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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> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">a1</font>, <font color="Olive" title="b2">a2</font>, <font color="Olive" title="b3">a3</font>, <font color="Olive" title="b4">b1</font>, <font color="Olive" title="b5">b2</font>, <font color="Olive" title="b6">b3</font> being   <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>  holds  <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b1">a1</font> <a href="margrel1.html#K16" title="MARGREL1:func.16">'&amp;'</a> <font color="Olive" title="b2">a2</font></span>)</span> <a href="margrel1.html#K16" title="MARGREL1:func.16">'&amp;'</a> <font color="Olive" title="b3">a3</font></span>)</span> <a href="bvfunc_1.html#K12" title="BVFUNC_1:func.12">'imp'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b4">b1</font> <a href="bvfunc_1.html#K6" title="BVFUNC_1:func.6">'or'</a> <font color="Olive" title="b5">b2</font></span>)</span> <a href="bvfunc_1.html#K6" title="BVFUNC_1:func.6">'or'</a> <font color="Olive" title="b6">b3</font></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="margrel1.html#K15" title="MARGREL1:func.15">'not'</a> <font color="Olive" title="b4">b1</font></span>)</span> <a href="margrel1.html#K16" title="MARGREL1:func.16">'&amp;'</a> <span class="p3">(<span class="default"><a href="margrel1.html#K15" title="MARGREL1:func.15">'not'</a> <font color="Olive" title="b5">b2</font></span>)</span></span>)</span> <a href="margrel1.html#K16" title="MARGREL1:func.16">'&amp;'</a> <font color="Olive" title="b3">a3</font></span>)</span> <a href="bvfunc_1.html#K12" title="BVFUNC_1:func.12">'imp'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="margrel1.html#K15" title="MARGREL1:func.15">'not'</a> <font color="Olive" title="b1">a1</font></span>)</span> <a href="bvfunc_1.html#K6" title="BVFUNC_1:func.6">'or'</a> <span class="p3">(<span class="default"><a href="margrel1.html#K15" title="MARGREL1:func.15">'not'</a> <font color="Olive" title="b2">a2</font></span>)</span></span>)</span> <a href="bvfunc_1.html#K6" title="BVFUNC_1:func.6">'or'</a> <font color="Olive" title="b6">b3</font></span>)</span></span><br/><b>let </b><font color="Maroon" title="c2">a1</font>, <font color="Maroon" title="c3">a2</font>, <font color="Maroon" title="c4">a3</font>, <font color="Maroon" title="c5">b1</font>, <font color="Maroon" title="c6">b2</font>, <font color="Maroon" title="c7">b3</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> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">a1</font> <a href="margrel1.html#K16" title="MARGREL1:func.16">'&amp;'</a> <font color="Maroon" title="c3">a2</font></span>)</span> <a href="margrel1.html#K16" title="MARGREL1:func.16">'&amp;'</a> <font color="Maroon" title="c4">a3</font></span>)</span> <a href="bvfunc_1.html#K12" title="BVFUNC_1:func.12">'imp'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">b1</font> <a href="bvfunc_1.html#K6" title="BVFUNC_1:func.6">'or'</a> <font color="Maroon" title="c6">b2</font></span>)</span> <a href="bvfunc_1.html#K6" title="BVFUNC_1:func.6">'or'</a> <font color="Maroon" title="c7">b3</font></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="margrel1.html#K15" title="MARGREL1:func.15">'not'</a> <font color="Maroon" title="c5">b1</font></span>)</span> <a href="margrel1.html#K16" title="MARGREL1:func.16">'&amp;'</a> <span class="p3">(<span class="default"><a href="margrel1.html#K15" title="MARGREL1:func.15">'not'</a> <font color="Maroon" title="c6">b2</font></span>)</span></span>)</span> <a href="margrel1.html#K16" title="MARGREL1:func.16">'&amp;'</a> <font color="Maroon" title="c4">a3</font></span>)</span> <a href="bvfunc_1.html#K12" title="BVFUNC_1:func.12">'imp'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="margrel1.html#K15" title="MARGREL1:func.15">'not'</a> <font color="Maroon" title="c2">a1</font></span>)</span> <a href="bvfunc_1.html#K6" title="BVFUNC_1:func.6">'or'</a> <span class="p3">(<span class="default"><a href="margrel1.html#K15" title="MARGREL1:func.15">'not'</a> <font color="Maroon" title="c3">a2</font></span>)</span></span>)</span> <a href="bvfunc_1.html#K6" title="BVFUNC_1:func.6">'or'</a> <font color="Maroon" title="c7">b3</font></span>)</span></span><br/>



