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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> be   <a href="subset_1.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="bvfunc_2.html#K1">PARTITIONS</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>;<br/><b>let </b><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> be    <a href="eqrel_1.html#M1">a_partition</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>7</sub></font>, <font color="Maroon">c<sub>8</sub></font> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>













<b>assume </b><a NAME="E1:19"/><i><font color="Green">E13</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> is <a href="bvfunc_2.html#V2">independent</a> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="enumset1.html#K2">{</a><span class="default"><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></span><a href="enumset1.html#K2">}</a></span> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>4</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>6</sub></font> &amp;  <a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>7</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> )
 ;<br/>

<a NAME="E2:19"/><b>then </b><i><font color="Green">E14</font></i>: 
 <a href="bvfunc_2.html#K5">CompF</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">c<sub>6</sub></font>
 
<b>by </b><i><a class="ref" href="bvfunc14.html#T8" target="_self">Th8</a></i>;<br/>
<b>set </b><font color="Maroon">c<sub>9</sub></font> =  <a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>7</sub></font>,<span class="p1">(<span class="default"><a href="bvfunc_2.html#K5">CompF</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>;<br/>
<b>set </b><font color="Maroon">c<sub>10</sub></font> =  <a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>3</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>11</sub></font> =  <a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">c<sub>6</sub></font></span>)</span>;<br/>
<b>set </b><font color="Maroon">c<sub>12</sub></font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p2">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span>;<br/>
<a NAME="E3:19"/><i><font color="Green">E15</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p5">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p5">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="bvfunc14.html#E1:19"><i><font color="Green">E13</font></i></a>, <a class="ref" href="bvfunc14.html#T19" target="_self">Th19</a></i>;<br/>
<a NAME="E4:19"/><i><font color="Green">E16</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"><font color="Maroon">c<sub>4</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p5">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p5">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="ref" href="yellow14.html#T3">YELLOW14:3</a></i>;<br/>
<a NAME="E5:19"/><i><font color="Green">E17</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"><font color="Maroon">c<sub>4</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p5">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p5">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a>  <a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="txt" href="bvfunc14.html#E1:19"><i><font color="Green">E13</font></i></a>, <a class="ref" href="bvfunc14.html#T18" target="_self">Th18</a></i>;<br/>
<a NAME="E6:19"/><i><font color="Green">E18</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"><font color="Maroon">c<sub>4</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p5">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p5">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a>  <a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="txt" href="bvfunc14.html#E1:19"><i><font color="Green">E13</font></i></a>, <a class="ref" href="bvfunc14.html#T18" target="_self">Th18</a></i>;<br/>
<a NAME="E7:19"/><i><font color="Green">E19</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"><font color="Maroon">c<sub>4</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p5">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p5">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a>  <a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>6</sub></font>
 
