<?xml version="1.0"?>
<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E46">Th33</font></span>: <a NAME="T33"><span class="comment"><font color="firebrick">:: IDEA_1:33</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">n</font> being   non  <a href="ordinal1.html#V8" title="ORDINAL1:attr.8">zero</a>  <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a><br/>  for <font color="Olive" title="b2">m</font>, <font color="Olive" title="b3">k1</font>, <font color="Olive" title="b4">k2</font> being    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>   st <span class="p1">(<span class="default">2 <a href="series_1.html#K5" title="SERIES_1:func.5">to_power</a> <font color="Olive" title="b1">n</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 is  <a href="int_2.html#V1" title="INT_2:attr.1">prime</a>  &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b2">m</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 4 &amp; <font color="Olive" title="b2">m</font> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> 1 <a href="idea_1.html#R1" title="IDEA_1:pred.1">is_expressible_by</a> <font color="Olive" title="b1">n</font> &amp; <font color="Olive" title="b2">m</font> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> 2 <a href="idea_1.html#R1" title="IDEA_1:pred.1">is_expressible_by</a> <font color="Olive" title="b1">n</font> &amp; <font color="Olive" title="b2">m</font> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> 3 <a href="idea_1.html#R1" title="IDEA_1:pred.1">is_expressible_by</a> <font color="Olive" title="b1">n</font> &amp; <font color="Olive" title="b2">m</font> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> 4 <a href="idea_1.html#R1" title="IDEA_1:pred.1">is_expressible_by</a> <font color="Olive" title="b1">n</font> &amp; <font color="Olive" title="b3">k1</font> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> 1 <a href="idea_1.html#R1" title="IDEA_1:pred.1">is_expressible_by</a> <font color="Olive" title="b1">n</font> &amp; <font color="Olive" title="b3">k1</font> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> 2 <a href="idea_1.html#R1" title="IDEA_1:pred.1">is_expressible_by</a> <font color="Olive" title="b1">n</font> &amp; <font color="Olive" title="b3">k1</font> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> 3 <a href="idea_1.html#R1" title="IDEA_1:pred.1">is_expressible_by</a> <font color="Olive" title="b1">n</font> &amp; <font color="Olive" title="b3">k1</font> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> 4 <a href="idea_1.html#R1" title="IDEA_1:pred.1">is_expressible_by</a> <font color="Olive" title="b1">n</font> &amp; <font color="Olive" title="b4">k2</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="idea_1.html#K10" title="IDEA_1:func.10">INV_MOD</a> (<span class="p1">(<span class="default"><font color="Olive" title="b3">k1</font> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> 1</span>)</span>,<font color="Olive" title="b1">n</font>) &amp; <font color="Olive" title="b4">k2</font> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> 2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="idea_1.html#K6" title="IDEA_1:func.6">NEG_MOD</a> (<span class="p1">(<span class="default"><font color="Olive" title="b3">k1</font> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> 3</span>)</span>,<font color="Olive" title="b1">n</font>) &amp; <font color="Olive" title="b4">k2</font> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> 3 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="idea_1.html#K6" title="IDEA_1:func.6">NEG_MOD</a> (<span class="p1">(<span class="default"><font color="Olive" title="b3">k1</font> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> 2</span>)</span>,<font color="Olive" title="b1">n</font>) &amp; <font color="Olive" title="b4">k2</font> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> 4 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="idea_1.html#K10" title="IDEA_1:func.10">INV_MOD</a> (<span class="p1">(<span class="default"><font color="Olive" title="b3">k1</font> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> 4</span>)</span>,<font color="Olive" title="b1">n</font>) &amp; <font color="Olive" title="b4">k2</font> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> 5 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">k1</font> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> 5 &amp; <font color="Olive" title="b4">k2</font> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> 6 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">k1</font> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> 6 holds <br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="idea_1.html#K16" title="IDEA_1:func.16">IDEA_Q</a> (<font color="Olive" title="b4">k2</font>,<font color="Olive" title="b1">n</font>)</span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <span class="p2">(<span class="default"><a href="idea_1.html#K15" title="IDEA_1:func.15">IDEA_P</a> (<font color="Olive" title="b3">k1</font>,<font color="Olive" title="b1">n</font>)</span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b2">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">m</font></div></div>
