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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E15">Th15</font></span>: <a NAME="T11"><span class="comment"><font color="firebrick">:: ALGNUM_1:11</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">A</font>, <font color="Olive" title="b2">B</font> being   <a href="vectsp_1.html#NM3" title="VECTSP_1:NM.3">Ring</a><br/>  for <font color="Olive" title="b3">n</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a><br/>  for <font color="Olive" title="b4">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">A</font><br/>  for <font color="Olive" title="b5">p</font> being   <a href="polynom3.html#NM1" title="POLYNOM3:NM.1">Polynomial</a> of <font color="Olive" title="b1">A</font>  st <font color="Olive" title="b1">A</font> is    <a href="c0sp1.html#M1" title="C0SP1:mode.1">Subring</a> of <font color="Olive" title="b2">B</font> holds <br/><span class="p1">(<span class="default"><a href="struct_0.html#K9" title="STRUCT_0:func.9">In</a> (<span class="p2">(<span class="default"><font color="Olive" title="b5">p</font> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <span class="p3">(<span class="default"><font color="Olive" title="b3">n</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span>,<font color="Olive" title="b2">B</font>)</span>)</span> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="group_1.html#K4" title="GROUP_1:func.4">power</a> <font color="Olive" title="b2">B</font></span>)</span> <a href="nat_1.html#K9" title="NAT_1:func.9">.</a> (<span class="p2">(<span class="default"><a href="struct_0.html#K9" title="STRUCT_0:func.9">In</a> (<font color="Olive" title="b4">x</font>,<font color="Olive" title="b2">B</font>)</span>)</span>,<span class="p2">(<span class="default"><font color="Olive" title="b3">n</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K9" title="STRUCT_0:func.9">In</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b5">p</font> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <span class="p3">(<span class="default"><font color="Olive" title="b3">n</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="group_1.html#K4" title="GROUP_1:func.4">power</a> <font color="Olive" title="b1">A</font></span>)</span> <a href="nat_1.html#K9" title="NAT_1:func.9">.</a> (<font color="Olive" title="b4">x</font>,<span class="p3">(<span class="default"><font color="Olive" title="b3">n</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span>)</span>)</span></span>)</span>,<font color="Olive" title="b2">B</font>)</div></div>
