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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E15">lem9</font></span>: <a NAME="T10"><span class="comment"><font color="firebrick">:: LAGRA4SQ:10</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">x1</font>, <font color="Olive" title="b2">h</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a><br/>  for <font color="Olive" title="b3">y1</font> being   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a>  st 1 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Olive" title="b2">h</font> &amp; <font color="Olive" title="b1">x1</font> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> <font color="Olive" title="b2">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">y1</font> <a href="int_1.html#K5" title="INT_1:func.5">mod</a> <font color="Olive" title="b2">h</font> &amp;  <a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <font color="Olive" title="b2">h</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> 2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Olive" title="b3">y1</font> &amp; <span class="p1">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Olive" title="b3">y1</font></span>)</span> <a href="pepin.html#K1" title="PEPIN:func.1">^2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">h</font> <a href="pepin.html#K1" title="PEPIN:func.1">^2</a>  holds <br/>( 2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Olive" title="b3">y1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">h</font> &amp;  ex <font color="Olive" title="b4">m1</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> st 2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Olive" title="b1">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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="b4">m1</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Olive" title="b2">h</font> )</div></div>
