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<b>consider </b><font color="Maroon" title="c1">M</font> being   <a href="midsp_1.html#NM1" title="MIDSP_1:NM.1">MidSp</a>;<br/>
<b>set </b><font color="Maroon" title="c2">G</font> =  <a href="midsp_1.html#K18" title="MIDSP_1:func.18">vectgroup</a> <font color="Maroon" title="c1">M</font>;<br/>
<a NAME="E2:23_1_1"/>
( ( for <font color="Olive" title="b1">a</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="midsp_1.html#K18" title="MIDSP_1:func.18">vectgroup</a> <font color="Maroon" title="c1">M</font></span>)</span>  ex <font color="Olive" title="b2">x</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="midsp_1.html#K18" title="MIDSP_1:func.18">vectgroup</a> <font color="Maroon" title="c1">M</font></span>)</span> st  <a href="midsp_2.html#K1" title="MIDSP_2:func.1">Double</a> <font color="Olive" title="b2">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> ) &amp; ( for <font color="Olive" title="b1">a</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="midsp_1.html#K18" title="MIDSP_1:func.18">vectgroup</a> <font color="Maroon" title="c1">M</font></span>)</span>  st  <a href="midsp_2.html#K1" title="MIDSP_2:func.1">Double</a> <font color="Olive" title="b1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">0.</a> <span class="p1">(<span class="default"><a href="midsp_1.html#K18" title="MIDSP_1:func.18">vectgroup</a> <font color="Maroon" title="c1">M</font></span>)</span> holds <br/><font color="Olive" title="b1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">0.</a> <span class="p1">(<span class="default"><a href="midsp_1.html#K18" title="MIDSP_1:func.18">vectgroup</a> <font color="Maroon" title="c1">M</font></span>)</span> ) )
 
<b>by </b><i><a class="txt" href="midsp_2.html#E24"><i><font color="Green" title="E20">Lm2</font></i></a></i>;<br/>
<a NAME="E3:23_1_1"/><b>then </b>
 <a href="midsp_1.html#K18" title="MIDSP_1:func.18">vectgroup</a> <font color="Maroon" title="c1">M</font> is <a href="midsp_2.html#V1" title="MIDSP_2:attr.1">midpoint_operator</a>
 
<b>by </b><i><a class="ref" href="midsp_2.html#D5" target="_self" title="MIDSP_2:def.5">Def5</a></i>;<br/>
<b>hence </b><a NAME="E4:23_1_1"/>
 ex <font color="Olive">b<sub>1</sub></font> being non <a href="struct_0.html#V3" title="STRUCT_0:attr.3">empty</a>  <a href="rlvect_1.html#L1" title="RLVECT_1:struct.1">LoopStr</a>  st <br/>( <font color="Olive">b<sub>1</sub></font> is <a href="rlvect_1.html#V1" title="RLVECT_1:attr.1">strict</a> &amp; <font color="Olive">b<sub>1</sub></font> is <a href="midsp_2.html#V1" title="MIDSP_2:attr.1">midpoint_operator</a> &amp; <font color="Olive">b<sub>1</sub></font> is <a href="rlvect_1.html#V4" title="RLVECT_1:attr.4">add-associative</a> &amp; <font color="Olive">b<sub>1</sub></font> is <a href="rlvect_1.html#V5" title="RLVECT_1:attr.5">right_zeroed</a> &amp; <font color="Olive">b<sub>1</sub></font> is <a href="rlvect_1.html#V6" title="RLVECT_1:attr.6">right_complementable</a> &amp; <font color="Olive">b<sub>1</sub></font> is <a href="rlvect_1.html#V3" title="RLVECT_1:attr.3">Abelian</a> )
 ;<br/>


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