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<b>let </b><font color="Maroon" title="c3">i</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="pboole.html#D16" title="PBOOLE:def.16">PBOOLE:def 16</a><br/>

<b>assume </b><a NAME="E1:32_1_1"/><i><font color="Green" title="E18">A1</font></i>: 
<font color="Maroon" title="c3">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">J</font>
 ;<br/>

<b>then consider </b><font color="Maroon" title="c4">R</font> being    <a href="struct_0.html#L1" title="STRUCT_0:struct.1">1-sorted</a> <b> such that </b><br/><a NAME="E3:32_1_1"/><i><font color="Green" title="E19">A2</font></i>: 
<font color="Maroon" title="c4">R</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">A</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">i</font>
 <b>and </b><br/><a NAME="E4:32_1_1"/><i><font color="Green" title="E20">A3</font></i>: 
<span class="p1">(<span class="default"><a href="pralg_1.html#K12" title="PRALG_1:func.12">Carrier</a> <font color="Maroon" title="c2">A</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c4">R</font>
 <b>by </b><i><a class="ref" href="pralg_1.html#D13" target="_self" title="PRALG_1:def.13">Def13</a></i>;<br/>
<a NAME="E5:32_1_1"/>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c2">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">J</font>
 
<b>by </b><i><a class="ref" href="pboole.html#D3" title="PBOOLE:def.3">PBOOLE:def 3</a></i>;<br/>
<a NAME="E6:32_1_1"/><b>then </b>
<font color="Maroon" title="c4">R</font> is   <a href="unialg_1.html#NM2" title="UNIALG_1:NM.2">Universal_Algebra</a>
 
<b>by </b><i><a class="txt" href="pralg_1.html#E1:32_1_1"><i><font color="Green" title="E18">A1</font></i></a>, <a class="txt" href="pralg_1.html#E3:32_1_1"><i><font color="Green" title="E19">A2</font></i></a>, <a class="ref" href="pralg_1.html#D10" target="_self" title="PRALG_1:def.10">Def10</a></i>;<br/>
<b>hence </b><a NAME="E7:32_1_1"/>
not <span class="p1">(<span class="default"><a href="pralg_1.html#K12" title="PRALG_1:func.12">Carrier</a> <font color="Maroon" title="c2">A</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">i</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>
 <b>by </b><i><a class="txt" href="pralg_1.html#E4:32_1_1"><i><font color="Green" title="E20">A3</font></i></a>, <a class="ref" href="struct_0.html#D1" title="STRUCT_0:def.1">STRUCT_0:def 1</a></i>;<br/>


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