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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E18">Th18</font></span>: <a NAME="T18"><span class="comment"><font color="firebrick">:: HILB10_2:18</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">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="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#V4" title="VECTSP_1:attr.4">well-unital</a>   <a href="vectsp_1.html#V5" title="VECTSP_1:attr.5">distributive</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">x</font> being   <a href="struct_0.html#NM5" title="STRUCT_0:NM.5">Function</a> of <font color="Olive" title="b1">n</font>,<font color="Olive" title="b2">L</font><br/>  for <font color="Olive" title="b5">y</font> being   <a href="struct_0.html#NM5" title="STRUCT_0:NM.5">Function</a> of <span class="p1">(<span class="default"><font color="Olive" title="b1">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>,<font color="Olive" title="b2">L</font>  st <font color="Olive" title="b5">y</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Olive" title="b1">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">x</font> holds <br/> <a href="polynom2.html#K2" title="POLYNOM2:func.2">eval</a> (<font color="Olive" title="b3">p</font>,<font color="Olive" title="b4">x</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="polynom2.html#K2" title="POLYNOM2:func.2">eval</a> (<span class="p1">(<span class="default"><font color="Olive" title="b3">p</font> <a href="hilb10_2.html#K3" title="HILB10_2:func.3">extended_by_0</a></span>)</span>,<font color="Olive" title="b5">y</font>)</div></div>
