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<b>let </b><font color="Maroon">c<sub>1</sub></font> be  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font>, <font color="Maroon">c<sub>5</sub></font>, <font color="Maroon">c<sub>6</sub></font>, <font color="Maroon">c<sub>7</sub></font>, <font color="Maroon">c<sub>8</sub></font> be    <a href="fraenkel.html#M2">Element</a> of  <a href="fraenkel.html#K1">Funcs</a> <font color="Maroon">c<sub>1</sub></font>,<a href="margrel1.html#K6">BOOLEAN</a> ;<br/>



<a NAME="E1:7"/><i><font color="Green">E8</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">c<sub>2</sub></font> <a href="valuat_1.html#K6">'&amp;'</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="valuat_1.html#K6">'&amp;'</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="valuat_1.html#K6">'&amp;'</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="valuat_1.html#K6">'&amp;'</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="valuat_1.html#K6">'&amp;'</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="valuat_1.html#K6">'&amp;'</a> <font color="Maroon">c<sub>8</sub></font> <a href="bvfunc_1.html#R1">'&lt;'</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="bvfunc_9.html#E6"><i><font color="Green">Lemma6</font></i></a></i>;<br/>
<a NAME="E2:7"/><i><font color="Green">E9</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">c<sub>2</sub></font> <a href="valuat_1.html#K6">'&amp;'</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="valuat_1.html#K6">'&amp;'</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="valuat_1.html#K6">'&amp;'</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="valuat_1.html#K6">'&amp;'</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="valuat_1.html#K6">'&amp;'</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="valuat_1.html#K6">'&amp;'</a> <font color="Maroon">c<sub>8</sub></font> <a href="bvfunc_1.html#R1">'&lt;'</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="txt" href="bvfunc_9.html#E6"><i><font color="Green">Lemma6</font></i></a></i>;<br/>
<a NAME="E3:7"/><i><font color="Green">E10</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">c<sub>2</sub></font> <a href="valuat_1.html#K6">'&amp;'</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="valuat_1.html#K6">'&amp;'</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="valuat_1.html#K6">'&amp;'</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="valuat_1.html#K6">'&amp;'</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="valuat_1.html#K6">'&amp;'</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="valuat_1.html#K6">'&amp;'</a> <font color="Maroon">c<sub>8</sub></font> <a href="bvfunc_1.html#R1">'&lt;'</a> <font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="txt" href="bvfunc_9.html#E5"><i><font color="Green">Lemma5</font></i></a></i>;<br/>
<a NAME="E4:7"/><i><font color="Green">E11</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">c<sub>2</sub></font> <a href="valuat_1.html#K6">'&amp;'</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="valuat_1.html#K6">'&amp;'</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="valuat_1.html#K6">'&amp;'</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="valuat_1.html#K6">'&amp;'</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="valuat_1.html#K6">'&amp;'</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="valuat_1.html#K6">'&amp;'</a> <font color="Maroon">c<sub>8</sub></font> <a href="bvfunc_1.html#R1">'&lt;'</a> <font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="txt" href="bvfunc_9.html#E4"><i><font color="Green">Lemma4</font></i></a></i>;<br/>
<a NAME="E5:7"/><i><font color="Green">E12</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">c<sub>2</sub></font> <a href="valuat_1.html#K6">'&amp;'</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="valuat_1.html#K6">'&amp;'</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="valuat_1.html#K6">'&amp;'</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="valuat_1.html#K6">'&amp;'</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="valuat_1.html#K6">'&amp;'</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="valuat_1.html#K6">'&amp;'</a> <font color="Maroon">c<sub>8</sub></font> <a href="bvfunc_1.html#R1">'&lt;'</a> <font color="Maroon">c<sub>6</sub></font>
 
<b>by </b><i><a class="txt" href="bvfunc_9.html#E3"><i><font color="Green">Lemma3</font></i></a></i>;<br/>
<a NAME="E6:7"/><i><font color="Green">E13</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">c<sub>2</sub></font> <a href="valuat_1.html#K6">'&amp;'</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="valuat_1.html#K6">'&amp;'</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="valuat_1.html#K6">'&amp;'</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="valuat_1.html#K6">'&amp;'</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="valuat_1.html#K6">'&amp;'</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="valuat_1.html#K6">'&amp;'</a> <font color="Maroon">c<sub>8</sub></font> <a href="bvfunc_1.html#R1">'&lt;'</a> <font color="Maroon">c<sub>7</sub></font>
 
<b>by </b><i><a class="txt" href="bvfunc_9.html#E2"><i><font color="Green">Lemma2</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">c<sub>2</sub></font> <a href="valuat_1.html#K6">'&amp;'</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="valuat_1.html#K6">'&amp;'</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="valuat_1.html#K6">'&amp;'</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="valuat_1.html#K6">'&amp;'</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="valuat_1.html#K6">'&amp;'</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="valuat_1.html#K6">'&amp;'</a> <font color="Maroon">c<sub>8</sub></font> <a href="bvfunc_1.html#R1">'&lt;'</a> <font color="Maroon">c<sub>8</sub></font>
 
