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<b>let </b><font color="Maroon">d</font> be  non <a href="xboole_0.html#V1">zero</a>  <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>let </b><font color="Maroon">l</font> be    <a href="finseq_2.html#M2">Element</a> of  <a href="euclid.html#K1">REAL</a> <font color="Maroon">d</font>;<br/><b>let </b><font color="Maroon">r</font> be    <a href="finseq_2.html#M2">Element</a> of  <a href="euclid.html#K1">REAL</a> <font color="Maroon">d</font>;<br/>





<a NAME="E1:43"/>
( ( for <font color="Olive">i</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">d</font> holds <br/> ( <font color="Maroon">l</font> <a href="chain_1.html#K2" target="_self">.</a> <font color="Olive">i</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">l</font> <a href="chain_1.html#K2" target="_self">.</a> <font color="Olive">i</font> &amp; <font color="Maroon">l</font> <a href="chain_1.html#K2" target="_self">.</a> <font color="Olive">i</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">r</font> <a href="chain_1.html#K2" target="_self">.</a> <font color="Olive">i</font> ) or  ex <font color="Olive">i</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">d</font> st <br/>( <font color="Maroon">r</font> <a href="chain_1.html#K2" target="_self">.</a> <font color="Olive">i</font> <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">l</font> <a href="chain_1.html#K2" target="_self">.</a> <font color="Olive">i</font> &amp; ( <font color="Maroon">l</font> <a href="chain_1.html#K2" target="_self">.</a> <font color="Olive">i</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">r</font> <a href="chain_1.html#K2" target="_self">.</a> <font color="Olive">i</font> or <font color="Maroon">l</font> <a href="chain_1.html#K2" target="_self">.</a> <font color="Olive">i</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">l</font> <a href="chain_1.html#K2" target="_self">.</a> <font color="Olive">i</font> ) ) ) &amp; ( for <font color="Olive">i</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">d</font> holds <br/> ( <font color="Maroon">l</font> <a href="chain_1.html#K2" target="_self">.</a> <font color="Olive">i</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">r</font> <a href="chain_1.html#K2" target="_self">.</a> <font color="Olive">i</font> &amp; <font color="Maroon">r</font> <a href="chain_1.html#K2" target="_self">.</a> <font color="Olive">i</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">r</font> <a href="chain_1.html#K2" target="_self">.</a> <font color="Olive">i</font> ) or  ex <font color="Olive">i</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">d</font> st <br/>( <font color="Maroon">r</font> <a href="chain_1.html#K2" target="_self">.</a> <font color="Olive">i</font> <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">l</font> <a href="chain_1.html#K2" target="_self">.</a> <font color="Olive">i</font> &amp; ( <font color="Maroon">r</font> <a href="chain_1.html#K2" target="_self">.</a> <font color="Olive">i</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">r</font> <a href="chain_1.html#K2" target="_self">.</a> <font color="Olive">i</font> or <font color="Maroon">l</font> <a href="chain_1.html#K2" target="_self">.</a> <font color="Olive">i</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">r</font> <a href="chain_1.html#K2" target="_self">.</a> <font color="Olive">i</font> ) ) ) )
 
;<br/>
<b>hence </b><a NAME="E2:43"/>
( <font color="Maroon">l</font> <a href="hidden.html#R2">in</a>  <a href="chain_1.html#K4" target="_self">cell</a> <font color="Maroon">l</font>,<font color="Maroon">r</font> &amp; <font color="Maroon">r</font> <a href="hidden.html#R2">in</a>  <a href="chain_1.html#K4" target="_self">cell</a> <font color="Maroon">l</font>,<font color="Maroon">r</font> )
 ;<br/>


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