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<b>let </b><font color="Maroon" title="c1">Y</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c2">a</font>, <font color="Maroon" title="c3">b</font>, <font color="Maroon" title="c4">c</font>, <font color="Maroon" title="c5">d</font>, <font color="Maroon" title="c6">e</font>, <font color="Maroon" title="c7">f</font>, <font color="Maroon" title="c8">g</font> be    <a href="fraenkel.html#M2" title="FRAENKEL:mode.2">Element</a> of  <a href="fraenkel.html#K1" title="FRAENKEL:func.1">Funcs</a> <font color="Maroon" title="c1">Y</font>,<a href="margrel1.html#K6" title="MARGREL1:func.6">BOOLEAN</a> ;<br/>



<a NAME="E1:7"/><i><font color="Green" title="E8">A1</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="valuat_1.html#K6" title="VALUAT_1:func.6">'&amp;'</a> <font color="Maroon" title="c3">b</font></span>)</span> <a href="valuat_1.html#K6" title="VALUAT_1:func.6">'&amp;'</a> <font color="Maroon" title="c4">c</font></span>)</span> <a href="valuat_1.html#K6" title="VALUAT_1:func.6">'&amp;'</a> <font color="Maroon" title="c5">d</font></span>)</span> <a href="valuat_1.html#K6" title="VALUAT_1:func.6">'&amp;'</a> <font color="Maroon" title="c6">e</font></span>)</span> <a href="valuat_1.html#K6" title="VALUAT_1:func.6">'&amp;'</a> <font color="Maroon" title="c7">f</font></span>)</span> <a href="valuat_1.html#K6" title="VALUAT_1:func.6">'&amp;'</a> <font color="Maroon" title="c8">g</font> <a href="bvfunc_1.html#R1" title="BVFUNC_1:pred.1">'&lt;'</a> <font color="Maroon" title="c2">a</font>
 
<b>by </b><i><a class="txt" href="bvfunc_9.html#E6"><i><font color="Green" title="E6">Lm6</font></i></a></i>;<br/>
<a NAME="E2:7"/><i><font color="Green" title="E9">A2</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="valuat_1.html#K6" title="VALUAT_1:func.6">'&amp;'</a> <font color="Maroon" title="c3">b</font></span>)</span> <a href="valuat_1.html#K6" title="VALUAT_1:func.6">'&amp;'</a> <font color="Maroon" title="c4">c</font></span>)</span> <a href="valuat_1.html#K6" title="VALUAT_1:func.6">'&amp;'</a> <font color="Maroon" title="c5">d</font></span>)</span> <a href="valuat_1.html#K6" title="VALUAT_1:func.6">'&amp;'</a> <font color="Maroon" title="c6">e</font></span>)</span> <a href="valuat_1.html#K6" title="VALUAT_1:func.6">'&amp;'</a> <font color="Maroon" title="c7">f</font></span>)</span> <a href="valuat_1.html#K6" title="VALUAT_1:func.6">'&amp;'</a> <font color="Maroon" title="c8">g</font> <a href="bvfunc_1.html#R1" title="BVFUNC_1:pred.1">'&lt;'</a> <font color="Maroon" title="c3">b</font>
 
<b>by </b><i><a class="txt" href="bvfunc_9.html#E6"><i><font color="Green" title="E6">Lm6</font></i></a></i>;<br/>
<a NAME="E3:7"/><i><font color="Green" title="E10">A3</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="valuat_1.html#K6" title="VALUAT_1:func.6">'&amp;'</a> <font color="Maroon" title="c3">b</font></span>)</span> <a href="valuat_1.html#K6" title="VALUAT_1:func.6">'&amp;'</a> <font color="Maroon" title="c4">c</font></span>)</span> <a href="valuat_1.html#K6" title="VALUAT_1:func.6">'&amp;'</a> <font color="Maroon" title="c5">d</font></span>)</span> <a href="valuat_1.html#K6" title="VALUAT_1:func.6">'&amp;'</a> <font color="Maroon" title="c6">e</font></span>)</span> <a href="valuat_1.html#K6" title="VALUAT_1:func.6">'&amp;'</a> <font color="Maroon" title="c7">f</font></span>)</span> <a href="valuat_1.html#K6" title="VALUAT_1:func.6">'&amp;'</a> <font color="Maroon" title="c8">g</font> <a href="bvfunc_1.html#R1" title="BVFUNC_1:pred.1">'&lt;'</a> <font color="Maroon" title="c4">c</font>
 
