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<div><span class="kw">theorem </span><a NAME="T33"><span class="comment"><font color="firebrick">:: RINGDER1:33</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">R</font> being   <a href="vectsp_2.html#NM2" title="VECTSP_2:NM.2">domRing</a><br/>  for <font color="Olive" title="b2">f</font>, <font color="Olive" title="b3">g</font> being   <a href="ring_4.html#V3" title="RING_4:attr.3">constant</a>   <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#K13" title="POLYNOM3:func.13">Polynom-Ring</a> <font color="Olive" title="b1">R</font></span>)</span> holds  <span class="p1">(<span class="default"><a href="ringder1.html#K9" title="RINGDER1:func.9">Der1</a> <font color="Olive" title="b1">R</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="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Olive" title="b3">g</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ringder1.html#K9" title="RINGDER1:func.9">Der1</a> <font color="Olive" title="b1">R</font></span>)</span> <a href="ringder1.html#K8" title="RINGDER1:func.8">.</a> <font color="Olive" title="b2">f</font></span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Olive" title="b3">g</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">f</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ringder1.html#K9" title="RINGDER1:func.9">Der1</a> <font color="Olive" title="b1">R</font></span>)</span> <a href="ringder1.html#K8" title="RINGDER1:func.8">.</a> <font color="Olive" title="b3">g</font></span>)</span></span>)</span></div></div>