<b>by </b><i><a class="txt" href="bvfunc14.html#E1:19"><i><font color="Green">E13</font></i></a>, <a class="ref" href="bvfunc14.html#T18" target="_self">Th18</a></i>;<br/>
<a NAME="E8:19"/><i><font color="Green">E20</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> holds <br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p5">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p5">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Olive">b<sub>1</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="19_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>13</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><a NAME="E1:19_1"/><i><font color="Green">E21</font></i>: 
<font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="19_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:19_1_1"/>
( <font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> or <font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> or <font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> or <font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font> )
 </span><b>by </b><i><a class="txt" href="bvfunc14.html#E1:19"><i><font color="Green">E13</font></i></a>, <a class="txt" href="bvfunc14.html#E1:19_1"><i><font color="Green">E21</font></i></a>, <a class="ref" href="enumset1.html#D2">ENUMSET1:def 2</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="19_1_1_1"><b>suppose </b></a><a NAME="E1:19_1_1_1"/><i><font color="Green">E22</font></i>: 
<font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/><div class="add"><a NAME="E2:19_1_1_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p5">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p5">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="ref" href="yellow14.html#T3">YELLOW14:3</a></i>;<br/><b>hence </b><a NAME="E3:19_1_1_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p5">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p5">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>13</sub></font>
 <b>by </b><i><a class="txt" href="bvfunc14.html#E1:19_1_1_1"><i><font color="Green">E22</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="19_1_1_2"><b>suppose </b></a><a NAME="E1:19_1_1_2"/><i><font color="Green">E22</font></i>: 
<font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font>
 ;<br/><div class="add"><a NAME="E2:19_1_1_2"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p5">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p5">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a>  <a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="txt" href="bvfunc14.html#E1:19"><i><font color="Green">E13</font></i></a>, <a class="ref" href="bvfunc14.html#T18" target="_self">Th18</a></i>;<br/><b>hence </b><a NAME="E3:19_1_1_2"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p5">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p5">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>13</sub></font>
 <b>by </b><i><a class="txt" href="bvfunc14.html#E1:19_1_1_2"><i><font color="Green">E22</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="19_1_1_3"><b>suppose </b></a><a NAME="E1:19_1_1_3"/><i><font color="Green">E22</font></i>: 
<font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font>
 ;<br/><div class="add"><a NAME="E2:19_1_1_3"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p5">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p5">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a>  <a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="txt" href="bvfunc14.html#E1:19"><i><font color="Green">E13</font></i></a>, <a class="ref" href="bvfunc14.html#T18" target="_self">Th18</a></i>;<br/><b>hence </b><a NAME="E3:19_1_1_3"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p5">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p5">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>13</sub></font>
 <b>by </b><i><a class="txt" href="bvfunc14.html#E1:19_1_1_3"><i><font color="Green">E22</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="19_1_1_4"><b>suppose </b></a><a NAME="E1:19_1_1_4"/><i><font color="Green">E22</font></i>: 
<font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font>
 ;<br/><div class="add"><a NAME="E2:19_1_1_4"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p5">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p5">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a>  <a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="txt" href="bvfunc14.html#E1:19"><i><font color="Green">E13</font></i></a>, <a class="ref" href="bvfunc14.html#T18" target="_self">Th18</a></i>;<br/><b>hence </b><a NAME="E3:19_1_1_4"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p5">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p5">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>13</sub></font>
 <b>by </b><i><a class="txt" href="bvfunc14.html#E1:19_1_1_4"><i><font color="Green">E22</font></i></a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div>
<a NAME="E9:19"/>
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p5">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p5">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="bvfunc14.html#E1:19"><i><font color="Green">E13</font></i></a>, <a class="txt" href="bvfunc14.html#E3:19"><i><font color="Green">E15</font></i></a>, <a class="ref" href="enumset1.html#D2">ENUMSET1:def 2</a></i>;<br/>
<a NAME="E10:19"/><b>then </b><i><font color="Green">E21</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"><font color="Maroon">c<sub>4</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p5">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p5">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p5">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p5">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/>
<a NAME="E11:19"/>
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p5">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p5">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="bvfunc14.html#E1:19"><i><font color="Green">E13</font></i></a>, <a class="txt" href="bvfunc14.html#E3:19"><i><font color="Green">E15</font></i></a>, <a class="ref" href="enumset1.html#D2">ENUMSET1:def 2</a></i>;<br/>
<a NAME="E12:19"/><b>then </b><i><font color="Green">E22</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"><font color="Maroon">c<sub>4</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p5">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p5">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p5">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p5">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/>
<a NAME="E13:19"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p5">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p5">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="bvfunc14.html#E1:19"><i><font color="Green">E13</font></i></a>, <a class="txt" href="bvfunc14.html#E3:19"><i><font color="Green">E15</font></i></a>, <a class="ref" href="enumset1.html#D2">ENUMSET1:def 2</a></i>;<br/>
<a NAME="E14:19"/><b>then </b><i><font color="Green">E23</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"><font color="Maroon">c<sub>4</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p5">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p5">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p5">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p5">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/>
<a NAME="E15:19"/>
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p5">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p5">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="bvfunc14.html#E1:19"><i><font color="Green">E13</font></i></a>, <a class="txt" href="bvfunc14.html#E3:19"><i><font color="Green">E15</font></i></a>, <a class="ref" href="enumset1.html#D2">ENUMSET1:def 2</a></i>;<br/>
<a NAME="E16:19"/><b>then </b><i><font color="Green">E24</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"><font color="Maroon">c<sub>4</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p5">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p5">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p5">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p5">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/>
<a NAME="E17:19"/><i><font color="Green">E25</font></i>: 
 <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p5">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p5">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="enumset1.html#K2">{</a><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>4</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p1">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p1">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p0">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p5">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>,<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>4</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p1">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p1">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p0">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p5">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>,<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>4</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p1">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p1">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p0">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p5">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>,<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>4</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p1">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p1">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p0">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p5">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span><a href="enumset1.html#K2">}</a></span>
 
