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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E40">Th47</font></span>: <a NAME="T49"><span class="comment"><font color="firebrick">:: NIVEN:49</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">L</font> being   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="algstr_0.html#V13" title="ALGSTR_0:attr.13">right_complementable</a>   <a href="rlvect_1.html#V2" title="RLVECT_1:attr.2">Abelian</a>   <a href="rlvect_1.html#V3" title="RLVECT_1:attr.3">add-associative</a>   <a href="rlvect_1.html#V4" title="RLVECT_1:attr.4">right_zeroed</a>   <a href="vectsp_1.html#V5" title="VECTSP_1:attr.5">distributive</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="b2">z1</font>, <font color="Olive" title="b3">z2</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">L</font><br/>  for <font color="Olive" title="b4">p</font> being   <a href="polynom3.html#NM1" title="POLYNOM3:NM.1">Polynomial</a> of <font color="Olive" title="b1">L</font>  st  <a href="polynom4.html#K2" title="POLYNOM4:func.2">eval</a> (<font color="Olive" title="b4">p</font>,<font color="Olive" title="b2">z1</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">z2</font> holds <br/> <a href="polynom4.html#K2" title="POLYNOM4:func.2">eval</a> (<span class="p1">(<span class="default"><font color="Olive" title="b4">p</font> <a href="normsp_1.html#K2" title="NORMSP_1:func.2">-</a> <span class="p2"><a href="algseq_1.html#K2" title="ALGSEQ_1:func.2">&lt;%</a><span class="default"><font color="Olive" title="b3">z2</font></span><a href="algseq_1.html#K2" title="ALGSEQ_1:func.2">%&gt;</a></span></span>)</span>,<font color="Olive" title="b2">z1</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="b1">L</font></div></div>