<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="margrel1.html#K15" title="MARGREL1:func.15">'not'</a> <font color="Maroon" title="c5">b1</font></span>)</span> <a href="margrel1.html#K16" title="MARGREL1:func.16">'&amp;'</a> <span class="p3">(<span class="default"><a href="margrel1.html#K15" title="MARGREL1:func.15">'not'</a> <font color="Maroon" title="c6">b2</font></span>)</span></span>)</span> <a href="margrel1.html#K16" title="MARGREL1:func.16">'&amp;'</a> <font color="Maroon" title="c4">a3</font></span>)</span> <a href="bvfunc_1.html#K12" title="BVFUNC_1:func.12">'imp'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="margrel1.html#K15" title="MARGREL1:func.15">'not'</a> <font color="Maroon" title="c2">a1</font></span>)</span> <a href="bvfunc_1.html#K6" title="BVFUNC_1:func.6">'or'</a> <span class="p3">(<span class="default"><a href="margrel1.html#K15" title="MARGREL1:func.15">'not'</a> <font color="Maroon" title="c3">a2</font></span>)</span></span>)</span> <a href="bvfunc_1.html#K6" title="BVFUNC_1:func.6">'or'</a> <font color="Maroon" title="c7">b3</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="margrel1.html#K15" title="MARGREL1:func.15">'not'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="margrel1.html#K15" title="MARGREL1:func.15">'not'</a> <font color="Maroon" title="c5">b1</font></span>)</span> <a href="margrel1.html#K16" title="MARGREL1:func.16">'&amp;'</a> <span class="p4">(<span class="default"><a href="margrel1.html#K15" title="MARGREL1:func.15">'not'</a> <font color="Maroon" title="c6">b2</font></span>)</span></span>)</span> <a href="margrel1.html#K16" title="MARGREL1:func.16">'&amp;'</a> <font color="Maroon" title="c4">a3</font></span>)</span></span>)</span> <a href="bvfunc_1.html#K6" title="BVFUNC_1:func.6">'or'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="margrel1.html#K15" title="MARGREL1:func.15">'not'</a> <font color="Maroon" title="c2">a1</font></span>)</span> <a href="bvfunc_1.html#K6" title="BVFUNC_1:func.6">'or'</a> <span class="p3">(<span class="default"><a href="margrel1.html#K15" title="MARGREL1:func.15">'not'</a> <font color="Maroon" title="c3">a2</font></span>)</span></span>)</span> <a href="bvfunc_1.html#K6" title="BVFUNC_1:func.6">'or'</a> <font color="Maroon" title="c7">b3</font></span>)</span>
<b>by </b><i><a class="ref" href="bvfunc_4.html#T8" title="BVFUNC_4:th.8">BVFUNC_4:8</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="margrel1.html#K15" title="MARGREL1:func.15">'not'</a> <span class="p4">(<span class="default"><a href="margrel1.html#K15" title="MARGREL1:func.15">'not'</a> <font color="Maroon" title="c5">b1</font></span>)</span></span>)</span> <a href="bvfunc_1.html#K6" title="BVFUNC_1:func.6">'or'</a> <span class="p3">(<span class="default"><a href="margrel1.html#K15" title="MARGREL1:func.15">'not'</a> <span class="p4">(<span class="default"><a href="margrel1.html#K15" title="MARGREL1:func.15">'not'</a> <font color="Maroon" title="c6">b2</font></span>)</span></span>)</span></span>)</span> <a href="bvfunc_1.html#K6" title="BVFUNC_1:func.6">'or'</a> <span class="p2">(<span class="default"><a href="margrel1.html#K15" title="MARGREL1:func.15">'not'</a> <font