<b>by </b><i><a class="txt" href="bvfunc14.html#E1:19"><i><font color="Green">E13</font></i></a>, <a class="ref" href="bvfunc14.html#T20" target="_self">Th20</a></i>;<br/>
<a NAME="E18:19"/>
 <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p5">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p5">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="zfmisc_1.html#K1">bool</a> <font color="Maroon">c<sub>1</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="19_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>13</sub></font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:19_2"/><i><font color="Green">E26</font></i>: 
<font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p5">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p5">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span>
 ;<br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="19_2_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:19_2_1"/>
( <font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p5">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p5">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>3</sub></font> or <font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p5">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p5">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>4</sub></font> or <font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p5">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p5">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>5</sub></font> or <font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p5">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p5">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>6</sub></font> )
 </span><b>by </b><i><a class="txt" href="bvfunc14.html#E17:19"><i><font color="Green">E25</font></i></a>, <a class="txt" href="bvfunc14.html#E1:19_2"><i><font color="Green">E26</font></i></a>, <a class="ref" href="enumset1.html#D2">ENUMSET1:def 2</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="19_2_1_1"><b>suppose </b></a><a NAME="E1:19_2_1_1"/>
<font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p5">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p5">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/><div class="add"><a NAME="E2:19_2_1_1"/><b>then </b>
<font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#R1">=</a>  <a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="ref" href="yellow14.html#T3">YELLOW14:3</a></i>;<br/><b>hence </b><a NAME="E3:19_2_1_1"/>
<font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#R2">in</a>  <a href="zfmisc_1.html#K1">bool</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="19_2_1_2"><b>suppose </b></a><a NAME="E1:19_2_1_2"/>
<font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p5">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p5">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>4</sub></font>
 ;<br/><div class="add"><a NAME="E2:19_2_1_2"/><b>then </b>
<font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#R1">=</a>  <a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="txt" href="bvfunc14.html#E1:19"><i><font color="Green">E13</font></i></a>, <a class="ref" href="bvfunc14.html#T18" target="_self">Th18</a></i>;<br/><b>hence </b><a NAME="E3:19_2_1_2"/>
<font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#R2">in</a>  <a href="zfmisc_1.html#K1">bool</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="19_2_1_3"><b>suppose </b></a><a NAME="E1:19_2_1_3"/>
<font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p5">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p5">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>5</sub></font>
 ;<br/><div class="add"><a NAME="E2:19_2_1_3"/><b>then </b>
<font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#R1">=</a>  <a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="txt" href="bvfunc14.html#E1:19"><i><font color="Green">E13</font></i></a>, <a class="ref" href="bvfunc14.html#T18" target="_self">Th18</a></i>;<br/><b>hence </b><a NAME="E3:19_2_1_3"/>
<font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#R2">in</a>  <a href="zfmisc_1.html#K1">bool</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="19_2_1_4"><b>suppose </b></a><a NAME="E1:19_2_1_4"/>
<font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p5">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p5">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>6</sub></font>
 ;<br/><div class="add"><a NAME="E2:19_2_1_4"/><b>then </b>
<font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#R1">=</a>  <a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="txt" href="bvfunc14.html#E1:19"><i><font color="Green">E13</font></i></a>, <a class="ref" href="bvfunc14.html#T18" target="_self">Th18</a></i>;<br/><b>hence </b><a NAME="E3:19_2_1_4"/>
<font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#R2">in</a>  <a href="zfmisc_1.html#K1">bool</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div>
<b>then reconsider </b><font color="Maroon">c<sub>13</sub></font> =  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p5">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p5">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span> as   <a href="setfam_1.html#NM1">Subset-Family</a> of <font color="Maroon">c<sub>1</sub></font> ;<br/>
<a NAME="E20:19"/>
(  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p5">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p5">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> &amp;  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p5">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p5">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>13</sub></font> &amp; ( for <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> holds <br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p5">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p5">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Olive">b<sub>1</sub></font> ) )
 
