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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">m</font> be    <a href="midsp_3.html#M1" target="_self">Nat</a> of <font color="Maroon">n</font>;<br/><b>let </b><font color="Maroon">RAS</font> be    <a href="midsp_3.html#M2" target="_self">ReperAlgebra</a> of <font color="Maroon">n</font>;<br/>





<b>assume </b><b>that </b><br/><a NAME="E1:54"/><i><font color="Green">E35</font></i>: 
<font color="Maroon">RAS</font> <a href="midsp_3.html#R1" target="_self">has_property_of_zero_in</a> <font color="Maroon">m</font>
 <b>and </b><br/><a NAME="E2:54"/><i><font color="Green">E36</font></i>: 
<font color="Maroon">RAS</font> <a href="midsp_3.html#R3" target="_self">is_additive_in</a> <font color="Maroon">m</font>
 ;<br/>

<b>let </b><font color="Maroon">a</font> be   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">RAS</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="midsp_3.html#D7" target="_self">MIDSP_3:def 7</a><br/><b>let </b><font color="Maroon">pm</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>assume </b><a NAME="E3:54"/><i><font color="Green">E37</font></i>: 
<font color="Maroon">p</font> <a href="midsp_3.html#K5" target="_self">.</a> <font color="Maroon">m</font> <a href="hidden.html#R1">=</a> <font color="Maroon">pm</font>
 ;<br/>

 <a href="midsp_3.html#K4" target="_self">*'</a> <font color="Maroon">a</font>,<span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="midsp_3.html#K1" target="_self">+*</a> <font color="Maroon">m</font>,<span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="midsp_1.html#K4">@</a> <font color="Maroon">pm</font></span>)</span></span>)</span> = 
<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> <a href="midsp_1.html#K4">@</a> <span class="p1">(<span class="default"><a href="midsp_3.html#K4" target="_self">*'</a> <font color="Maroon">a</font>,<span class="p2">(<span class="default"><font color="Maroon">p</font> <a href="midsp_3.html#K1" target="_self">+*</a> <font color="Maroon">m</font>,<font color="Maroon">a</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="midsp_3.html#E3:54"><i><font color="Green">E37</font></i></a>, , </i>
<br/>.= 
<font color="Maroon">a</font> <a href="midsp_1.html#K4">@</a> <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><a class="txt" href="midsp_3.html#E2:54"><i><font color="Green">E36</font></i></a>, </i>
;<br/>
<b>hence </b><a NAME="E5:54"/>
 <a href="midsp_3.html#K4" target="_self">*'</a> <font color="Maroon">a</font>,<span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="midsp_3.html#K1" target="_self">+*</a> <font color="Maroon">m</font>,<span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="midsp_1.html#K4">@</a> <font color="Maroon">pm</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> <a href="midsp_1.html#K4">@</a> <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>
 ;<br/>


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