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<div><span class="kw">theorem </span><a NAME="T30"><span class="comment"><font color="firebrick">:: BCIALG_6:30</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">X</font> being   <a href="bcialg_1.html#NM1" title="BCIALG_1:NM.1">BCI-algebra</a><br/>  for <font color="Olive" title="b2">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">X</font><br/>  for <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>  st <font color="Olive" title="b2">x</font> is  <a href="bcialg_6.html#V1" title="BCIALG_6:attr.1">finite-period</a>  &amp; <font color="Olive" title="b2">x</font> <a href="bcialg_6.html#K2" title="BCIALG_6:func.2">|^</a> <font color="Olive" title="b3">m</font> is  <a href="bcialg_6.html#V1" title="BCIALG_6:attr.1">finite-period</a>  &amp;  <a href="bcialg_6.html#K3" title="BCIALG_6:func.3">ord</a> <font color="Olive" title="b2">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">n</font> &amp; <font color="Olive" title="b3">m</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  holds <br/> <a href="bcialg_6.html#K3" title="BCIALG_6:func.3">ord</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">x</font> <a href="bcialg_6.html#K2" title="BCIALG_6:func.2">|^</a> <font color="Olive" title="b3">m</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">n</font> <a href="int_1.html#K4" title="INT_1:func.4">div</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">m</font> <a href="nat_d.html#K6" title="NAT_D:func.6">gcd</a> <font color="Olive" title="b4">n</font></span>)</span></div></div>
