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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>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c1">X</font> is    <a href="bcialg_1.html#M1" title="BCIALG_1:mode.1">SubAlgebra</a> of <font color="Maroon" title="c1">X</font></span><br/>

<a NAME="E1:40"/><i><font color="Green" title="E20">A1</font></i>: 
( the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font> &amp;  <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>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">X</font> )
 
;<br/>
<a NAME="E2:40"/>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> the <a href="bcialg_1.html#U1" title="BCIALG_1:sel.1">InternalDiff</a> of <font color="Maroon" title="c1">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 
<b>by </b><i><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></i>;<br/>
<a NAME="E3:40"/><b>then </b>
the <a href="bcialg_1.html#U1" title="BCIALG_1:sel.1">InternalDiff</a> of <font color="Maroon" title="c1">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="bcialg_1.html#U1" title="BCIALG_1:sel.1">InternalDiff</a> of <font color="Maroon" title="c1">X</font> <a href="realset1.html#K1" title="REALSET1:func.1">||</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font>
 
<b>by </b><i><a class="ref" href="relat_1.html#T97" title="RELAT_1:th.97">RELAT_1:97</a></i>;<br/>
<b>hence </b><a NAME="E4:40"/>
<font color="Maroon" title="c1">X</font> is    <a href="bcialg_1.html#M1" title="BCIALG_1:mode.1">SubAlgebra</a> of <font color="Maroon" title="c1">X</font>
 <b>by </b><i><a class="txt" href="bcialg_1.html#E1:40"><i><font color="Green" title="E20">A1</font></i></a>, <a class="ref" href="bcialg_1.html#D10" target="_self" title="BCIALG_1:def.10">Def10</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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