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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E15">Th15</font></span>: <a NAME="T15"><span class="comment"><font color="firebrick">:: MIDSP_2:15</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">M</font> being   <a href="midsp_1.html#NM1" title="MIDSP_1:NM.1">MidSp</a> holds <br/> ( (  for <font color="Olive" title="b2">a</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>  holds <br/> ( <font color="Olive" title="b2">a</font> is   <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#K15" title="MIDSP_1:func.15">vectgroup</a> <font color="Olive" title="b1">M</font></span>)</span> iff <font color="Olive" title="b2">a</font> is    <a href="midsp_1.html#M1" title="MIDSP_1:mode.1">Vector</a> of <font color="Olive" title="b1">M</font> ) ) &amp;  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <span class="p1">(<span class="default"><a href="midsp_1.html#K15" title="MIDSP_1:func.15">vectgroup</a> <font color="Olive" title="b1">M</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="midsp_1.html#K6" title="MIDSP_1:func.6">ID</a> <font color="Olive" title="b1">M</font> &amp; (  for <font color="Olive" title="b2">a</font>, <font color="Olive" title="b3">b</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#K15" title="MIDSP_1:func.15">vectgroup</a> <font color="Olive" title="b1">M</font></span>)</span><br/>  for <font color="Olive" title="b4">x</font>, <font color="Olive" title="b5">y</font> being    <a href="midsp_1.html#M1" title="MIDSP_1:mode.1">Vector</a> of <font color="Olive" title="b1">M</font>  st <font color="Olive" title="b2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">x</font> &amp; <font color="Olive" title="b3">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b5">y</font> holds <br/><font color="Olive" title="b2">a</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Olive" title="b3">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">x</font> <a href="midsp_1.html#K7" title="MIDSP_1:func.7">+</a> <font color="Olive" title="b5">y</font> ) )</div></div>
