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<b>let </b><font color="Maroon" title="c1">S</font> be    <a href="struct_0.html#L1" title="STRUCT_0:struct.1">1-sorted</a> ;<br/>

<b>assume </b><a NAME="E1:150"/><i><font color="Green" title="E69">A1</font></i>: 
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">S</font> is <a href="fraenkel.html#V1" title="FRAENKEL:attr.1">functional</a>
 ;<br/>

<b>let </b><font color="Maroon" title="c2">a</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">S</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="monoid_0.html#D1" target="_self" title="MONOID_0:def.1">MONOID_0:def 1</a><br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="150_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:150_1"/>
( the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">S</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  or the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">S</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="150_1_1"><b>suppose </b></a><a NAME="E1:150_1_1"/>
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">S</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 ;<br/><div class="add"><b>hence </b><a NAME="E2:150_1_1"/>
<font color="Maroon" title="c2">a</font> is   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a>
 <b>by </b><i><a class="ref" href="subset_1.html#D2" title="SUBSET_1:def.2">SUBSET_1:def 2</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="150_1_2"><b>suppose </b></a><a NAME="E1:150_1_2"/>
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">S</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 ;<br/><div class="add"><b>hence </b><a NAME="E2:150_1_2"/>
<font color="Maroon" title="c2">a</font> is   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a>
 <b>by </b><i><a class="txt" href="monoid_0.html#E1:150"><i><font color="Green" title="E69">A1</font></i></a>, <a class="ref" href="fraenkel.html#D1" title="FRAENKEL:def.1">FRAENKEL:def 1</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

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