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<div>:: <span class="kw">deftheorem </span><span class="lab"><font color="Green" title="E31">Def17</font></span>   defines <a href="bcialg_2.html#K7" title="BCIALG_2:func.7">EqClaOp</a> <a onclick="hs(this)" href="javascript:()">BCIALG_2:def 17 : <br/></a><span> 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">E</font> being    <a href="bcialg_2.html#M1" title="BCIALG_2:mode.1">Congruence</a> of <font color="Olive" title="b1">X</font><br/>  for <font color="Olive">b<sub>3</sub></font> being   <a href="binop_1.html#NM2" title="BINOP_1:NM.2">BinOp</a> of <span class="p1">(<span class="default"><a href="eqrel_1.html#K8" title="EQREL_1:func.8">Class</a> <font color="Olive" title="b2">E</font></span>)</span> holds <br/> ( <font color="Olive">b<sub>3</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="bcialg_2.html#K7" title="BCIALG_2:func.7">EqClaOp</a> <font color="Olive" title="b2">E</font> iff  for <font color="Olive" title="b4">W1</font>, <font color="Olive" title="b5">W2</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="eqrel_1.html#K8" title="EQREL_1:func.8">Class</a> <font color="Olive" title="b2">E</font><br/>  for <font color="Olive" title="b6">x</font>, <font color="Olive" title="b7">y</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="b4">W1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> (<font color="Olive" title="b2">E</font>,<font color="Olive" title="b6">x</font>) &amp; <font color="Olive" title="b5">W2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> (<font color="Olive" title="b2">E</font>,<font color="Olive" title="b7">y</font>) holds <br/><font color="Olive">b<sub>3</sub></font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Olive" title="b4">W1</font>,<font color="Olive" title="b5">W2</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> (<font color="Olive" title="b2">E</font>,<span class="p1">(<span class="default"><font color="Olive" title="b6">x</font> <a href="bcialg_1.html#K1" title="BCIALG_1:func.1">\</a> <font color="Olive" title="b7">y</font></span>)</span>) );<br/></span></div>
