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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E23">Th19</font></span>: <a NAME="T19"><span class="comment"><font color="firebrick">:: E_TRANS1:19</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">k</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a><br/>  for <font color="Olive" title="b2">f</font> being    <a href="ring_4.html#M1" title="RING_4:mode.1">Element</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> <a href="int_3.html#K1" title="INT_3:func.1">INT.Ring</a></span>)</span>  st <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ringder1.html#K9" title="RINGDER1:func.9">Der1</a> <a href="int_3.html#K1" title="INT_3:func.1">INT.Ring</a></span>)</span> <a href="vectsp11.html#K1" title="VECTSP11:func.1">|^</a> 1</span>)</span> <a href="ringder1.html#K8" title="RINGDER1:func.8">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">f</font> <a href="binom.html#K2" title="BINOM:func.2">|^</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <span class="p1">(<span class="default"><a href="polynom3.html#K12" title="POLYNOM3:func.12">Polynom-Ring</a> <a href="int_3.html#K1" title="INT_3:func.1">INT.Ring</a></span>)</span> holds <br/> for <font color="Olive" title="b3">j</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b3">j</font> &amp; <font color="Olive" title="b3">j</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b1">k</font> holds <br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ringder1.html#K9" title="RINGDER1:func.9">Der1</a> <a href="int_3.html#K1" title="INT_3:func.1">INT.Ring</a></span>)</span> <a href="vectsp11.html#K1" title="VECTSP11:func.1">|^</a> <font color="Olive" title="b3">j</font></span>)</span> <a href="ringder1.html#K8" title="RINGDER1:func.8">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">f</font> <a href="binom.html#K2" title="BINOM:func.2">|^</a> <font color="Olive" title="b1">k</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="e_trans1.html#K2" title="E_TRANS1:func.2">eta</a> (<font color="Olive" title="b1">k</font>,<font color="Olive" title="b3">j</font>)</span>)</span> <a href="binom.html#K5" title="BINOM:func.5">*</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">f</font> <a href="binom.html#K2" title="BINOM:func.2">|^</a> <span class="p2">(<span class="default"><font color="Olive" title="b1">k</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> <font color="Olive" title="b3">j</font></span>)</span></span>)</span></div></div>
