<?xml version="1.0"?>
<div>:: <span class="kw">deftheorem </span><span class="lab"><font color="Green" title="E32">Def12</font></span>   defines <a href="midsp_2.html#V4" title="MIDSP_2:attr.4">ATLAS-like</a> <a onclick="hs(this)" href="javascript:()">MIDSP_2:def 12 : <br/></a><span> for <font color="Olive" title="b1">M</font> being   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="midsp_1.html#L1" title="MIDSP_1:struct.1">MidStr</a> <br/>  for <font color="Olive" title="b2">IT</font> being    <a href="midsp_2.html#L1" title="MIDSP_2:struct.1">AtlasStr</a> over <font color="Olive" title="b1">M</font> holds <br/> ( <font color="Olive" title="b2">IT</font> is  <a href="midsp_2.html#V4" title="MIDSP_2:attr.4">ATLAS-like</a>  iff (  the <a href="midsp_2.html#U1" title="MIDSP_2:sel.1">algebra</a> of <font color="Olive" title="b2">IT</font> is  <a href="midsp_2.html#V2" title="MIDSP_2:attr.2">midpoint_operator</a>  &amp;  the <a href="midsp_2.html#U1" title="MIDSP_2:sel.1">algebra</a> of <font color="Olive" title="b2">IT</font> is  <a href="rlvect_1.html#V3" title="RLVECT_1:attr.3">add-associative</a>  &amp;  the <a href="midsp_2.html#U1" title="MIDSP_2:sel.1">algebra</a> of <font color="Olive" title="b2">IT</font> is  <a href="rlvect_1.html#V4" title="RLVECT_1:attr.4">right_zeroed</a>  &amp;  the <a href="midsp_2.html#U1" title="MIDSP_2:sel.1">algebra</a> of <font color="Olive" title="b2">IT</font> is  <a href="algstr_0.html#V13" title="ALGSTR_0:attr.13">right_complementable</a>  &amp;  the <a href="midsp_2.html#U1" title="MIDSP_2:sel.1">algebra</a> of <font color="Olive" title="b2">IT</font> is  <a href="rlvect_1.html#V2" title="RLVECT_1:attr.2">Abelian</a>  &amp;  the <a href="midsp_2.html#U2" title="MIDSP_2:sel.2">function</a> of <font color="Olive" title="b2">IT</font> is  <a href="midsp_2.html#V1" title="MIDSP_2:attr.1">associating</a>  &amp;  the <a href="midsp_2.html#U2" title="MIDSP_2:sel.2">function</a> of <font color="Olive" title="b2">IT</font> <a href="midsp_2.html#R1" title="MIDSP_2:pred.1">is_atlas_of</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b1">M</font>, the <a href="midsp_2.html#U1" title="MIDSP_2:sel.1">algebra</a> of <font color="Olive" title="b2">IT</font> ) );<br/></span></div>
