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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E13">Th12</font></span>: <a NAME="T12"><span class="comment"><font color="firebrick">:: HILBASIS:12</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">X</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <br/>  for <font color="Olive" title="b2">L</font> being   non  <a href="struct_0.html#V7" title="STRUCT_0:attr.7">trivial</a>   <a href="group_1.html#V1" title="GROUP_1:attr.1">unital</a>   <a href="algstr_0.html#L6" title="ALGSTR_0:struct.6">doubleLoopStr</a> <br/>  for <font color="Olive" title="b3">x</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Olive" title="b1">X</font> holds <br/> ( <span class="p1">(<span class="default"><a href="hilbasis.html#K3" title="HILBASIS:func.3">1_1</a> (<font color="Olive" title="b3">x</font>,<font color="Olive" title="b2">L</font>)</span>)</span> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p1">(<span class="default"><a href="hilbasis.html#K2" title="HILBASIS:func.2">UnitBag</a> <font color="Olive" title="b3">x</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="group_1.html#K1" title="GROUP_1:func.1">1_</a> <font color="Olive" title="b2">L</font> &amp; (  for <font color="Olive" title="b4">b</font> being   <a href="pre_poly.html#NM2" title="PRE_POLY:NM.2">bag</a> of <font color="Olive" title="b1">X</font>  st <font color="Olive" title="b4">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="hilbasis.html#K2" title="HILBASIS:func.2">UnitBag</a> <font color="Olive" title="b3">x</font> holds <br/><span class="p1">(<span class="default"><a href="hilbasis.html#K3" title="HILBASIS:func.3">1_1</a> (<font color="Olive" title="b3">x</font>,<font color="Olive" title="b2">L</font>)</span>)</span> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <font color="Olive" title="b4">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Olive" title="b2">L</font> ) )</div></div>
