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<b>let </b><font color="Maroon" title="c1">n</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/><b>let </b><font color="Maroon" title="c2">RAS</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="midsp_1.html#V2" title="MIDSP_1:attr.2">MidSp-like</a>  <a href="midsp_3.html#L1" title="MIDSP_3:struct.1">ReperAlgebraStr</a> of <font color="Maroon" title="c1">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2;<br/><b>let </b><font color="Maroon" title="c3">a</font>, <font color="Maroon" title="c4">b</font> be   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c2">RAS</font>;<br/><b>let </b><font color="Maroon" title="c5">p</font> be   <a href="midsp_3.html#NM1" title="MIDSP_3:NM.1">Tuple</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>,<font color="Maroon" title="c2">RAS</font>;<br/><b>let </b><font color="Maroon" title="c6">W</font> be   <a href="midsp_2.html#NM1" title="MIDSP_2:NM.1">ATLAS</a> of <font color="Maroon" title="c2">RAS</font>;<br/><b>let </b><font color="Maroon" title="c7">v</font> be   <a href="midsp_2.html#NM2" title="MIDSP_2:NM.2">Vector</a> of <font color="Maroon" title="c6">W</font>;<br/><b>let </b><font color="Maroon" title="c8">x</font> be   <a href="midsp_3.html#NM3" title="MIDSP_3:NM.3">Tuple</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>,<font color="Maroon" title="c6">W</font>;<br/>















<b>assume </b><a NAME="E1:39"/><i><font color="Green" title="E22">A1</font></i>: 
( <font color="Maroon" title="c6">W</font> <a href="midsp_3.html#K7" title="MIDSP_3:func.7">.</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c5">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">x</font> &amp; <font color="Maroon" title="c6">W</font> <a href="midsp_2.html#K9" title="MIDSP_2:func.9">.</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">v</font> )
 ;<br/>

<a NAME="E2:39"/><b>then </b>
 <a href="midsp_3.html#K8" title="MIDSP_3:func.8">Phi</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c8">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">W</font> <a href="midsp_2.html#K9" title="MIDSP_2:func.9">.</a> <font color="Maroon" title="c3">a</font>,<span class="p1">(<span class="default"><a href="midsp_3.html#K4" title="MIDSP_3:func.4">*'</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c5">p</font></span>)</span>
 
<b>by </b><i><a class="ref" href="midsp_3.html#T17" target="_self" title="MIDSP_3:th.17">Th17</a></i>;<br/>
<b>hence </b><a NAME="E3:39"/>
(  <a href="midsp_3.html#K4" title="MIDSP_3:func.4">*'</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c5">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> iff  <a href="midsp_3.html#K8" title="MIDSP_3:func.8">Phi</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c8">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">v</font> )
 <b>by </b><i><a class="txt" href="midsp_3.html#E1:39"><i><font color="Green" title="E22">A1</font></i></a>, <a class="ref" href="midsp_2.html#T38" title="MIDSP_2:th.38">MIDSP_2:38</a></i>;<br/>


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