<b>by </b><i><a class="txt" href="bvfunc_9.html#E5"><i><font color="Green" title="E5">Lm5</font></i></a></i>;<br/>
<a NAME="E4:7"/><i><font color="Green" title="E11">A4</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="valuat_1.html#K6" title="VALUAT_1:func.6">'&amp;'</a> <font color="Maroon" title="c3">b</font></span>)</span> <a href="valuat_1.html#K6" title="VALUAT_1:func.6">'&amp;'</a> <font color="Maroon" title="c4">c</font></span>)</span> <a href="valuat_1.html#K6" title="VALUAT_1:func.6">'&amp;'</a> <font color="Maroon" title="c5">d</font></span>)</span> <a href="valuat_1.html#K6" title="VALUAT_1:func.6">'&amp;'</a> <font color="Maroon" title="c6">e</font></span>)</span> <a href="valuat_1.html#K6" title="VALUAT_1:func.6">'&amp;'</a> <font color="Maroon" title="c7">f</font></span>)</span> <a href="valuat_1.html#K6" title="VALUAT_1:func.6">'&amp;'</a> <font color="Maroon" title="c8">g</font> <a href="bvfunc_1.html#R1" title="BVFUNC_1:pred.1">'&lt;'</a> <font color="Maroon" title="c5">d</font>
 
<b>by </b><i><a class="txt" href="bvfunc_9.html#E4"><i><font color="Green" title="E4">Lm4</font></i></a></i>;<br/>
<a NAME="E5:7"/><i><font color="Green" title="E12">A5</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="valuat_1.html#K6" title="VALUAT_1:func.6">'&amp;'</a> <font color="Maroon" title="c3">b</font></span>)</span> <a href="valuat_1.html#K6" title="VALUAT_1:func.6">'&amp;'</a> <font color="Maroon" title="c4">c</font></span>)</span> <a href="valuat_1.html#K6" title="VALUAT_1:func.6">'&amp;'</a> <font color="Maroon" title="c5">d</font></span>)</span> <a href="valuat_1.html#K6" title="VALUAT_1:func.6">'&amp;'</a> <font color="Maroon" title="c6">e</font></span>)</span> <a href="valuat_1.html#K6" title="VALUAT_1:func.6">'&amp;'</a> <font color="Maroon" title="c7">f</font></span>)</span> <a href="valuat_1.html#K6" title="VALUAT_1:func.6">'&amp;'</a> <font color="Maroon" title="c8">g</font> <a href="bvfunc_1.html#R1" title="BVFUNC_1:pred.1">'&lt;'</a> <font color="Maroon" title="c6">e</font>
 
<b>by </b><i><a class="txt" href="bvfunc_9.html#E3"><i><font color="Green" title="E3">Lm3</font></i></a></i>;<br/>
<a NAME="E6:7"/><i><font color="Green" title="E13">A6</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="valuat_1.html#K6" title="VALUAT_1:func.6">'&amp;'</a> <font color="Maroon" title="c3">b</font></span>)</span> <a href="valuat_1.html#K6" title="VALUAT_1:func.6">'&amp;'</a> <font color="Maroon" title="c4">c</font></span>)</span> <a href="valuat_1.html#K6" title="VALUAT_1:func.6">'&amp;'</a> <font color="Maroon" title="c5">d</font></span>)</span> <a href="valuat_1.html#K6" title="VALUAT_1:func.6">'&amp;'</a> <font color="Maroon" title="c6">e</font></span>)</span> <a href="valuat_1.html#K6" title="VALUAT_1:func.6">'&amp;'</a> <font color="Maroon" title="c7">f</font></span>)</span> <a href="valuat_1.html#K6" title="VALUAT_1:func.6">'&amp;'</a> <font color="Maroon" title="c8">g</font> <a href="bvfunc_1.html#R1" title="BVFUNC_1:pred.1">'&lt;'</a> <font color="Maroon" title="c7">f</font>
 
<b>by </b><i><a class="txt" href="bvfunc_9.html#E2"><i><font color="Green" title="E2">Lm2</font></i></a></i>;<br/>
<a NAME="E7:7"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="valuat_1.html#K6" title="VALUAT_1:func.6">'&amp;'</a> <font color="Maroon" title="c3">b</font></span>)</span> <a href="valuat_1.html#K6" title="VALUAT_1:func.6">'&amp;'</a> <font color="Maroon" title="c4">c</font></span>)</span> <a href="valuat_1.html#K6" title="VALUAT_1:func.6">'&amp;'</a> <font color="Maroon" title="c5">d</font></span>)</span> <a href="valuat_1.html#K6" title="VALUAT_1:func.6">'&amp;'</a> <font color="Maroon" title="c6">e</font></span>)</span> <a href="valuat_1.html#K6" title="VALUAT_1:func.6">'&amp;'</a> <font color="Maroon" title="c7">f</font></span>)</span> <a href="valuat_1.html#K6" title="VALUAT_1:func.6">'&amp;'</a> <font color="Maroon" title="c8">g</font> <a href="bvfunc_1.html#R1" title="BVFUNC_1:pred.1">'&lt;'</a> <font color="Maroon" title="c8">g</font>
 
