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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E8">Th0X</font></span>: <a NAME="T8"><span class="comment"><font color="firebrick">:: NDIFF_9:8</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">E</font>, <font color="Olive" title="b2">F</font>, <font color="Olive" title="b3">G</font> being   <a href="normsp_1.html#NM1" title="NORMSP_1:NM.1">RealNormSpace</a><br/>  for <font color="Olive" title="b4">L</font> being   <a href="lopban_1.html#NM1" title="LOPBAN_1:NM.1">LinearOperator</a> of <span class="p1"><a href="prvect_3.html#K9" title="PRVECT_3:func.9">[:</a><span class="default"><font color="Olive" title="b1">E</font>,<font color="Olive" title="b2">F</font></span><a href="prvect_3.html#K9" title="PRVECT_3:func.9">:]</a></span>,<font color="Olive" title="b3">G</font><br/>  for <font color="Olive" title="b5">L11</font> being   <a href="lopban_1.html#NM1" title="LOPBAN_1:NM.1">LinearOperator</a> of <font color="Olive" title="b1">E</font>,<font color="Olive" title="b3">G</font><br/>  for <font color="Olive" title="b6">L12</font> being   <a href="lopban_1.html#NM1" title="LOPBAN_1:NM.1">LinearOperator</a> of <font color="Olive" title="b2">F</font>,<font color="Olive" title="b3">G</font><br/>  for <font color="Olive" title="b7">L21</font> being   <a href="lopban_1.html#NM1" title="LOPBAN_1:NM.1">LinearOperator</a> of <font color="Olive" title="b1">E</font>,<font color="Olive" title="b3">G</font><br/>  for <font color="Olive" title="b8">L22</font> being   <a href="lopban_1.html#NM1" title="LOPBAN_1:NM.1">LinearOperator</a> of <font color="Olive" title="b2">F</font>,<font color="Olive" title="b3">G</font>  st (  for <font color="Olive" title="b9">x</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Olive" title="b1">E</font><br/>  for <font color="Olive" title="b10">y</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Olive" title="b2">F</font> holds  <font color="Olive" title="b4">L</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1"><a href="prvect_3.html#K10" title="PRVECT_3:func.10">[</a><span class="default"><font color="Olive" title="b9">x</font>,<font color="Olive" title="b10">y</font></span><a href="prvect_3.html#K10" title="PRVECT_3:func.10">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b5">L11</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b9">x</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="b6">L12</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b10">y</font></span>)</span> ) &amp; (  for <font color="Olive" title="b9">x</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Olive" title="b1">E</font><br/>  for <font color="Olive" title="b10">y</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Olive" title="b2">F</font> holds  <font color="Olive" title="b4">L</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1"><a href="prvect_3.html#K10" title="PRVECT_3:func.10">[</a><span class="default"><font color="Olive" title="b9">x</font>,<font color="Olive" title="b10">y</font></span><a href="prvect_3.html#K10" title="PRVECT_3:func.10">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b7">L21</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b9">x</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="b8">L22</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b10">y</font></span>)</span> ) holds <br/>( <font color="Olive" title="b5">L11</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Olive" title="b7">L21</font> &amp; <font color="Olive" title="b6">L12</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Olive" title="b8">L22</font> )</div></div>