color="Maroon" title="c4">a3</font></span>)</span></span>)</span> <a href="bvfunc_1.html#K6" title="BVFUNC_1:func.6">'or'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="margrel1.html#K15" title="MARGREL1:func.15">'not'</a> <font color="Maroon" title="c2">a1</font></span>)</span> <a href="bvfunc_1.html#K6" title="BVFUNC_1:func.6">'or'</a> <span class="p3">(<span class="default"><a href="margrel1.html#K15" title="MARGREL1:func.15">'not'</a> <font color="Maroon" title="c3">a2</font></span>)</span></span>)</span> <a href="bvfunc_1.html#K6" title="BVFUNC_1:func.6">'or'</a> <font color="Maroon" title="c7">b3</font></span>)</span>
<b>by </b><i><a class="ref" href="bvfunc_5.html#T38" title="BVFUNC_5:th.38">BVFUNC_5:38</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c5">b1</font> <a href="bvfunc_1.html#K6" title="BVFUNC_1:func.6">'or'</a> <font color="Maroon" title="c6">b2</font></span>)</span> <a href="bvfunc_1.html#K6" title="BVFUNC_1:func.6">'or'</a> <span class="p3">(<span class="default"><a href="margrel1.html#K15" title="MARGREL1:func.15">'not'</a> <font color="Maroon" title="c4">a3</font></span>)</span></span>)</span> <a href="bvfunc_1.html#K6" title="BVFUNC_1:func.6">'or'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="margrel1.html#K15" title="MARGREL1:func.15">'not'</a> <font color="Maroon" title="c2">a1</font></span>)</span> <a href="bvfunc_1.html#K6" title="BVFUNC_1:func.6">'or'</a> <span class="p3">(<span class="default"><a href="margrel1.html#K15" title="MARGREL1:func.15">'not'</a> <font color="Maroon" title="c3">a2</font></span>)</span></span>)</span></span>)</span> <a href="bvfunc_1.html#K6" title="BVFUNC_1:func.6">'or'</a> <font color="Maroon" title="c7">b3</font>
<b>by </b><i><a class="ref" href="bvfunc_1.html#T11" title="BVFUNC_1:th.11">BVFUNC_1:11</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">b1</font> <a href="bvfunc_1.html#K6" title="BVFUNC_1:func.6">'or'</a> <font color="Maroon" title="c6">b2</font></span>)</span> <a href="bvfunc_1.html#K6" title="BVFUNC_1:func.6">'or'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="margrel1.html#K15" title="MARGREL1:func.15">'not'</a> <font color="Maroon" title="c2">a1</font></span>)</span> <a href="bvfunc_1.html#K6" title="BVFUNC_1:func.6">'or'</a> <span class="p4">(<span class="default"><a href="margrel1.html#K15" title="MARGREL1:func.15">'not'</a> <font color="Maroon" title="c3">a2</font></span>)</span></span>)</span> <a href="bvfunc_1.html#K6" title="BVFUNC_1:func.6">'or'</a> <span class="p3">(<span class="default"><a href="margrel1.html#K15" title="MARGREL1:func.15">'not'</a> <font color="Maroon" title="c4">a3</font></span>)</span></span>)</span></span>)</span> <a href="bvfunc_1.html#K6" title="BVFUNC_1:func.6">'or'</a> <font color="Maroon" title="c7">b3</font>
<b>by </b><i><a class="ref" href="bvfunc_1.html#T11" title="BVFUNC_1:th.11">BVFUNC_1:11</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="margrel1.html#K15" title="MARGREL1:func.15">'not'</a> <font color="Maroon" title="c2">a1</font></span>)</span> <a href="bvfunc_1.html#K6" title="BVFUNC_1:func.6">'or'</a> <span class="p3">(<span class="default"><a href="margrel1.html#K15" title="MARGREL1:func.15">'not'</a> <font color="Maroon" title="c3">a2</font></span>)</span></span>)</span> <a href="bvfunc_1.html#K6" title="BVFUNC_1:func.6">'or'</a> <span class="p2">(<span class="default"><a href="margrel1.html#K15" title="MARGREL1:func.15">'not'</a> <font color="Maroon" title="c4">a3</font></span>)</span></span>)</span> <a href="bvfunc_1.html#K6" title="BVFUNC_1:func.6">'or'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">b1</font> <a href="bvfunc_1.html#K6" title="BVFUNC_1:func.6">'or'</a> <font color="Maroon" title="c6">b2</font></span>)</span> <a href="bvfunc_1.html#K6" title="BVFUNC_1:func.6">'or'</a> <font color="Maroon" title="c7">b3</font></span>)</span>
