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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E19">Th19</font></span>: <a NAME="T19"><span class="comment"><font color="firebrick">:: RINGDER1:19</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">R</font> being   non  <a href="struct_0.html#V6" title="STRUCT_0:attr.6">degenerated</a>  <a href="vectsp_2.html#NM1" title="VECTSP_2:NM.1">comRing</a><br/>  for <font color="Olive" title="b2">n</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a><br/>  for <font color="Olive" title="b3">x</font>, <font color="Olive" title="b4">y</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">R</font><br/>  for <font color="Olive" title="b5">D</font> being   <a href="ringder1.html#NM1" title="RINGDER1:NM.1">Derivation</a> of <font color="Olive" title="b1">R</font> holds   <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">Sum</a> <span class="p1">(<span class="default"><a href="ringder1.html#K5" title="RINGDER1:func.5">LBZ0</a> (<font color="Olive" title="b5">D</font>,<font color="Olive" title="b2">n</font>,<font color="Olive" title="b3">x</font>,<font color="Olive" title="b4">y</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K4" title="RLVECT_1:func.4">Sum</a> <span class="p2">(<span class="default"><a href="ringder1.html#K6" title="RINGDER1:func.6">LBZ1</a> (<font color="Olive" title="b5">D</font>,<font color="Olive" title="b2">n</font>,<font color="Olive" title="b3">x</font>,<font color="Olive" title="b4">y</font>)</span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K4" title="RLVECT_1:func.4">Sum</a> <span class="p2">(<span class="default"><a href="ringder1.html#K7" title="RINGDER1:func.7">LBZ2</a> (<font color="Olive" title="b5">D</font>,<font color="Olive" title="b2">n</font>,<font color="Olive" title="b3">x</font>,<font color="Olive" title="b4">y</font>)</span>)</span></span>)</span></div></div>
