<?xml version="1.0"?>
<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E24">Th9</font></span>: <a NAME="T9"><span class="comment"><font color="firebrick">:: E_TRANS2:9</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">f</font>, <font color="Olive" title="b2">g</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"><a href="algseq_1.html#K1" title="ALGSEQ_1:func.1">len</a> <span class="p2">(<span class="default"><a href="basel_2.html#K2" title="BASEL_2:func.2">~</a> <font color="Olive" title="b1">f</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <span class="p1">(<span class="default"><a href="algseq_1.html#K1" title="ALGSEQ_1:func.1">len</a> <span class="p2">(<span class="default"><a href="basel_2.html#K2" title="BASEL_2:func.2">~</a> <font color="Olive" title="b2">g</font></span>)</span></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  holds <br/> <a href="algseq_1.html#K1" title="ALGSEQ_1:func.1">len</a> <span class="p1">(<span class="default"><a href="basel_2.html#K2" title="BASEL_2:func.2">~</a> <span class="p2">(<span class="default"><font color="Olive" title="b1">f</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Olive" title="b2">g</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="algseq_1.html#K1" title="ALGSEQ_1:func.1">len</a> <span class="p3">(<span class="default"><a href="basel_2.html#K2" title="BASEL_2:func.2">~</a> <font color="Olive" title="b1">f</font></span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p2">(<span class="default"><a href="algseq_1.html#K1" title="ALGSEQ_1:func.1">len</a> <span class="p3">(<span class="default"><a href="basel_2.html#K2" title="BASEL_2:func.2">~</a> <font color="Olive" title="b2">g</font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1</div></div>
