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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E12">LM10</font></span>: <a NAME="T7"><span class="comment"><font color="firebrick">:: PDIFFEQ1:7</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">X</font>, <font color="Olive" title="b2">T</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a><br/>  for <font color="Olive" title="b3">f</font>, <font color="Olive" title="b4">g</font> being   <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>,<a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>  st <font color="Olive" title="b1">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Olive" title="b3">f</font> &amp; <font color="Olive" title="b2">T</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Olive" title="b4">g</font> holds <br/> ex <font color="Olive" title="b5">u</font> being   <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <span class="p1">(<span class="default"><a href="euclid.html#K1" title="EUCLID:func.1">REAL</a> 2</span>)</span>,<a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> st <br/>(  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Olive" title="b5">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"> { <span class="default"> <span class="p2"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Olive" title="b6">x</font>,<font color="Olive" title="b7">t</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span> where <font color="Olive" title="b6">x</font>, <font color="Olive" title="b7">t</font> is   <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</a> : ( <font color="Olive" title="b6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">X</font> &amp; <font color="Olive" title="b7">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b2">T</font> ) </span> } </span>  &amp; (  for <font color="Olive" title="b6">x</font>, <font color="Olive" title="b7">t</font> being   <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</a>  st <font color="Olive" title="b6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">X</font> &amp; <font color="Olive" title="b7">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b2">T</font> holds <br/><font color="Olive" title="b5">u</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Olive" title="b6">x</font>,<font color="Olive" title="b7">t</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Olive" title="b6">x</font></span>)</span> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p1">(<span class="default"><font color="Olive" title="b4">g</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Olive" title="b7">t</font></span>)</span> ) )</div></div>
