<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">M</font> be   <a href="midsp_1.html#NM1">MidSp</a>;<br/><b>let </b><font color="Maroon">W</font> be   <a href="midsp_2.html#NM1">ATLAS</a> of <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">M</font>;<br/><b>let </b><font color="Maroon">c</font> be   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">M</font>;<br/><b>let </b><font color="Maroon">b</font> be   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">M</font>;<br/>









<b>set </b><font color="Maroon">w</font> = the <a href="midsp_2.html#U2" target="_self">function</a> of <font color="Maroon">W</font>;<br/>
<b>set </b><font color="Maroon">G</font> = the <a href="midsp_2.html#U1" target="_self">algebra</a> of <font color="Maroon">W</font>;<br/>
<a NAME="E1:56"/><i><font color="Green">E25</font></i>: 
the <a href="midsp_2.html#U2" target="_self">function</a> of <font color="Maroon">W</font> <a href="midsp_2.html#R2" target="_self">is_atlas_of</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">M</font>,the <a href="midsp_2.html#U1" target="_self">algebra</a> of <font color="Maroon">W</font>
 
<b>by </b><i><a class="ref" href="midsp_2.html#T5" target="_self">Th5</a></i>;<br/>
<a NAME="E2:56"/><i><font color="Green">E38</font></i>: 
<font color="Maroon">M</font>,the <a href="midsp_2.html#U1" target="_self">algebra</a> of <font color="Maroon">W</font> <a href="midsp_2.html#R1" target="_self">are_associated_wrp</a> the <a href="midsp_2.html#U2" target="_self">function</a> of <font color="Maroon">W</font>
 
<b>by </b><i><a class="ref" href="midsp_2.html#T5" target="_self">Th5</a></i>;<br/>
<a NAME="E3:56"/><i><font color="Green">E42</font></i>: 
( the <a href="midsp_2.html#U1" target="_self">algebra</a> of <font color="Maroon">W</font> is <a href="midsp_2.html#V1" target="_self">midpoint_operator</a> &amp; the <a href="midsp_2.html#U1" target="_self">algebra</a> of <font color="Maroon">W</font> is <a href="rlvect_1.html#V4">add-associative</a> &amp; the <a href="midsp_2.html#U1" target="_self">algebra</a> of <font color="Maroon">W</font> is <a href="rlvect_1.html#V5">right_zeroed</a> &amp; the <a href="midsp_2.html#U1" target="_self">algebra</a> of <font color="Maroon">W</font> is <a href="rlvect_1.html#V6">right_complementable</a> &amp; the <a href="midsp_2.html#U1" target="_self">algebra</a> of <font color="Maroon">W</font> is <a href="rlvect_1.html#V3">Abelian</a> )
 
<b>by </b><i><a class="ref" href="midsp_2.html#T5" target="_self">Th5</a></i>;<br/>
<b>thus </b><a NAME="E4:56"/>
( <font color="Maroon">a</font> <a href="midsp_1.html#K4">@</a> <font color="Maroon">c</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> iff <font color="Maroon">W</font> <a href="midsp_2.html#K9" target="_self">.</a> <font color="Maroon">a</font>,<font color="Maroon">c</font> <a href="hidden.html#R1">=</a>  <a href="midsp_2.html#K1" target="_self">Double</a> <span class="p1">(<span class="default"><font color="Maroon">W</font> <a href="midsp_2.html#K9" target="_self">.</a> <font color="Maroon">a</font>,<font color="Maroon">b</font></span>)</span> )
 <b>by </b><i><a class="ref" href="midsp_2.html#T7" target="_self">Th7</a>, <a class="ref" href="midsp_2.html#T8" target="_self">Th8</a>, <a class="txt" href="midsp_2.html#E3:56"><i><font color="Green">E42</font></i></a>, <a class="ref" href="midsp_2.html#T6" target="_self">Th6</a></i>;<br/>


</div>
