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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E35">Th36</font></span>: <a NAME="T36"><span class="comment"><font color="firebrick">:: EUCLIDLP:36</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">a1</font>, <font color="Olive" title="b2">a2</font>, <font color="Olive" title="b3">b1</font>, <font color="Olive" title="b4">b2</font> being   <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</a><br/>  for <font color="Olive" title="b5">n</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a><br/>  for <font color="Olive" title="b6">y2</font>, <font color="Olive" title="b7">x1</font>, <font color="Olive" title="b8">x2</font>, <font color="Olive" title="b9">y1</font>, <font color="Olive" title="b10">y1</font> being    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of  <a href="euclid.html#K1" title="EUCLID:func.1">REAL</a> <font color="Olive" title="b5">n</font>  st <font color="Olive" title="b10">y1</font>,<font color="Olive" title="b6">y2</font> <a href="euclidlp.html#R3" title="EUCLIDLP:pred.3">are_lindependent2</a>  &amp; <font color="Olive" title="b10">y1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">a1</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Olive" title="b7">x1</font></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">a2</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Olive" title="b8">x2</font></span>)</span> &amp; <font color="Olive" title="b6">y2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">b1</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Olive" title="b7">x1</font></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p1">(<span class="default"><font color="Olive" title="b4">b2</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Olive" title="b8">x2</font></span>)</span> holds <br/> ex <font color="Olive" title="b11">c1</font>, <font color="Olive" title="b12">c2</font>, <font color="Olive" title="b13">d1</font>, <font color="Olive" title="b14">d2</font> being   <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</a> st <br/>( <font color="Olive" title="b7">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b11">c1</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Olive" title="b10">y1</font></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p1">(<span class="default"><font color="Olive" title="b12">c2</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Olive" title="b6">y2</font></span>)</span> &amp; <font color="Olive" title="b8">x2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b13">d1</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Olive" title="b10">y1</font></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p1">(<span class="default"><font color="Olive" title="b14">d2</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Olive" title="b6">y2</font></span>)</span> )</div></div>
