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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E42">Th31</font></span>: <a NAME="T31"><span class="comment"><font color="firebrick">:: POLYRED:31</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">n</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</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#V2" title="BAGORDER:attr.2">admissible</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="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="algstr_0.html#L6" title="ALGSTR_0:struct.6">doubleLoopStr</a> <br/>  for <font color="Olive" title="b4">P</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="polynom1.html#K12" title="POLYNOM1:func.12">Polynom-Ring</a> (<font color="Olive" title="b1">n</font>,<font color="Olive" title="b3">L</font>)</span>)</span>  ex <font color="Olive" title="b5">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> st <br/>( <font color="Olive" title="b5">p</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b4">P</font> &amp; (  for <font color="Olive" title="b6">q</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>  st <font color="Olive" title="b6">q</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b4">P</font> holds <br/><font color="Olive" title="b5">p</font> <a href="polyred.html#R1" title="POLYRED:pred.1">&lt;=</a> <font color="Olive" title="b6">q</font>,<font color="Olive" title="b2">T</font> ) )</div></div>
