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<div><span class="kw">theorem </span><a NAME="T10"><span class="comment"><font color="firebrick">:: E_TRANS1:10</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">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="gaussint.html#K11" title="GAUSSINT:func.11">F_Rat</a></span>)</span><br/>  for <font color="Olive" title="b2">i</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> holds <br/> (  <a href="ring_3.html#K9" title="RING_3:func.9">denominator</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">f</font> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <font color="Olive" title="b2">i</font></span>)</span> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="e_trans1.html#K3" title="E_TRANS1:func.3">denomi-set</a> <font color="Olive" title="b1">f</font> &amp;  ex <font color="Olive" title="b3">z</font> being   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a> st <font color="Olive" title="b3">z</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<span class="default"><a href="ring_3.html#K9" title="RING_3:func.9">denominator</a> <span class="p2">(<span class="default"><font color="Olive" title="b1">f</font> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <font color="Olive" title="b2">i</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="wsierp_1.html#K2" title="WSIERP_1:func.2">Product</a> <span class="p1">(<span class="default"><a href="e_trans1.html#K4" title="E_TRANS1:func.4">denomi-seq</a> <font color="Olive" title="b1">f</font></span>)</span> )</div></div>
