<?xml version="1.0"?>
<div><span class="kw">theorem </span><a NAME="T44"><span class="comment"><font color="firebrick">:: BCIALG_4:44</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>, <font color="Olive" title="b3">b</font>, <font color="Olive" title="b4">c</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">X</font>  st  <a href="bcialg_4.html#K3" title="BCIALG_4:func.3">Condition_S</a> (<font color="Olive" title="b2">a</font>,<font color="Olive" title="b3">b</font>) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="bcialg_4.html#K8" title="BCIALG_4:func.8">Initial_section</a> <font color="Olive" title="b4">c</font> holds <br/> for <font color="Olive" title="b5">x</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="bcialg_4.html#K3" title="BCIALG_4:func.3">Condition_S</a> (<font color="Olive" title="b2">a</font>,<font color="Olive" title="b3">b</font>) holds  <font color="Olive" title="b5">x</font> <a href="bcialg_1.html#R1" title="BCIALG_1:pred.1">&lt;=</a> <font color="Olive" title="b4">c</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="b4">c</font> <a href="bcialg_1.html#K1" title="BCIALG_1:func.1">\</a> <font color="Olive" title="b2">a</font></span>)</span> <a href="bcialg_1.html#K1" title="BCIALG_1:func.1">\</a> <font color="Olive" title="b3">b</font></span>)</span></div></div>
