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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E34">RNG0</font></span>: <a NAME="T37"><span class="comment"><font color="firebrick">:: ASYMPT_3:37</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">c</font>, <font color="Olive" title="b2">s</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="partfun3.html#V1" title="PARTFUN3:attr.1">positive-yielding</a>  <a href="afinsq_1.html#NM2" title="AFINSQ_1:NM.2">XFinSequence</a> of  <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>   ex <font color="Olive" title="b3">d</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="partfun3.html#V1" title="PARTFUN3:attr.1">positive-yielding</a>  <a href="afinsq_1.html#NM2" title="AFINSQ_1:NM.2">XFinSequence</a> of  <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>  ex <font color="Olive" title="b4">N</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> st <br/> for <font color="Olive" title="b5">x</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st <font color="Olive" title="b4">N</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b5">x</font> holds <br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="asympt_3.html#NK1" title="ASYMPT_3:NK.1">polynom</a> <font color="Olive" title="b1">c</font></span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <font color="Olive" title="b5">x</font></span>)</span> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="asympt_3.html#NK1" title="ASYMPT_3:NK.1">polynom</a> <font color="Olive" title="b2">s</font></span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <font color="Olive" title="b5">x</font></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><a href="asympt_3.html#NK1" title="ASYMPT_3:NK.1">polynom</a> <font color="Olive" title="b3">d</font></span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <font color="Olive" title="b5">x</font></div></div>
