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<b>let </b><font color="Maroon" title="c1">X</font> be   <a href="bcialg_1.html#NM1" title="BCIALG_1:NM.1">BCI-algebra</a>;<br/><b>let </b><font color="Maroon" title="c2">x</font>, <font color="Maroon" title="c3">a</font>, <font color="Maroon" title="c4">b</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>assume </b><a NAME="E1:128"/><i><font color="Green" title="E78">A1</font></i>: 
( <font color="Maroon" title="c1">X</font> is <a href="bcialg_1.html#V20" title="BCIALG_1:attr.20">alternative</a> &amp; <font color="Maroon" title="c2">x</font> <a href="bcialg_1.html#K1" title="BCIALG_1:func.1">\</a> <font color="Maroon" title="c3">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">x</font> <a href="bcialg_1.html#K1" title="BCIALG_1:func.1">\</a> <font color="Maroon" title="c4">b</font> )
 ;<br/>

<a NAME="E2:128"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="bcialg_1.html#K1" title="BCIALG_1:func.1">\</a> <font color="Maroon" title="c2">x</font></span>)</span> <a href="bcialg_1.html#K1" title="BCIALG_1:func.1">\</a> <font color="Maroon" title="c3">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">x</font> <a href="bcialg_1.html#K1" title="BCIALG_1:func.1">\</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="bcialg_1.html#K1" title="BCIALG_1:func.1">\</a> <font color="Maroon" title="c4">b</font></span>)</span>
 
<b>by </b><i><a class="ref" href="bcialg_1.html#D27" target="_self" title="BCIALG_1:def.27">Def27</a></i>;<br/>
<a NAME="E3:128"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="bcialg_1.html#K1" title="BCIALG_1:func.1">\</a> <font color="Maroon" title="c2">x</font></span>)</span> <a href="bcialg_1.html#K1" title="BCIALG_1:func.1">\</a> <font color="Maroon" title="c3">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="bcialg_1.html#K1" title="BCIALG_1:func.1">\</a> <font color="Maroon" title="c2">x</font></span>)</span> <a href="bcialg_1.html#K1" title="BCIALG_1:func.1">\</a> <font color="Maroon" title="c4">b</font>
 
<b>by </b><i><a class="txt" href="bcialg_1.html#E1:128"><i><font color="Green" title="E78">A1</font></i></a>, <a class="ref" href="bcialg_1.html#D27" target="_self" title="BCIALG_1:def.27">Def27</a></i>;<br/>
<a NAME="E4:128"/><b>then </b>
<font color="Maroon" title="c3">a</font> <a href="bcialg_1.html#K2" title="BCIALG_1:func.2">`</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="bcialg_1.html#K1" title="BCIALG_1:func.1">\</a> <font color="Maroon" title="c2">x</font></span>)</span> <a href="bcialg_1.html#K1" title="BCIALG_1:func.1">\</a> <font color="Maroon" title="c4">b</font>
 
<b>by </b><i><a class="ref" href="bcialg_1.html#D5" target="_self" title="BCIALG_1:def.5">Def5</a></i>;<br/>
<a NAME="E5:128"/><b>then </b>
<font color="Maroon" title="c3">a</font> <a href="bcialg_1.html#K2" title="BCIALG_1:func.2">`</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> <a href="bcialg_1.html#K2" title="BCIALG_1:func.2">`</a> 
 
<b>by </b><i><a class="ref" href="bcialg_1.html#D5" target="_self" title="BCIALG_1:def.5">Def5</a></i>;<br/>
<a NAME="E6:128"/><b>then </b>
<font color="Maroon" title="c3">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> <a href="bcialg_1.html#K2" title="BCIALG_1:func.2">`</a> 
 
<b>by </b><i><a class="ref" href="bcialg_1.html#T76" target="_self" title="BCIALG_1:th.76">Th76</a>, <a class="txt" href="bcialg_1.html#E1:128"><i><font color="Green" title="E78">A1</font></i></a></i>;<br/>
<b>hence </b><a NAME="E7:128"/>
<font color="Maroon" title="c3">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font>
 <b>by </b><i><a class="ref" href="bcialg_1.html#T76" target="_self" title="BCIALG_1:th.76">Th76</a>, <a class="txt" href="bcialg_1.html#E1:128"><i><font color="Green" title="E78">A1</font></i></a></i>;<br/>


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