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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E32">Th25</font></span>: <a NAME="T25"><span class="comment"><font color="firebrick">:: E_TRANS1:25</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">N0</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a><br/>  for <font color="Olive" title="b2">L</font> being   <a href="vectsp_2.html#NM1" title="VECTSP_2:NM.1">comRing</a><br/>  for <font color="Olive" title="b3">F</font> being    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="polynom3.html#K12" title="POLYNOM3:func.12">Polynom-Ring</a> <font color="Olive" title="b2">L</font></span>)</span><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="b2">L</font>  st  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b3">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">N0</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 holds <br/> <a href="e_trans1.html#K7" title="E_TRANS1:func.7">eval</a> (<font color="Olive" title="b3">F</font>,<font color="Olive" title="b4">x</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="e_trans1.html#K7" title="E_TRANS1:func.7">eval</a> (<span class="p2">(<span class="default"><font color="Olive" title="b3">F</font> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <font color="Olive" title="b1">N0</font></span>)</span>,<font color="Olive" title="b4">x</font>)</span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="polynom4.html#K2" title="POLYNOM4:func.2">eval</a> (<span class="p3">(<span class="default"><a href="basel_2.html#K2" title="BASEL_2:func.2">~</a> <span class="p4">(<span class="default"><font color="Olive" title="b3">F</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b3">F</font></span>)</span></span>)</span></span>)</span>,<font color="Olive" title="b4">x</font>)</span>)</span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span></div></div>
