<?xml version="1.0"?>
<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E34">Th27</font></span>: <a NAME="T27"><span class="comment"><font color="firebrick">:: E_TRANS1:27</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">p</font>, <font color="Olive" title="b2">q</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> holds <br/> (  <a href="e_trans1.html#K5" title="E_TRANS1:func.5">^</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">p</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Olive" title="b2">q</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="e_trans1.html#K5" title="E_TRANS1:func.5">^</a> <font color="Olive" title="b1">p</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><a href="e_trans1.html#K5" title="E_TRANS1:func.5">^</a> <font color="Olive" title="b2">q</font></span>)</span> &amp;  <a href="e_trans1.html#K5" title="E_TRANS1:func.5">^</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">p</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Olive" title="b2">q</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="e_trans1.html#K5" title="E_TRANS1:func.5">^</a> <font color="Olive" title="b1">p</font></span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p1">(<span class="default"><a href="e_trans1.html#K5" title="E_TRANS1:func.5">^</a> <font color="Olive" title="b2">q</font></span>)</span> )</div></div>
