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<b>let </b><font color="Maroon">D</font> be  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">f</font> be    <a href="finseq_1.html#M2">FinSequence</a> of <font color="Maroon">D</font>;<br/><b>let </b><font color="Maroon">k1</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> , <font color="Maroon">k2</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/>





<b>assume </b><a NAME="E1:6"/><i><font color="Green">E17</font></i>: 
<font color="Maroon">k1</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">k2</font>
 ;<br/>

<a NAME="E2:6"/><i><font color="Green">E18</font></i>: 
<font color="Maroon">k1</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">k2</font> <a href="nat_1.html#K1">+</a> 1
 
<b>by </b><i>, <a class="ref" href="nat_1.html#T37">NAT_1:37</a></i>;<br/>
<span class="p1">(<span class="default"><font color="Maroon">k2</font> <a href="binarith.html#K3">-'</a> <font color="Maroon">k1</font></span>)</span> <a href="nat_1.html#K1">+</a> 1 = 
<span class="p1">(<span class="default"><font color="Maroon">k2</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">k1</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> 1
<b>by </b><i>, <a class="ref" href="binarith.html#T50">BINARITH:50</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">k2</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">k1</font>

<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">k2</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">k1</font>
<b>by </b><i>, <a class="ref" href="binarith.html#T50">BINARITH:50</a></i>
;<br/>
<b>hence </b><a NAME="E4:6"/>
 <a href="finseq_8.html#K2" target="_self">smid</a> <font color="Maroon">f</font>,<font color="Maroon">k1</font>,<font color="Maroon">k2</font> <a href="hidden.html#R1">=</a>  <a href="jordan3.html#K1">mid</a> <font color="Maroon">f</font>,<font color="Maroon">k1</font>,<font color="Maroon">k2</font>
 <b>by </b><i>, <a class="ref" href="jordan3.html#D1">JORDAN3:def 1</a></i>;<br/>


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