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<div><span class="kw">theorem </span><a NAME="T84"><span class="comment"><font color="firebrick">:: EUCLIDLP:84</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">n</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a><br/>  for <font color="Olive" title="b2">A</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="euclid.html#K1" title="EUCLID:func.1">REAL</a> <font color="Olive" title="b1">n</font></span>)</span><br/>  for <font color="Olive" title="b3">x</font>, <font color="Olive" title="b4">x1</font>, <font color="Olive" title="b5">x2</font>, <font color="Olive" title="b6">x3</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="b1">n</font>  st <font color="Olive" title="b3">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="euclidlp.html#K4" title="EUCLIDLP:func.4">plane</a> (<font color="Olive" title="b4">x1</font>,<font color="Olive" title="b5">x2</font>,<font color="Olive" title="b6">x3</font>) &amp;  ex <font color="Olive" title="b7">c1</font>, <font color="Olive" title="b8">c2</font>, <font color="Olive" title="b9">c3</font> being   <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</a> st <br/>( <span class="p1">(<span class="default"><font color="Olive" title="b7">c1</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Olive" title="b8">c2</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Olive" title="b9">c3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  &amp; <font color="Olive" title="b3">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b7">c1</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Olive" title="b4">x1</font></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p2">(<span class="default"><font color="Olive" title="b8">c2</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Olive" title="b5">x2</font></span>)</span></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p1">(<span class="default"><font color="Olive" title="b9">c3</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Olive" title="b6">x3</font></span>)</span> ) holds <br/> <a href="euclid.html#K5" title="EUCLID:func.5">0*</a> <font color="Olive" title="b1">n</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="euclidlp.html#K4" title="EUCLIDLP:func.4">plane</a> (<font color="Olive" title="b4">x1</font>,<font color="Olive" title="b5">x2</font>,<font color="Olive" title="b6">x3</font>)</div></div>
