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<b>let </b><font color="Maroon">n</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>let </b><font color="Maroon">RAS</font> be  non <a href="struct_0.html#V3">empty</a> <a href="midsp_1.html#V2">MidSp-like</a>  <a href="midsp_3.html#L1" target="_self">ReperAlgebraStr</a> of <font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 2;<br/><b>let </b><font color="Maroon">a</font> be   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">RAS</font>;<br/><b>let </b><font color="Maroon">b</font> be   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">RAS</font>;<br/><b>let </b><font color="Maroon">p</font> be   <a href="midsp_3.html#NM1">Tuple</a> of <span class="p1">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">RAS</font>;<br/><b>let </b><font color="Maroon">W</font> be   <a href="midsp_2.html#NM1">ATLAS</a> of <font color="Maroon">RAS</font>;<br/><b>let </b><font color="Maroon">v</font> be   <a href="midsp_2.html#NM2">Vector</a> of <font color="Maroon">W</font>;<br/><b>let </b><font color="Maroon">x</font> be   <a href="midsp_3.html#NM3">Tuple</a> of <span class="p1">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">W</font>;<br/>















<b>assume </b><a NAME="E1:39"/><i><font color="Green">E35</font></i>: 
( <font color="Maroon">W</font> <a href="midsp_3.html#K7" target="_self">.</a> <font color="Maroon">a</font>,<font color="Maroon">p</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font> &amp; <font color="Maroon">W</font> <a href="midsp_2.html#K9">.</a> <font color="Maroon">a</font>,<font color="Maroon">b</font> <a href="hidden.html#R1">=</a> <font color="Maroon">v</font> )
 ;<br/>

<a NAME="E2:39"/>
 <a href="midsp_3.html#K8" target="_self">Phi</a> <font color="Maroon">a</font>,<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">W</font> <a href="midsp_2.html#K9">.</a> <font color="Maroon">a</font>,<span class="p1">(<span class="default"><a href="midsp_3.html#K4" target="_self">*'</a> <font color="Maroon">a</font>,<font color="Maroon">p</font></span>)</span>
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E3:39"/>
(  <a href="midsp_3.html#K4" target="_self">*'</a> <font color="Maroon">a</font>,<font color="Maroon">p</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> iff  <a href="midsp_3.html#K8" target="_self">Phi</a> <font color="Maroon">a</font>,<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">v</font> )
 <b>by </b><i>, <a class="ref" href="midsp_2.html#T38">MIDSP_2:38</a></i>;<br/>


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