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<b>let </b><font color="Maroon" title="c1">X</font> be   <a href="bcialg_4.html#NM1" title="BCIALG_4:NM.1">BCI-Algebra_with_Condition(S)</a>;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="31_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c2">a</font>, <font color="Maroon" title="c3">b</font>, <font color="Maroon" title="c4">c</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font>;<br/><b>thus </b>the <a href="bcialg_4.html#U1" title="BCIALG_4:sel.1">ExternalDiff</a> of <font color="Maroon" title="c1">X</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <font color="Maroon" title="c2">a</font>,<span class="p1">(<span class="default">the <a href="bcialg_4.html#U1" title="BCIALG_4:sel.1">ExternalDiff</a> of <font color="Maroon" title="c1">X</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font></span>)</span> = 
<font color="Maroon" title="c2">a</font> <a href="bcialg_4.html#K1" title="BCIALG_4:func.1">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="bcialg_4.html#K1" title="BCIALG_4:func.1">*</a> <font color="Maroon" title="c4">c</font></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="bcialg_4.html#K1" title="BCIALG_4:func.1">*</a> <font color="Maroon" title="c3">b</font></span>)</span> <a href="bcialg_4.html#K1" title="BCIALG_4:func.1">*</a> <font color="Maroon" title="c4">c</font>
<b>by </b><i><a class="ref" href="bcialg_4.html#T10" target="_self" title="BCIALG_4:th.10">Th10</a></i>
<br/>.= 
the <a href="bcialg_4.html#U1" title="BCIALG_4:sel.1">ExternalDiff</a> of <font color="Maroon" title="c1">X</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <span class="p1">(<span class="default">the <a href="bcialg_4.html#U1" title="BCIALG_4:sel.1">ExternalDiff</a> of <font color="Maroon" title="c1">X</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font></span>)</span>,<font color="Maroon" title="c4">c</font>

;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:31"/>
the <a href="bcialg_4.html#U1" title="BCIALG_4:sel.1">ExternalDiff</a> of <font color="Maroon" title="c1">X</font> is <a href="binop_1.html#V2" title="BINOP_1:attr.2">associative</a>
 <b>by </b><i><a class="ref" href="binop_1.html#D3" title="BINOP_1:def.3">BINOP_1:def 3</a></i>;<br/>


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