<b>by </b><i><a class="ref" href="bvfunc_1.html#T11" title="BVFUNC_1:th.11">BVFUNC_1:11</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="margrel1.html#K15" title="MARGREL1:func.15">'not'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">a1</font> <a href="margrel1.html#K16" title="MARGREL1:func.16">'&amp;'</a> <font color="Maroon" title="c3">a2</font></span>)</span> <a href="margrel1.html#K16" title="MARGREL1:func.16">'&amp;'</a> <font color="Maroon" title="c4">a3</font></span>)</span></span>)</span> <a href="bvfunc_1.html#K6" title="BVFUNC_1:func.6">'or'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">b1</font> <a href="bvfunc_1.html#K6" title="BVFUNC_1:func.6">'or'</a> <font color="Maroon" title="c6">b2</font></span>)</span> <a href="bvfunc_1.html#K6" title="BVFUNC_1:func.6">'or'</a> <font color="Maroon" title="c7">b3</font></span>)</span>
<b>by </b><i><a class="ref" href="bvfunc_5.html#T38" title="BVFUNC_5:th.38">BVFUNC_5:38</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">a1</font> <a href="margrel1.html#K16" title="MARGREL1:func.16">'&amp;'</a> <font color="Maroon" title="c3">a2</font></span>)</span> <a href="margrel1.html#K16" title="MARGREL1:func.16">'&amp;'</a> <font color="Maroon" title="c4">a3</font></span>)</span> <a href="bvfunc_1.html#K12" title="BVFUNC_1:func.12">'imp'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">b1</font> <a href="bvfunc_1.html#K6" title="BVFUNC_1:func.6">'or'</a> <font color="Maroon" title="c6">b2</font></span>)</span> <a href="bvfunc_1.html#K6" title="BVFUNC_1:func.6">'or'</a> <font color="Maroon" title="c7">b3</font></span>)</span>
<b>by </b><i><a class="ref" href="bvfunc_4.html#T8" title="BVFUNC_4:th.8">BVFUNC_4:8</a></i>
;<br/>
<b>hence </b><a NAME="E2:16"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">a1</font> <a href="margrel1.html#K16" title="MARGREL1:func.16">'&amp;'</a> <font color="Maroon" title="c3">a2</font></span>)</span> <a href="margrel1.html#K16" title="MARGREL1:func.16">'&amp;'</a> <font color="Maroon" title="c4">a3</font></span>)</span> <a href="bvfunc_1.html#K12" title="BVFUNC_1:func.12">'imp'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">b1</font> <a href="bvfunc_1.html#K6" title="BVFUNC_1:func.6">'or'</a> <font color="Maroon" title="c6">b2</font></span>)</span> <a href="bvfunc_1.html#K6" title="BVFUNC_1:func.6">'or'</a> <font color="Maroon" title="c7">b3</font></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="margrel1.html#K15" title="MARGREL1:func.15">'not'</a> <font color="Maroon" title="c5">b1</font></span>)</span> <a href="margrel1.html#K16" title="MARGREL1:func.16">'&amp;'</a> <span class="p3">(<span class="default"><a href="margrel1.html#K15" title="MARGREL1:func.15">'not'</a> <font color="Maroon" title="c6">b2</font></span>)</span></span>)</span> <a href="margrel1.html#K16" title="MARGREL1:func.16">'&amp;'</a> <font color="Maroon" title="c4">a3</font></span>)</span> <a href="bvfunc_1.html#K12" title="BVFUNC_1:func.12">'imp'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="margrel1.html#K15" title="MARGREL1:func.15">'not'</a> <font color="Maroon" title="c2">a1</font></span>)</span> <a href="bvfunc_1.html#K6" title="BVFUNC_1:func.6">'or'</a> <span class="p3">(<span class="default"><a href="margrel1.html#K15" title="MARGREL1:func.15">'not'</a> <font color="Maroon" title="c3">a2</font></span>)</span></span>)</span> <a href="bvfunc_1.html#K6" title="BVFUNC_1:func.6">'or'</a> <font color="Maroon" title="c7">b3</font></span>)</span>
 ; <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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