<b>by </b><i><a class="txt" href="bvfunc14.html#E1:19"><i><font color="Green">E13</font></i></a>, <a class="txt" href="bvfunc14.html#E8:19"><i><font color="Green">E20</font></i></a>, <a class="ref" href="bvfunc14.html#T19" target="_self">Th19</a></i>;<br/>
<a NAME="E21:19"/><b>then </b>
 <a href="setfam_1.html#K8">Intersect</a> <font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i><a class="txt" href="bvfunc14.html#E1:19"><i><font color="Green">E13</font></i></a>, <a class="ref" href="bvfunc_2.html#D5">BVFUNC_2:def 5</a></i>;<br/>
<b>then consider </b><font color="Maroon">c<sub>14</sub></font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E23:19"/><i><font color="Green">E26</font></i>: 
<font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#R2">in</a>  <a href="setfam_1.html#K8">Intersect</a> <font color="Maroon">c<sub>13</sub></font>
 <b>by </b><i><a class="ref" href="xboole_0.html#D1">XBOOLE_0:def 1</a></i>;<br/>
<a NAME="E24:19"/>
<font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#R2">in</a>  <a href="setfam_1.html#K6">meet</a> <font color="Maroon">c<sub>13</sub></font>
 
<b>by </b><i><a class="txt" href="bvfunc14.html#E10:19"><i><font color="Green">E21</font></i></a>, <a class="txt" href="bvfunc14.html#E23:19"><i><font color="Green">E26</font></i></a>, <a class="ref" href="setfam_1.html#D10">SETFAM_1:def 10</a></i>;<br/>
<a NAME="E25:19"/><b>then </b><i><font color="Green">E27</font></i>: 
( <font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p5">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p5">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p5">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p5">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>4</sub></font> &amp; <font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p5">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p5">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p5">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p5">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>6</sub></font> )
 
<b>by </b><i><a class="txt" href="bvfunc14.html#E10:19"><i><font color="Green">E21</font></i></a>, <a class="txt" href="bvfunc14.html#E12:19"><i><font color="Green">E22</font></i></a>, <a class="txt" href="bvfunc14.html#E14:19"><i><font color="Green">E23</font></i></a>, <a class="txt" href="bvfunc14.html#E16:19"><i><font color="Green">E24</font></i></a>, <a class="ref" href="setfam_1.html#D1">SETFAM_1:def 1</a></i>;<br/>
<a NAME="E26:19"/><i><font color="Green">E28</font></i>: 
 <a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="bvfunc14.html#T1" target="_self">Th1</a></i>;<br/>
<a NAME="E27:19"/>
<font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="bvfunc14.html#E5:19"><i><font color="Green">E17</font></i></a>, <a class="txt" href="bvfunc14.html#E6:19"><i><font color="Green">E18</font></i></a>, <a class="txt" href="bvfunc14.html#E25:19"><i><font color="Green">E27</font></i></a>, <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/>
<a NAME="E28:19"/><b>then </b>
<font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p2">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="bvfunc14.html#E7:19"><i><font color="Green">E19</font></i></a>, <a class="txt" href="bvfunc14.html#E25:19"><i><font color="Green">E27</font></i></a>, <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/>
<a NAME="E29:19"/><b>then </b>
<font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p2">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="bvfunc14.html#E4:19"><i><font color="Green">E16</font></i></a>, <a class="txt" href="bvfunc14.html#E25:19"><i><font color="Green">E27</font></i></a>, <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/>
<a NAME="E30:19"/><b>then </b>
<span class="p1">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i><a class="txt" href="bvfunc14.html#E26:19"><i><font color="Green">E28</font></i></a>, <a class="ref" href="bvfunc14.html#T1" target="_self">Th1</a></i>;<br/>
<b>then consider </b><font color="Maroon">c<sub>15</sub></font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E32:19"/><i><font color="Green">E29</font></i>: 
<font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="xboole_0.html#D1">XBOOLE_0:def 1</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>16</sub></font> = <font color="Maroon">c<sub>15</sub></font> as    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">c<sub>1</sub></font> <b>by </b><i><a class="txt" href="bvfunc14.html#E32:19"><i><font color="Green">E29</font></i></a></i>;<br/>
<b>set </b><font color="Maroon">c<sub>17</sub></font> =  <a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>16</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">c<sub>6</sub></font></span>)</span>;<br/>
<a NAME="E34:19"/><i><font color="Green">E30</font></i>: 
( <font color="Maroon">c<sub>16</sub></font> <a href="hidden.html#R2">in</a>  <a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>16</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> &amp;  <a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>16</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>5</sub></font> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">c<sub>6</sub></font> )
 