<b>by </b><i><a class="txt" href="bvfunc_9.html#E1"><i><font color="Green" title="E1">Lm1</font></i></a></i>;<br/>
<b>hence </b><a NAME="E8:7"/>
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="valuat_1.html#K6" title="VALUAT_1:func.6">'&amp;'</a> <font color="Maroon" title="c3">b</font></span>)</span> <a href="valuat_1.html#K6" title="VALUAT_1:func.6">'&amp;'</a> <font color="Maroon" title="c4">c</font></span>)</span> <a href="valuat_1.html#K6" title="VALUAT_1:func.6">'&amp;'</a> <font color="Maroon" title="c5">d</font></span>)</span> <a href="valuat_1.html#K6" title="VALUAT_1:func.6">'&amp;'</a> <font color="Maroon" title="c6">e</font></span>)</span> <a href="valuat_1.html#K6" title="VALUAT_1:func.6">'&amp;'</a> <font color="Maroon" title="c7">f</font></span>)</span> <a href="valuat_1.html#K6" title="VALUAT_1:func.6">'&amp;'</a> <font color="Maroon" title="c8">g</font></span>)</span> <a href="bvfunc_1.html#K12" title="BVFUNC_1:func.12">'imp'</a> <font color="Maroon" title="c2">a</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="bvfunc_1.html#K17" title="BVFUNC_1:func.17">I_el</a> <font color="Maroon" title="c1">Y</font> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="valuat_1.html#K6" title="VALUAT_1:func.6">'&amp;'</a> <font color="Maroon" title="c3">b</font></span>)</span> <a href="valuat_1.html#K6" title="VALUAT_1:func.6">'&amp;'</a> <font color="Maroon" title="c4">c</font></span>)</span> <a href="valuat_1.html#K6" title="VALUAT_1:func.6">'&amp;'</a> <font color="Maroon" title="c5">d</font></span>)</span> <a href="valuat_1.html#K6" title="VALUAT_1:func.6">'&amp;'</a> <font color="Maroon" title="c6">e</font></span>)</span> <a href="valuat_1.html#K6" title="VALUAT_1:func.6">'&amp;'</a> <font color="Maroon" title="c7">f</font></span>)</span> <a href="valuat_1.html#K6" title="VALUAT_1:func.6">'&amp;'</a> <font color="Maroon" title="c8">g</font></span>)</span> <a href="bvfunc_1.html#K12" title="BVFUNC_1:func.12">'imp'</a> <font color="Maroon" title="c3">b</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="bvfunc_1.html#K17" title="BVFUNC_1:func.17">I_el</a> <font color="Maroon" title="c1">Y</font> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="valuat_1.html#K6" title="VALUAT_1:func.6">'&amp;'</a> <font color="Maroon" title="c3">b</font></span>)</span> <a href="valuat_1.html#K6" title="VALUAT_1:func.6">'&amp;'</a> <font color="Maroon" title="c4">c</font></span>)</span> <a href="valuat_1.html#K6" title="VALUAT_1:func.6">'&amp;'</a> <font color="Maroon" title="c5">d</font></span>)</span> <a href="valuat_1.html#K6" title="VALUAT_1:func.6">'&amp;'</a> <font color="Maroon" title="c6">e</font></span>)</span> <a href="valuat_1.html#K6" title="VALUAT_1:func.6">'&amp;'</a> <font color="Maroon" title="c7">f</font></span>)</span> <a href="valuat_1.html#K6" title="VALUAT_1:func.6">'&amp;'</a> <font color="Maroon" title="c8">g</font></span>)</span> <a href="bvfunc_1.html#K12" title="BVFUNC_1:func.12">'imp'</a> <font color="Maroon" title="c4">c</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="bvfunc_1.html#K17" title="BVFUNC_1:func.17">I_el</a> <font color="Maroon" title="c1">Y</font> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="valuat_1.html#K6" title="VALUAT_1:func.6">'&amp;'</a> <font color="Maroon" title="c3">b</font></span>)</span> <a href="valuat_1.html#K6" title="VALUAT_1:func.6">'&amp;'</a> <font color="Maroon" title="c4">c</font></span>)</span> <a href="valuat_1.html#K6" title="VALUAT_1:func.6">'&amp;'</a> <font color="Maroon" title="c5">d</font></span>)</span> <a href="valuat_1.html#K6" title="VALUAT_1:func.6">'&amp;'</a> <font color="Maroon" title="c6">e</font></span>)</span> <a href="valuat_1.html#K6" title="VALUAT_1:func.6">'&amp;'</a> <font color="Maroon" title="c7">f</font></span>)</span> <a href="valuat_1.html#K6" title="VALUAT_1:func.6">'&amp;'</a> <font color="Maroon" title="c8">g</font></span>)</span> <a