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<div><span class="kw">theorem </span><a NAME="T38"><span class="comment"><font color="firebrick">:: RINGDER1:38</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">R</font> being   <a href="vectsp_2.html#NM2" title="VECTSP_2:NM.2">domRing</a><br/>  for <font color="Olive" title="b3">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="polynom3.html#K13" title="POLYNOM3:func.13">Polynom-Ring</a> <font color="Olive" title="b2">R</font></span>)</span>  st <font color="Olive" title="b3">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="field_1.html#NK3" title="FIELD_1:NK.3">anpoly</a> (<span class="p1">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Olive" title="b2">R</font></span>)</span>,1) holds <br/> ex <font color="Olive" title="b4">y</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="polynom3.html#K13" title="POLYNOM3:func.13">Polynom-Ring</a> <font color="Olive" title="b2">R</font></span>)</span> st <br/>( <font color="Olive" title="b4">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="field_1.html#NK3" title="FIELD_1:NK.3">anpoly</a> (<span class="p1">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Olive" title="b2">R</font></span>)</span>,<font color="Olive" title="b1">n</font>) &amp; <span class="p1">(<span class="default"><a href="ringder1.html#K9" title="RINGDER1:func.9">Der1</a> <font color="Olive" title="b2">R</font></span>)</span> <a href="ringder1.html#K8" title="RINGDER1:func.8">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">x</font> <a href="binom.html#K2" title="BINOM:func.2">|^</a> <span class="p2">(<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></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <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> <a href="binom.html#K5" title="BINOM:func.5">*</a> <font color="Olive" title="b4">y</font> )</div></div>
