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<span class="kw">set </span><font color="Maroon" title="c2">S</font> =  the   <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="algstr_0.html#L3" title="ALGSTR_0:struct.3">multMagma</a> ;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c3">A</font> =  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of  the   <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="algstr_0.html#L3" title="ALGSTR_0:struct.3">multMagma</a>  as    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>  ;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c4">X</font> = <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Maroon" title="c3">A</font>,<font color="Maroon" title="c3">A</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> as    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>  ;<br/>
 the <a href="algstr_0.html#U2" title="ALGSTR_0:sel.2">multF</a> of  the   <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="algstr_0.html#L3" title="ALGSTR_0:struct.3">multMagma</a>  = 
 the <a href="algstr_0.html#U2" title="ALGSTR_0:sel.2">multF</a> of <font color="Maroon" title="c1">M</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c4">X</font>

<br/>.= 
 the <a href="algstr_0.html#U2" title="ALGSTR_0:sel.2">multF</a> of <font color="Maroon" title="c1">M</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  the   <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="algstr_0.html#L3" title="ALGSTR_0:struct.3">multMagma</a> 
<span class="kw">by</span> <span class="lab"><a class="ref" href="realset1.html#D2" onmouseover="rs('realset1/D2')" onmouseout="rh()">REALSET1:def 2</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E4:30_1_1"/>
 ex <font color="Olive">b<sub>1</sub></font> being    <a href="algstr_0.html#L3" title="ALGSTR_0:struct.3">multMagma</a>  st <br/>(  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive">b<sub>1</sub></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">M</font> &amp;  the <a href="algstr_0.html#U2" title="ALGSTR_0:sel.2">multF</a> of <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="algstr_0.html#U2" title="ALGSTR_0:sel.2">multF</a> of <font color="Maroon" title="c1">M</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="Olive">b<sub>1</sub></font> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_1.html#T2" onmouseover="rs('xboole_1/T2')" onmouseout="rh()">XBOOLE_1:2</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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