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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E9">Th12</font></span>: <a NAME="T12"><span class="comment"><font color="firebrick">:: NUMBER16:12</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">i</font>, <font color="Olive" title="b2">j</font>, <font color="Olive" title="b3">k</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Olive" title="b2">j</font> &amp; <font color="Olive" title="b3">k</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Olive" title="b1">i</font> &amp; (  for <font color="Olive" title="b4">x</font>, <font color="Olive" title="b5">y</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st <font color="Olive" title="b4">x</font>,<font color="Olive" title="b5">y</font> <a href="int_1.html#R2" title="INT_1:pred.2">are_congruent_mod</a> <font color="Olive" title="b2">j</font> holds <br/> <a href="pre_ff.html#K2" title="PRE_FF:func.2">Fib</a> <font color="Olive" title="b4">x</font>, <a href="pre_ff.html#K2" title="PRE_FF:func.2">Fib</a> <font color="Olive" title="b5">y</font> <a href="int_1.html#R2" title="INT_1:pred.2">are_congruent_mod</a> <font color="Olive" title="b1">i</font> ) &amp; (  for <font color="Olive" title="b4">x</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st <font color="Olive" title="b4">x</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Olive" title="b2">j</font> holds <br/><span class="p1">(<span class="default"><a href="pre_ff.html#K2" title="PRE_FF:func.2">Fib</a> <font color="Olive" title="b4">x</font></span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> <font color="Olive" title="b1">i</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b3">k</font> ) holds <br/> for <font color="Olive" title="b4">m</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  holds  not <span class="p1">(<span class="default"><a href="number06.html#K1" title="NUMBER06:func.1">ArProg</a> (<font color="Olive" title="b3">k</font>,<font color="Olive" title="b1">i</font>)</span>)</span> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Olive" title="b4">m</font> is  <a href="number06.html#V3" title="NUMBER06:attr.3">Fibonacci</a> </div></div>
