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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E8">Th11</font></span>: <a NAME="T11"><span class="comment"><font color="firebrick">:: NUMBER16:11</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">n</font>, <font color="Olive" title="b2">i</font>, <font color="Olive" title="b3">j</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st  <a href="pre_ff.html#K2" title="PRE_FF:func.2">Fib</a> <font color="Olive" title="b1">n</font>, <a href="pre_ff.html#K2" title="PRE_FF:func.2">Fib</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">n</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Olive" title="b2">i</font></span>)</span> <a href="int_1.html#R2" title="INT_1:pred.2">are_congruent_mod</a> <font color="Olive" title="b3">j</font> &amp;  <a href="pre_ff.html#K2" title="PRE_FF:func.2">Fib</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>, <a href="pre_ff.html#K2" title="PRE_FF:func.2">Fib</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b1">n</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Olive" title="b2">i</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="int_1.html#R2" title="INT_1:pred.2">are_congruent_mod</a> <font color="Olive" title="b3">j</font> holds <br/> 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">i</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="b3">j</font></div></div>
