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<div><span class="kw">theorem </span><a NAME="T53"><span class="comment"><font color="firebrick">:: BCIALG_5:53</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">n</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a><br/>  for <font color="Olive" title="b2">X</font> being   <a href="bcialg_5.html#V1" title="BCIALG_5:attr.1">quasi-commutative</a>  <a href="bcialg_1.html#NM2" title="BCIALG_1:NM.2">BCK-algebra</a> holds <br/> ( <font color="Olive" title="b2">X</font> is   <a href="bcialg_5.html#NM2" title="BCIALG_5:NM.2">BCK-algebra</a> of <font color="Olive" title="b1">n</font>,<font color="Olive" title="b1">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1,<font color="Olive" title="b1">n</font>,<font color="Olive" title="b1">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 iff  for <font color="Olive" title="b3">x</font>, <font color="Olive" title="b4">y</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b2">X</font> holds  (<font color="Olive" title="b3">x</font>,<font color="Olive" title="b4">y</font>) <a href="bcialg_2.html#K1" title="BCIALG_2:func.1">to_power</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="hidden.html#R1" title="HIDDEN:pred.1">=</a> (<font color="Olive" title="b3">x</font>,<font color="Olive" title="b4">y</font>) <a href="bcialg_2.html#K1" title="BCIALG_2:func.1">to_power</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> 2</span>)</span> )</div></div>
