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<b>let </b><font color="Maroon">A</font> be    <a href="msualg_1.html#L3">MSAlgebra</a> of <font color="Maroon">S</font>;<br/>

<b>assume </b><a NAME="E1:104_1_1"/><i><font color="Green">E24</font></i>: 
<font color="Maroon">A</font> is <a href="circcomb.html#V6" target="_self">Boolean</a>
 ;<br/>

<a NAME="E2:104_1_1"/><b>then </b>
the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">A</font> <a href="pboole.html#R6">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S</font> <a href="pre_circ.html#K2">--&gt;</a> <a href="circcomb.html#K10" target="_self">BOOLEAN</a> 
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E3:104_1_1"/>
<font color="Maroon">A</font> is <a href="msualg_1.html#V5">non-empty</a>
 <b>by </b><i><a class="ref" href="msualg_1.html#D8">MSUALG_1:def 8</a></i>;<br/>

<b>let </b><font color="Maroon">v</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="pre_circ.html#D3">PRE_CIRC:def 3</a>,<a class="ref" href="msafree2.html#D11">MSAFREE2:def 11</a><br/>

<b>assume </b><a NAME="E4:104_1_1"/>
<font color="Maroon">v</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S</font>
 ;<br/>

<b>hence </b><a NAME="E5:104_1_1"/>
the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">A</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">v</font> is <a href="finset_1.html#V1">finite</a>
 <b>by </b><i>, <a class="ref" href="circcomb.html#D2" target="_self">Def2</a></i>;<br/>


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