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<div><span class="kw">theorem </span><a NAME="T43"><span class="comment"><font color="firebrick">:: BCIALG_4:43</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">X</font> being   <a href="bcialg_4.html#V3" title="BCIALG_4:attr.3">commutative</a>  <a href="bcialg_4.html#NM2" title="BCIALG_4:NM.2">BCK-Algebra_with_Condition(S)</a><br/>  for <font color="Olive" title="b2">a</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">X</font>  st <font color="Olive" title="b2">a</font> is  <a href="bcialg_2.html#V4" title="BCIALG_2:attr.4">greatest</a>  holds <br/> 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="b1">X</font> holds  <font color="Olive" title="b3">x</font> <a href="bcialg_4.html#K1" title="BCIALG_4:func.1">*</a> <font color="Olive" title="b4">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">a</font> <a href="bcialg_1.html#K1" title="BCIALG_1:func.1">\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b2">a</font> <a href="bcialg_1.html#K1" title="BCIALG_1:func.1">\</a> <font color="Olive" title="b3">x</font></span>)</span> <a href="bcialg_1.html#K1" title="BCIALG_1:func.1">\</a> <font color="Olive" title="b4">y</font></span>)</span></div></div>
