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<b>let </b><font color="Maroon">M</font> be   <a href="midsp_1.html#NM1">MidSp</a>;<br/><b>let </b><font color="Maroon">u</font> be    <a href="midsp_1.html#M1" target="_self">Vector</a> of <font color="Maroon">M</font>;<br/><b>let </b><font color="Maroon">v</font> be    <a href="midsp_1.html#M1" target="_self">Vector</a> of <font color="Maroon">M</font>;<br/>





<b>consider </b><font color="Maroon">p</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">M</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">M</font></span><a href="zfmisc_1.html#K2">:]</a></span><b> such that </b><br/><a NAME="E2:44"/><i><font color="Green">E37</font></i>: 
<font color="Maroon">u</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p</font> <a href="midsp_1.html#K8" target="_self">~</a> 
 <b>by </b><i><a class="ref" href="midsp_1.html#D4" target="_self">Def4</a></i>;<br/>
<b>consider </b><font color="Maroon">q</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">M</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">M</font></span><a href="zfmisc_1.html#K2">:]</a></span><b> such that </b><br/><a NAME="E4:44"/><i><font color="Green">E38</font></i>: 
<font color="Maroon">v</font> <a href="hidden.html#R1">=</a> <font color="Maroon">q</font> <a href="midsp_1.html#K8" target="_self">~</a> 
 <b>by </b><i><a class="ref" href="midsp_1.html#D4" target="_self">Def4</a></i>;<br/>
<b>consider </b><font color="Maroon">d</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">M</font><b> such that </b><br/><a NAME="E6:44"/><i><font color="Green">E63</font></i>: 
<font color="Maroon">q</font> <a href="midsp_1.html#K5" target="_self">`1</a> ,<font color="Maroon">q</font> <a href="midsp_1.html#K6" target="_self">`2</a>  <a href="midsp_1.html#R1" target="_self">@@</a> <font color="Maroon">p</font> <a href="midsp_1.html#K6" target="_self">`2</a> ,<font color="Maroon">d</font>
 <b>by </b><i/>;<br/>
<b>take </b>
<span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">p</font> <a href="midsp_1.html#K5" target="_self">`1</a> </span>)</span>,<font color="Maroon">d</font></span><a href="domain_1.html#K1">]</a></span> <a href="midsp_1.html#K8" target="_self">~</a> 
;<br/>

<b>take </b><font color="Maroon">p'</font> = <font color="Maroon">p</font>;<br/>

<b>take </b><font color="Maroon">q'</font> = <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">p</font> <a href="midsp_1.html#K6" target="_self">`2</a> </span>)</span>,<font color="Maroon">d</font></span><a href="domain_1.html#K1">]</a></span>;<br/>

<b>thus </b><a NAME="E7:44"/>
<font color="Maroon">u</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p'</font> <a href="midsp_1.html#K8" target="_self">~</a> 
 <b>by </b><i/>;<br/>

<a NAME="E8:44"/>
( <font color="Maroon">q'</font> <a href="midsp_1.html#K5" target="_self">`1</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">p</font> <a href="midsp_1.html#K6" target="_self">`2</a>  &amp; <font color="Maroon">q'</font> <a href="midsp_1.html#K6" target="_self">`2</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">d</font> )
 
<b>by </b><i><a class="ref" href="mcart_1.html#T7">MCART_1:7</a></i>;<br/>
<a NAME="E9:44"/><b>then </b>
<font color="Maroon">q</font> <a href="midsp_1.html#R2" target="_self">##</a> <font color="Maroon">q'</font>
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E10:44"/>
<font color="Maroon">v</font> <a href="hidden.html#R1">=</a> <font color="Maroon">q'</font> <a href="midsp_1.html#K8" target="_self">~</a> 
 <b>by </b><i>, </i>;<br/>

<b>thus </b><a NAME="E11:44"/>
<font color="Maroon">p'</font> <a href="midsp_1.html#K6" target="_self">`2</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">q'</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="E12:44"/>
<span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">p</font> <a href="midsp_1.html#K5" target="_self">`1</a> </span>)</span>,<font color="Maroon">d</font></span><a href="domain_1.html#K1">]</a></span> <a href="midsp_1.html#K8" target="_self">~</a>  <a href="hidden.html#R1">=</a> <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">p'</font> <a href="midsp_1.html#K5" target="_self">`1</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">q'</font> <a href="midsp_1.html#K6" target="_self">`2</a> </span>)</span></span><a href="domain_1.html#K1">]</a></span> <a href="midsp_1.html#K8" 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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