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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E6">Th01</font></span>: <a NAME="T2"><span class="comment"><font color="firebrick">:: VSDIFF_1:2</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="vectsp_1.html#NM5" title="VECTSP_1:NM.5">Field</a><br/>  for <font color="Olive" title="b3">V</font> being   <a href="vectsp_1.html#NM9" title="VECTSP_1:NM.9">VectSp</a> of <font color="Olive" title="b1">F</font><br/>  for <font color="Olive" title="b4">W</font> being   <a href="vectsp_1.html#NM9" title="VECTSP_1:NM.9">VectSp</a> of <font color="Olive" title="b2">G</font><br/>  for <font color="Olive" title="b5">x</font>, <font color="Olive" title="b6">h</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b3">V</font><br/>  for <font color="Olive" title="b7">f</font> being   <a href="struct_0.html#NM12" title="STRUCT_0:NM.12">PartFunc</a> of <font color="Olive" title="b3">V</font>,<font color="Olive" title="b4">W</font>  st <font color="Olive" title="b5">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Olive" title="b7">f</font> &amp; <font color="Olive" title="b5">x</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Olive" title="b6">h</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Olive" title="b7">f</font> holds <br/><span class="p1">(<span class="default"><a href="vsdiff_1.html#K5" title="VSDIFF_1:func.5">fD</a> (<font color="Olive" title="b7">f</font>,<font color="Olive" title="b6">h</font>)</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Olive" title="b5">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b7">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p2">(<span class="default"><font color="Olive" title="b5">x</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Olive" title="b6">h</font></span>)</span></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p1">(<span class="default"><font color="Olive" title="b7">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Olive" title="b5">x</font></span>)</span></div></div>
