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<b>let </b><font color="Maroon" title="c2">A</font> be    <a href="msualg_1.html#L3" title="MSUALG_1:struct.3">MSAlgebra</a> of <font color="Maroon" title="c1">S</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">A</font> is <a href="msualg_1.html#V5" title="MSUALG_1:attr.5">non-empty</a> implies  not <font color="Maroon" title="c2">A</font> is <a href="catalg_1.html#V1" title="CATALG_1:attr.1">empty</a> )</span><br/>

<b>assume </b><a NAME="E1:17_1_1"/>
the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <font color="Maroon" title="c2">A</font> is <a href="relat_1.html#V2" title="RELAT_1:attr.2">non-empty</a>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="msualg_1.html#D8" title="MSUALG_1:def.8">MSUALG_1:def 8</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> not <font color="Maroon" title="c2">A</font> is <a href="catalg_1.html#V1" title="CATALG_1:attr.1">empty</a></span><br/>

<a NAME="E2:17_1_1"/><b>then </b>
the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <font color="Maroon" title="c2">A</font> is  <a href="relat_1.html#V2" title="RELAT_1:attr.2">V5</a>  <a href="pboole.html#M1" title="PBOOLE:mode.1">ManySortedSet</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">S</font>
 
;<br/>
<b>hence </b><a NAME="E3:17_1_1"/>
not the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <font color="Maroon" title="c2">A</font> is <a href="relat_1.html#V3" title="RELAT_1:attr.3">empty-yielding</a>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="catalg_1.html#D3" target="_self" title="CATALG_1:def.3">CATALG_1:def 3</a> <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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