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<div>:: <span class="kw">deftheorem </span><span class="lab"><font color="Green" title="E17">Def9</font></span>   defines <a href="radix_2.html#K9" title="RADIX_2:func.9">Pow_mod</a> <a onclick="hs(this)" href="javascript:()">RADIX_2:def 9 : <br/></a><span> for <font color="Olive" title="b1">k</font>, <font color="Olive" title="b2">f</font>, <font color="Olive" title="b3">m</font>, <font color="Olive" title="b4">n</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a><br/>  for <font color="Olive" title="b5">e</font> being   <a href="finseq_2.html#NM3" title="FINSEQ_2:NM.3">Tuple</a> of <font color="Olive" title="b4">n</font>, <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>   st <font color="Olive" title="b4">n</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 1 holds <br/> for <font color="Olive">b<sub>6</sub></font> being   <a href="finseq_2.html#NM3" title="FINSEQ_2:NM.3">Tuple</a> of <font color="Olive" title="b4">n</font>, <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>  holds <br/> ( <font color="Olive">b<sub>6</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="radix_2.html#K9" title="RADIX_2:func.9">Pow_mod</a> (<font color="Olive" title="b3">m</font>,<font color="Olive" title="b5">e</font>,<font color="Olive" title="b2">f</font>,<font color="Olive" title="b1">k</font>) iff ( <font color="Olive">b<sub>6</sub></font> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="radix_2.html#K8" title="RADIX_2:func.8">Table2</a> (<font color="Olive" title="b3">m</font>,<font color="Olive" title="b5">e</font>,<font color="Olive" title="b2">f</font>,<font color="Olive" title="b4">n</font>) &amp; (  for <font color="Olive" title="b7">i</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b7">i</font> &amp; <font color="Olive" title="b7">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b4">n</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1 holds <br/> ex <font color="Olive" title="b8">i1</font>, <font color="Olive" title="b9">i2</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> st <br/>( <font color="Olive" title="b8">i1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive">b<sub>6</sub></font> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Olive" title="b7">i</font> &amp; <font color="Olive" title="b9">i2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive">b<sub>6</sub></font> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b7">i</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> &amp; <font color="Olive" title="b9">i2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Olive" title="b8">i1</font> <a href="newton.html#K1" title="NEWTON:func.1">|^</a> <span class="p4">(<span class="default"><a href="radix_1.html#K1" title="RADIX_1:func.1">Radix</a> <font color="Olive" title="b1">k</font></span>)</span></span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> <font color="Olive" title="b2">f</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <span class="p2">(<span class="default"><a href="radix_2.html#K8" title="RADIX_2:func.8">Table2</a> (<font color="Olive" title="b3">m</font>,<font color="Olive" title="b5">e</font>,<font color="Olive" title="b2">f</font>,<span class="p3">(<span class="default"><font color="Olive" title="b4">n</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> <font color="Olive" title="b7">i</font></span>)</span>)</span>)</span></span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> <font color="Olive" title="b2">f</font> ) ) ) );<br/></span></div>
