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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E18">Th20</font></span>: <a NAME="T20"><span class="comment"><font color="firebrick">:: GROEB_2:20</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">n</font> being   <a href="ordinal1.html#NM3" title="ORDINAL1:NM.3">Ordinal</a><br/>  for <font color="Olive" title="b2">T</font> being   <a href="relat_2.html#V6" title="RELAT_2:attr.6">connected</a>  <a href="bagorder.html#NM1" title="BAGORDER:NM.1">TermOrder</a> of <font color="Olive" title="b1">n</font><br/>  for <font color="Olive" title="b3">L</font> being   non  <a href="struct_0.html#V7" title="STRUCT_0:attr.7">trivial</a>   <a href="algstr_0.html#V13" title="ALGSTR_0:attr.13">right_complementable</a>   <a href="algstr_0.html#V33" title="ALGSTR_0:attr.33">almost_left_invertible</a>   <a href="vectsp_1.html#V4" title="VECTSP_1:attr.4">well-unital</a>   <a href="vectsp_1.html#V5" title="VECTSP_1:attr.5">distributive</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="group_1.html#V3" title="GROUP_1:attr.3">associative</a>   <a href="group_1.html#V5" title="GROUP_1:attr.5">commutative</a>   <a href="algstr_0.html#L6" title="ALGSTR_0:struct.6">doubleLoopStr</a> <br/>  for <font color="Olive" title="b4">p</font> being   <a href="polynom1.html#NM2" title="POLYNOM1:NM.2">Polynomial</a> of <font color="Olive" title="b1">n</font>,<font color="Olive" title="b3">L</font> holds <br/> (  <a href="groeb_2.html#K3" title="GROEB_2:func.3">S-Poly</a> (<font color="Olive" title="b4">p</font>,<span class="p1">(<span class="default"><a href="polynom1.html#K8" title="POLYNOM1:func.8">0_</a> (<font color="Olive" title="b1">n</font>,<font color="Olive" title="b3">L</font>)</span>)</span>,<font color="Olive" title="b2">T</font>) <a href="pboole.html#R8" title="PBOOLE:pred.8">=</a>  <a href="polynom1.html#K8" title="POLYNOM1:func.8">0_</a> (<font color="Olive" title="b1">n</font>,<font color="Olive" title="b3">L</font>) &amp;  <a href="groeb_2.html#K3" title="GROEB_2:func.3">S-Poly</a> (<span class="p1">(<span class="default"><a href="polynom1.html#K8" title="POLYNOM1:func.8">0_</a> (<font color="Olive" title="b1">n</font>,<font color="Olive" title="b3">L</font>)</span>)</span>,<font color="Olive" title="b4">p</font>,<font color="Olive" title="b2">T</font>) <a href="pboole.html#R8" title="PBOOLE:pred.8">=</a>  <a href="polynom1.html#K8" title="POLYNOM1:func.8">0_</a> (<font color="Olive" title="b1">n</font>,<font color="Olive" title="b3">L</font>) )</div></div>
