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<div><span class="kw">theorem </span><a NAME="T31"><span class="comment"><font color="firebrick">:: GROEB_2:31</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">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="b3">f</font>, <font color="Olive" title="b4">g</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="b2">L</font><br/>  for <font color="Olive" title="b5">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="b2">L</font>)</span>)</span><br/>  for <font color="Olive" title="b6">A</font>, <font color="Olive" title="b7">B</font> being    <a href="ideal_1.html#M2" title="IDEAL_1:mode.2">LeftLinearCombination</a> of <font color="Olive" title="b5">P</font>  st <font color="Olive" title="b6">A</font> <a href="groeb_2.html#R2" title="GROEB_2:pred.2">is_MonomialRepresentation_of</a> <font color="Olive" title="b3">f</font> &amp; <font color="Olive" title="b7">B</font> <a href="groeb_2.html#R2" title="GROEB_2:pred.2">is_MonomialRepresentation_of</a> <font color="Olive" title="b4">g</font> holds <br/><font color="Olive" title="b6">A</font> <a href="groeb_2.html#K5" title="GROEB_2:func.5">^</a> <font color="Olive" title="b7">B</font> <a href="groeb_2.html#R2" title="GROEB_2:pred.2">is_MonomialRepresentation_of</a> <font color="Olive" title="b3">f</font> <a href="polynom1.html#K5" title="POLYNOM1:func.5">+</a> <font color="Olive" title="b4">g</font></div></div>
