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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E11">Lemma2To57</font></span>: <a NAME="T17"><span class="comment"><font color="firebrick">:: NUMBER12:17</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being   <a href="xxreal_0.html#V2" title="XXREAL_0:attr.2">positive</a>  <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a><br/>  for <font color="Olive" title="b3">k</font>, <font color="Olive" title="b4">x</font>, <font color="Olive" title="b5">m</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st <span class="p1">(<span class="default"><a href="number06.html#K1" title="NUMBER06:func.1">ArProg</a> (<font color="Olive" title="b2">b</font>,<font color="Olive" title="b1">a</font>)</span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <font color="Olive" title="b3">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">x</font> <a href="pepin.html#K1" title="PEPIN:func.1">^2</a>  holds <br/><span class="p1">(<span class="default"><a href="number06.html#K1" title="NUMBER06:func.1">ArProg</a> (<font color="Olive" title="b2">b</font>,<font color="Olive" title="b1">a</font>)</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"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Olive" title="b5">m</font> <a href="pepin.html#K1" title="PEPIN:func.1">^2</a></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Olive" title="b1">a</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Olive" title="b5">m</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Olive" title="b4">x</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Olive" title="b3">k</font></span>)</span> is  <a href="pythtrip.html#V1" title="PYTHTRIP:attr.1">square</a> </div></div>
