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









<b>given </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>, <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><a NAME="E1:45"/><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>and </b><br/><a NAME="E2:45"/><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>and </b><br/><a NAME="E3:45"/><i><font color="Green">E63</font></i>: 
<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>and </b><br/><a NAME="E4:45"/><i><font color="Green">E76</font></i>: 
<font color="Maroon">w</font> <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> 
 ;<br/>

<b>given </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>, <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><a NAME="E5:45"/><i><font color="Green">E77</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>and </b><br/><a NAME="E6:45"/><i><font color="Green">E78</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>and </b><br/><a NAME="E7:45"/><i><font color="Green">E79</font></i>: 
<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>and </b><br/><a NAME="E8:45"/><i><font color="Green">E80</font></i>: 
<font color="Maroon">w'</font> <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> 
 ;<br/>

<a NAME="E9:45"/>
<font color="Maroon">p</font> <a href="midsp_1.html#R2" target="_self">##</a> <font color="Maroon">p'</font>
 
<b>by </b><i>, <a class="ref" href="midsp_1.html#T16" target="_self">Th16</a>, </i>;<br/>
<a NAME="E10:45"/><b>then </b><i><font color="Green">E81</font></i>: 
<font color="Maroon">p</font> <a href="midsp_1.html#K5" target="_self">`1</a> ,<font color="Maroon">p</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#K5" target="_self">`1</a> ,<font color="Maroon">p'</font> <a href="midsp_1.html#K6" target="_self">`2</a> 
 
<b>by </b><i/>;<br/>
<a NAME="E11:45"/>
<font color="Maroon">q</font> <a href="midsp_1.html#R2" target="_self">##</a> <font color="Maroon">q'</font>
 
<b>by </b><i>, <a class="ref" href="midsp_1.html#T17" target="_self">Th17</a>, </i>;<br/>
<a NAME="E12:45"/><b>then </b>
<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">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> 
 
<b>by </b><i/>;<br/>
<a NAME="E13:45"/><b>then </b>
<font color="Maroon">p</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#K5" target="_self">`1</a> ,<font color="Maroon">q'</font> <a href="midsp_1.html#K6" target="_self">`2</a> 
 
<b>by </b><i>, <a class="txt" href="midsp_1.html#E1:45"><i><font color="Green">E37</font></i></a>, <a class="ref" href="midsp_1.html#T18" target="_self">Th18</a>, </i>;<br/>
<a NAME="E14:45"/><b>then </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>,<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#R2" target="_self">##</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>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E15:45"/>
<font color="Maroon">w</font> <a href="hidden.html#R1">=</a> <font color="Maroon">w'</font>
 <b>by </b><i><a class="ref" href="midsp_1.html#T15" target="_self">Th15</a>, <a class="txt" href="midsp_1.html#E2:45"><i><font color="Green">E38</font></i></a>, </i>;<br/>


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