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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>assume </b><a NAME="E1:34"/><i><font color="Green" title="E18">A1</font></i>: 
 <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">X</font> is <a href="bcialg_2.html#V3" title="BCIALG_2:attr.3">maximal</a>
 ;<br/>

<b>let </b><font color="Maroon" title="c2">a</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font>;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="34_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c3">x</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="E1:34_1"/>
<font color="Maroon" title="c3">x</font> <a href="bcialg_1.html#R1" title="BCIALG_1:pred.1">&lt;=</a> <font color="Maroon" title="c2">a</font>
 ;<br/><a NAME="E2:34_1"/><b>then </b><i><font color="Green" title="E19">A2</font></i>: 
<font color="Maroon" title="c3">x</font> <a href="bcialg_1.html#K1" title="BCIALG_1:func.1">\</a> <font color="Maroon" title="c2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">X</font>
 <b>by </b><i><a class="ref" href="bcialg_1.html#D11" title="BCIALG_1:def.11">BCIALG_1:def 11</a></i>;<br/><a NAME="E3:34_1"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="bcialg_1.html#K1" title="BCIALG_1:func.1">\</a> <font color="Maroon" title="c3">x</font></span>)</span> <a href="bcialg_1.html#K2" title="BCIALG_1:func.2">`</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">X</font>
 <b>by </b><i><a class="ref" href="bcialg_1.html#T6" title="BCIALG_1:th.6">BCIALG_1:6</a></i>;<br/><a NAME="E4:34_1"/><b>then </b>
 <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">X</font> <a href="bcialg_1.html#R1" title="BCIALG_1:pred.1">&lt;=</a> <font color="Maroon" title="c2">a</font> <a href="bcialg_1.html#K1" title="BCIALG_1:func.1">\</a> <font color="Maroon" title="c3">x</font>
 <b>by </b><i><a class="ref" href="bcialg_1.html#D11" title="BCIALG_1:def.11">BCIALG_1:def 11</a></i>;<br/><a NAME="E5:34_1"/><b>then </b>
 <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">a</font> <a href="bcialg_1.html#K1" title="BCIALG_1:func.1">\</a> <font color="Maroon" title="c3">x</font>
 <b>by </b><i><a class="txt" href="bcialg_2.html#E1:34"><i><font color="Green" title="E18">A1</font></i></a>, <a class="ref" href="bcialg_2.html#D4" target="_self" title="BCIALG_2:def.4">Def4</a></i>;<br/><b>hence </b><a NAME="E6:34_1"/>
<font color="Maroon" title="c3">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">a</font>
 <b>by </b><i><a class="txt" href="bcialg_2.html#E2:34_1"><i><font color="Green" title="E19">A2</font></i></a>, <a class="ref" href="bcialg_1.html#D7" title="BCIALG_1:def.7">BCIALG_1:def 7</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:34"/>
<font color="Maroon" title="c2">a</font> is <a href="bcialg_1.html#V10" title="BCIALG_1:attr.10">minimal</a>
 <b>by </b><i><a class="txt" href="bcialg_2.html#E28"><i><font color="Green" title="E15">Lm1</font></i></a></i>;<br/>


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