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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E23">Th15</font></span>: <a NAME="T15"><span class="comment"><font color="firebrick">:: LEIBNIZ1:15</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> holds <br/> ( <span class="p1">(<span class="default"><a href="series_1.html#K3" title="SERIES_1:func.3">Partial_Sums</a> <a href="leibniz1.html#K3" title="LEIBNIZ1:func.3">Leibniz_Series</a></span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Olive" title="b1">n</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="series_1.html#K4" title="SERIES_1:func.4">Sum</a> <a href="leibniz1.html#K3" title="LEIBNIZ1:func.3">Leibniz_Series</a> &amp;  <a href="series_1.html#K4" title="SERIES_1:func.4">Sum</a> <a href="leibniz1.html#K3" title="LEIBNIZ1:func.3">Leibniz_Series</a> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><a href="series_1.html#K3" title="SERIES_1:func.3">Partial_Sums</a> <a href="leibniz1.html#K3" title="LEIBNIZ1:func.3">Leibniz_Series</a></span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <span class="p1">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Olive" title="b1">n</font></span>)</span> )</div></div>