<b>by </b><i><a class="txt" href="bvfunc_9.html#E1"><i><font color="Green">Lemma1</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">c<sub>2</sub></font> <a href="valuat_1.html#K6">'&amp;'</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="valuat_1.html#K6">'&amp;'</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="valuat_1.html#K6">'&amp;'</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="valuat_1.html#K6">'&amp;'</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="valuat_1.html#K6">'&amp;'</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="valuat_1.html#K6">'&amp;'</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="bvfunc_1.html#K14">'imp'</a> <font color="Maroon">c<sub>2</sub></font> <a href="funct_2.html#R2">=</a>  <a href="bvfunc_1.html#K19">I_el</a> <font color="Maroon">c<sub>1</sub></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">c<sub>2</sub></font> <a href="valuat_1.html#K6">'&amp;'</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="valuat_1.html#K6">'&amp;'</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="valuat_1.html#K6">'&amp;'</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="valuat_1.html#K6">'&amp;'</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="valuat_1.html#K6">'&amp;'</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="valuat_1.html#K6">'&amp;'</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="bvfunc_1.html#K14">'imp'</a> <font color="Maroon">c<sub>3</sub></font> <a href="funct_2.html#R2">=</a>  <a href="bvfunc_1.html#K19">I_el</a> <font color="Maroon">c<sub>1</sub></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">c<sub>2</sub></font> <a href="valuat_1.html#K6">'&amp;'</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="valuat_1.html#K6">'&amp;'</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="valuat_1.html#K6">'&amp;'</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="valuat_1.html#K6">'&amp;'</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="valuat_1.html#K6">'&amp;'</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="valuat_1.html#K6">'&amp;'</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="bvfunc_1.html#K14">'imp'</a> <font color="Maroon">c<sub>4</sub></font> <a href="funct_2.html#R2">=</a>  <a href="bvfunc_1.html#K19">I_el</a> <font color="Maroon">c<sub>1</sub></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">c<sub>2</sub></font> <a href="valuat_1.html#K6">'&amp;'</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="valuat_1.html#K6">'&amp;'</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="valuat_1.html#K6">'&amp;'</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="valuat_1.html#K6">'&amp;'</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="valuat_1.html#K6">'&amp;'</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="valuat_1.html#K6">'&amp;'</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="bvfunc_1.html#K14">'imp'</a> <font color="Maroon">c<sub>5</sub></font> <a href="funct_2.html#R2">=</a>  <a href="bvfunc_1.html#K19">I_el</a> <font color="Maroon">c<sub>1</sub></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">c<sub>2</sub></font> <a href="valuat_1.html#K6">'&amp;'</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="valuat_1.html#K6">'&amp;'</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="valuat_1.html#K6">'&amp;'</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="valuat_1.html#K6">'&amp;'</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="valuat_1.html#K6">'&amp;'</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="valuat_1.html#K6">'&amp;'</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="bvfunc_1.html#K14">'imp'</a> <font color="Maroon">c<sub>6</sub></font> <a href="funct_2.html#R2">=</a>  <a href="bvfunc_1.html#K19">I_el</a> <font color="Maroon">c<sub>1</sub></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">c<sub>2</sub></font> <a href="valuat_1.html#K6">'&amp;'</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="valuat_1.html#K6">'&amp;'</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="valuat_1.html#K6">'&amp;'</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="valuat_1.html#K6">'&amp;'</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="valuat_1.html#K6">'&amp;'</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="valuat_1.html#K6">'&amp;'</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="bvfunc_1.html#K14">'imp'</a> <font color="Maroon">c<sub>7</sub></font> <a href="funct_2.html#R2">=</a>  <a href="bvfunc_1.html#K19">I_el</a> <font color="Maroon">c<sub>1</sub></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">c<sub>2</sub></font> <a href="valuat_1.html#K6">'&amp;'</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="valuat_1.html#K6">'&amp;'</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="valuat_1.html#K6">'&amp;'</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="valuat_1.html#K6">'&amp;'</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="valuat_1.html#K6">'&amp;'</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="valuat_1.html#K6">'&amp;'</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="bvfunc_1.html#K14">'imp'</a> <font color="Maroon">c<sub>8</sub></font> <a href="funct_2.html#R2">=</a>  <a href="bvfunc_1.html#K19">I_el</a> <font color="Maroon">c<sub>1</sub></font> )
 <b>by </b><i><a class="txt" href="bvfunc_9.html#E1:7"><i><font color="Green">E8</font></i></a>, <a class="txt" href="bvfunc_9.html#E2:7"><i><font color="Green">E9</font></i></a>, <a class="txt" href="bvfunc_9.html#E3:7"><i><font color="Green">E10</font></i></a>, <a class="txt" href="bvfunc_9.html#E4:7"><i><font color="Green">E11</font></i></a>, <a class="txt" href="bvfunc_9.html#E5:7"><i><font color="Green">E12</font></i></a>, <a class="txt" href="bvfunc_9.html#E6:7"><i><font color="Green">E13</font></i></a>, <a class="ref" href="bvfunc_1.html#T19">BVFUNC_1:19</a></i>;<br/>


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