href="bvfunc_1.html#K12" title="BVFUNC_1:func.12">'imp'</a> <font color="Maroon" title="c5">d</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="bvfunc_1.html#K17" title="BVFUNC_1:func.17">I_el</a> <font color="Maroon" title="c1">Y</font> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="valuat_1.html#K6" title="VALUAT_1:func.6">'&amp;'</a> <font color="Maroon" title="c3">b</font></span>)</span> <a href="valuat_1.html#K6" title="VALUAT_1:func.6">'&amp;'</a> <font color="Maroon" title="c4">c</font></span>)</span> <a href="valuat_1.html#K6" title="VALUAT_1:func.6">'&amp;'</a> <font color="Maroon" title="c5">d</font></span>)</span> <a href="valuat_1.html#K6" title="VALUAT_1:func.6">'&amp;'</a> <font color="Maroon" title="c6">e</font></span>)</span> <a href="valuat_1.html#K6" title="VALUAT_1:func.6">'&amp;'</a> <font color="Maroon" title="c7">f</font></span>)</span> <a href="valuat_1.html#K6" title="VALUAT_1:func.6">'&amp;'</a> <font color="Maroon" title="c8">g</font></span>)</span> <a href="bvfunc_1.html#K12" title="BVFUNC_1:func.12">'imp'</a> <font color="Maroon" title="c6">e</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="bvfunc_1.html#K17" title="BVFUNC_1:func.17">I_el</a> <font color="Maroon" title="c1">Y</font> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="valuat_1.html#K6" title="VALUAT_1:func.6">'&amp;'</a> <font color="Maroon" title="c3">b</font></span>)</span> <a href="valuat_1.html#K6" title="VALUAT_1:func.6">'&amp;'</a> <font color="Maroon" title="c4">c</font></span>)</span> <a href="valuat_1.html#K6" title="VALUAT_1:func.6">'&amp;'</a> <font color="Maroon" title="c5">d</font></span>)</span> <a href="valuat_1.html#K6" title="VALUAT_1:func.6">'&amp;'</a> <font color="Maroon" title="c6">e</font></span>)</span> <a href="valuat_1.html#K6" title="VALUAT_1:func.6">'&amp;'</a> <font color="Maroon" title="c7">f</font></span>)</span> <a href="valuat_1.html#K6" title="VALUAT_1:func.6">'&amp;'</a> <font color="Maroon" title="c8">g</font></span>)</span> <a href="bvfunc_1.html#K12" title="BVFUNC_1:func.12">'imp'</a> <font color="Maroon" title="c7">f</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="bvfunc_1.html#K17" title="BVFUNC_1:func.17">I_el</a> <font color="Maroon" title="c1">Y</font> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="valuat_1.html#K6" title="VALUAT_1:func.6">'&amp;'</a> <font color="Maroon" title="c3">b</font></span>)</span> <a href="valuat_1.html#K6" title="VALUAT_1:func.6">'&amp;'</a> <font color="Maroon" title="c4">c</font></span>)</span> <a href="valuat_1.html#K6" title="VALUAT_1:func.6">'&amp;'</a> <font color="Maroon" title="c5">d</font></span>)</span> <a href="valuat_1.html#K6" title="VALUAT_1:func.6">'&amp;'</a> <font color="Maroon" title="c6">e</font></span>)</span> <a href="valuat_1.html#K6" title="VALUAT_1:func.6">'&amp;'</a> <font color="Maroon" title="c7">f</font></span>)</span> <a href="valuat_1.html#K6" title="VALUAT_1:func.6">'&amp;'</a> <font color="Maroon" title="c8">g</font></span>)</span> <a href="bvfunc_1.html#K12" title="BVFUNC_1:func.12">'imp'</a> <font color="Maroon" title="c8">g</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="bvfunc_1.html#K17" title="BVFUNC_1:func.17">I_el</a> <font color="Maroon" title="c1">Y</font> )
 <b>by </b><i><a class="txt" href="bvfunc_9.html#E1:7"><i><font color="Green" title="E8">A1</font></i></a>, <a class="txt" href="bvfunc_9.html#E2:7"><i><font color="Green" title="E9">A2</font></i></a>, <a class="txt" href="bvfunc_9.html#E3:7"><i><font color="Green" title="E10">A3</font></i></a>, <a class="txt" href="bvfunc_9.html#E4:7"><i><font color="Green" title="E11">A4</font></i></a>, <a class="txt" href="bvfunc_9.html#E5:7"><i><font color="Green" title="E12">A5</font></i></a>, <a class="txt" href="bvfunc_9.html#E6:7"><i><font color="Green" title="E13">A6</font></i></a>, <a class="ref" href="bvfunc_1.html#T19" title="BVFUNC_1:th.19">BVFUNC_1:19</a></i>;<br/>


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