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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>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">a</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font> holds  <font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">a</font> <a href="bcialg_2.html#K1" title="BCIALG_2:func.1">to_power</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">x</font> <a href="bcialg_1.html#K1" title="BCIALG_1:func.1">\</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">a</font> <a href="bcialg_4.html#K6" title="BCIALG_4:func.6">|^</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span><br/><b>let </b><font color="Maroon" title="c2">x</font>, <font color="Maroon" title="c3">a</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">a</font> <a href="bcialg_2.html#K1" title="BCIALG_2:func.1">to_power</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <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="c3">a</font> <a href="bcialg_4.html#K6" title="BCIALG_4:func.6">|^</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span><br/>



<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="c3">a</font> <a href="bcialg_4.html#K6" title="BCIALG_4:func.6">|^</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> = 
<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"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">X</font></span>)</span>
<b>by </b><i><a class="ref" href="bcialg_4.html#D6" target="_self" title="BCIALG_4:def.6">Def6</a></i>
<br/>.= 
<font color="Maroon" title="c2">x</font>
<b>by </b><i><a class="ref" href="bcialg_1.html#T2" title="BCIALG_1:th.2">BCIALG_1:2</a></i>
;<br/>
<b>hence </b><a NAME="E2:45"/>
<font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">a</font> <a href="bcialg_2.html#K1" title="BCIALG_2:func.1">to_power</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <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="c3">a</font> <a href="bcialg_4.html#K6" title="BCIALG_4:func.6">|^</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>
 <b>by </b><i><a class="ref" href="bcialg_2.html#T1" title="BCIALG_2:th.1">BCIALG_2:1</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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