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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="midsp_1.html#NM1">MidSp</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> be    <a href="midsp_1.html#M1" target="_self">Vector</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>





<b>consider </b><font color="Maroon">c<sub>4</sub></font> being    <a href="subset_1.html#M1">Element</a> of <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span><b> such that </b><br/><a NAME="E2:45"/><i><font color="Green">E30</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="midsp_1.html#K9" target="_self">~</a> 
 <b>by </b><i><a class="ref" href="midsp_1.html#D8" target="_self">Def8</a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>5</sub></font> being    <a href="subset_1.html#M1">Element</a> of <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span><b> such that </b><br/><a NAME="E4:45"/><i><font color="Green">E31</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> <a href="midsp_1.html#K9" target="_self">~</a> 
 <b>by </b><i><a class="ref" href="midsp_1.html#D8" target="_self">Def8</a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>6</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E6:45"/><i><font color="Green">E32</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="midsp_1.html#K5" target="_self">`1</a> ,<font color="Maroon">c<sub>5</sub></font> <a href="midsp_1.html#K6" target="_self">`2</a>  <a href="midsp_1.html#R1" target="_self">@@</a> <font color="Maroon">c<sub>4</sub></font> <a href="midsp_1.html#K6" target="_self">`2</a> ,<font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="ref" href="midsp_1.html#T26" target="_self">Th26</a></i>;<br/>
<b>take </b>
<span class="p1"><a href="midsp_1.html#K7" target="_self">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="midsp_1.html#K5" target="_self">`1</a> </span>)</span>,<font color="Maroon">c<sub>6</sub></font></span><a href="midsp_1.html#K7" target="_self">]</a></span> <a href="midsp_1.html#K9" target="_self">~</a> 
;<br/>

<b>take </b><font color="Maroon">c<sub>7</sub></font> = <font color="Maroon">c<sub>4</sub></font>;<br/>

<b>take </b><font color="Maroon">c<sub>8</sub></font> = <span class="p1"><a href="midsp_1.html#K7" target="_self">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="midsp_1.html#K6" target="_self">`2</a> </span>)</span>,<font color="Maroon">c<sub>6</sub></font></span><a href="midsp_1.html#K7" target="_self">]</a></span>;<br/>

<b>thus </b><a NAME="E7:45"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font> <a href="midsp_1.html#K9" target="_self">~</a> 
 <b>by </b><i><a class="txt" href="midsp_1.html#E2:45"><i><font color="Green">E30</font></i></a></i>;<br/>

<a NAME="E8:45"/>
( <font color="Maroon">c<sub>8</sub></font> <a href="midsp_1.html#K5" target="_self">`1</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="midsp_1.html#K6" target="_self">`2</a>  &amp; <font color="Maroon">c<sub>8</sub></font> <a href="midsp_1.html#K6" target="_self">`2</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font> )
 
<b>by </b><i><a class="ref" href="mcart_1.html#T7">MCART_1:7</a></i>;<br/>
<a NAME="E9:45"/><b>then </b>
<font color="Maroon">c<sub>5</sub></font> <a href="midsp_1.html#R2" target="_self">##</a> <font color="Maroon">c<sub>8</sub></font>
 
<b>by </b><i><a class="txt" href="midsp_1.html#E6:45"><i><font color="Green">E32</font></i></a>, <a class="ref" href="midsp_1.html#D6" target="_self">Def6</a></i>;<br/>
<b>hence </b><a NAME="E10:45"/>
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>8</sub></font> <a href="midsp_1.html#K9" target="_self">~</a> 
 <b>by </b><i><a class="txt" href="midsp_1.html#E4:45"><i><font color="Green">E31</font></i></a>, <a class="ref" href="midsp_1.html#T42" target="_self">Th42</a></i>;<br/>

<b>thus </b><a NAME="E11:45"/>
<font color="Maroon">c<sub>7</sub></font> <a href="midsp_1.html#K6" target="_self">`2</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>8</sub></font> <a href="midsp_1.html#K5" target="_self">`1</a> 
 <b>by </b><i><a class="ref" href="mcart_1.html#T7">MCART_1:7</a></i>;<br/>

<b>thus </b><a NAME="E12:45"/>
<span class="p1"><a href="midsp_1.html#K7" target="_self">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="midsp_1.html#K5" target="_self">`1</a> </span>)</span>,<font color="Maroon">c<sub>6</sub></font></span><a href="midsp_1.html#K7" target="_self">]</a></span> <a href="midsp_1.html#K9" target="_self">~</a>  <a href="hidden.html#R1">=</a> <span class="p1"><a href="midsp_1.html#K7" target="_self">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="midsp_1.html#K5" target="_self">`1</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="midsp_1.html#K6" target="_self">`2</a> </span>)</span></span><a href="midsp_1.html#K7" target="_self">]</a></span> <a href="midsp_1.html#K9" target="_self">~</a> 
 <b>by </b><i><a class="ref" href="mcart_1.html#T7">MCART_1:7</a></i>;<br/>


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