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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E3">Th1</font></span>: <a NAME="T1"><span class="comment"><font color="firebrick">:: EUCLID12:1</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">lambda</font>, <font color="Olive" title="b3">mu</font> being   <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</a><br/>  for <font color="Olive" title="b4">x1</font>, <font color="Olive" title="b5">x2</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><br/>  for <font color="Olive" title="b6">An</font>, <font color="Olive" title="b7">Bn</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> <font color="Olive" title="b1">n</font></span>)</span>  st <font color="Olive" title="b6">An</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Olive" title="b2">lambda</font></span>)</span> <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="p1">(<span class="default"><font color="Olive" title="b2">lambda</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Olive" title="b5">x2</font></span>)</span> &amp; <font color="Olive" title="b7">Bn</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Olive" title="b3">mu</font></span>)</span> <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="p1">(<span class="default"><font color="Olive" title="b3">mu</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Olive" title="b5">x2</font></span>)</span> holds <br/><font color="Olive" title="b7">Bn</font> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <font color="Olive" title="b6">An</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">mu</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Olive" title="b2">lambda</font></span>)</span> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <span class="p1">(<span class="default"><font color="Olive" title="b5">x2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Olive" title="b4">x1</font></span>)</span></div></div>
