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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E15">Th7</font></span>: <a NAME="T7"><span class="comment"><font color="firebrick">:: POLYRED:7</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#V2" title="STRUCT_0:attr.2">empty</a>   <a href="algstr_0.html#V13" title="ALGSTR_0:attr.13">right_complementable</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">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="b2">L</font><br/>  for <font color="Olive" title="b4">m</font> being   <a href="polynom7.html#NM1" title="POLYNOM7:NM.1">Monomial</a> of <font color="Olive" title="b1">n</font>,<font color="Olive" title="b2">L</font><br/>  for <font color="Olive" title="b5">b</font> being   <a href="pre_poly.html#NM2" title="PRE_POLY:NM.2">bag</a> of <font color="Olive" title="b1">n</font> holds  <span class="p1">(<span class="default"><font color="Olive" title="b4">m</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Olive" title="b3">p</font></span>)</span> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Olive" title="b4">m</font></span>)</span> <a href="pre_poly.html#K11" title="PRE_POLY:func.11">+</a> <font color="Olive" title="b5">b</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b4">m</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p2">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Olive" title="b4">m</font></span>)</span></span>)</span> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">p</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <font color="Olive" title="b5">b</font></span>)</span></div></div>
