain_1.html#K2" target="_self">.</a> <font color="Maroon">c<sub>5</sub></font> )
 
<b>by </b><i><a class="txt" href="chain_1.html#E1:43"><i><font color="Green">E29</font></i></a>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/>
<b>hence </b><a NAME="E3:43"/>
( <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a>  <a href="chain_1.html#K4" target="_self">cell</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font> implies ex <font color="Olive">b<sub>1</sub></font> being   <a href="subset_1.html#M1">Element</a> of  <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">c<sub>1</sub></font> st <br/>( <font color="Maroon">c<sub>2</sub></font> <a href="chain_1.html#K2" target="_self">.</a> <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">c<sub>3</sub></font> <a href="chain_1.html#K2" target="_self">.</a> <font color="Olive">b<sub>1</sub></font> &amp; ( <font color="Maroon">c<sub>4</sub></font> <a href="chain_1.html#K2" target="_self">.</a> <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>2</sub></font> <a href="chain_1.html#K2" target="_self">.</a> <font color="Olive">b<sub>1</sub></font> or <font color="Maroon">c<sub>3</sub></font> <a href="chain_1.html#K2" target="_self">.</a> <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>4</sub></font> <a href="chain_1.html#K2" target="_self">.</a> <font color="Olive">b<sub>1</sub></font> ) ) )
 <b>by </b><i><a class="ref" href="chain_1.html#T24" target="_self">Th24</a></i>;<br/>

<b>thus </b><a NAME="E4:43"/>
( ex <font color="Olive">b<sub>1</sub></font> being   <a href="subset_1.html#M1">Element</a> of  <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">c<sub>1</sub></font> st <br/>( <font color="Maroon">c<sub>2</sub></font> <a href="chain_1.html#K2" target="_self">.</a> <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">c<sub>3</sub></font> <a href="chain_1.html#K2" target="_self">.</a> <font color="Olive">b<sub>1</sub></font> &amp; ( <font color="Maroon">c<sub>4</sub></font> <a href="chain_1.html#K2" target="_self">.</a> <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>2</sub></font> <a href="chain_1.html#K2" target="_self">.</a> <font color="Olive">b<sub>1</sub></font> or <font color="Maroon">c<sub>3</sub></font> <a href="chain_1.html#K2" target="_self">.</a> <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>4</sub></font> <a href="chain_1.html#K2" target="_self">.</a> <font color="Olive">b<sub>1</sub></font> ) ) implies <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a>  <a href="chain_1.html#K4" target="_self">cell</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font> )
 ;<br/>


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