<b>by </b><i><a class="ref" href="t_1topsp.html#D1">T_1TOPSP:def 1</a></i>;<br/>
<a NAME="E35:19"/><i><font color="Green">E31</font></i>: 
( <font color="Maroon">c<sub>16</sub></font> <a href="hidden.html#R2">in</a>  <a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> &amp; <font color="Maroon">c<sub>16</sub></font> <a href="hidden.html#R2">in</a>  <a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>3</sub></font> )
 
<b>by </b><i><a class="txt" href="bvfunc14.html#E32:19"><i><font color="Green">E29</font></i></a>, <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/>
<a NAME="E36:19"/><b>then </b>
<font color="Maroon">c<sub>16</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>16</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="bvfunc14.html#E34:19"><i><font color="Green">E30</font></i></a>, <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/>
<a NAME="E37:19"/><b>then </b>
( <span class="p1">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>16</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="hidden.html#R2">in</a>  <a href="setfam_1.html#K3">INTERSECTION</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> &amp; not <span class="p1">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>16</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><a href="xboole_0.html#K1">{}</a> </span><a href="tarski.html#K1">}</a></span> )
 
<b>by </b><i><a class="ref" href="setfam_1.html#D5">SETFAM_1:def 5</a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<a NAME="E38:19"/><b>then </b><i><font color="Green">E32</font></i>: 
<span class="p1">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>16</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="setfam_1.html#K3">INTERSECTION</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><a href="xboole_0.html#K1">{}</a> </span><a href="tarski.html#K1">}</a></span>
 
<b>by </b><i><a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/>
<b>set </b><font color="Maroon">c<sub>18</sub></font> =  <a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>7</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">c<sub>6</sub></font></span>)</span>;<br/>
<a NAME="E39:19"/>
 <a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="partit1.html#K2">'/\'</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="partit1.html#T16">PARTIT1:16</a></i>;<br/>
<a NAME="E40:19"/><b>then </b><i><font color="Green">E33</font></i>: 
 <a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">c<sub>6</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="bvfunc11.html#T3">BVFUNC11:3</a></i>;<br/>
<a NAME="E41:19"/><i><font color="Green">E34</font></i>: 
<font color="Maroon">c<sub>16</sub></font> <a href="hidden.html#R2">in</a>  <a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">c<sub>6</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="bvfunc14.html#E32:19"><i><font color="Green">E29</font></i></a>, <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/>
<a NAME="E42:19"/>
<font color="Maroon">c<sub>16</sub></font> <a href="hidden.html#R2">in</a>  <a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>16</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">c<sub>6</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="t_1topsp.html#D1">T_1TOPSP:def 1</a></i>;<br/>
<a NAME="E43:19"/><b>then </b>
 <a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>16</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="xboole_0.html#NR5" target="_self">meets</a>  <a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>7</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">c<sub>6</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="bvfunc14.html#E1:19"><i><font color="Green">E13</font></i></a>, <a class="txt" href="bvfunc14.html#E40:19"><i><font color="Green">E33</font></i></a>, <a class="txt" href="bvfunc14.html#E41:19"><i><font color="Green">E34</font></i></a>, <a class="ref" href="xboole_0.html#T3">XBOOLE_0:3</a></i>;<br/>
<a NAME="E44:19"/><b>then </b>
 <a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>16</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>7</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">c<sub>6</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="t_1topsp.html#T9">T_1TOPSP:9</a></i>;<br/>
<a NAME="E45:19"/><b>then </b><i><font color="Green">E35</font></i>: 
<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R2">in</a>  <a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>16</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">c<sub>6</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="t_1topsp.html#D1">T_1TOPSP:def 1</a></i>;<br/>
<a NAME="E46:19"/>
<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R2">in</a>  <a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="ref" href="t_1topsp.html#D1">T_1TOPSP:def 1</a></i>;<br/>
<a NAME="E47:19"/><b>then </b><i><font color="Green">E36</font></i>: 
<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>16</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="bvfunc14.html#E45:19"><i><font color="Green">E35</font></i></a>, <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/>
<a NAME="E48:19"/><i><font color="Green">E37</font></i>: 
<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R2">in</a>  <a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>7</sub></font>,<span class="p1">(<span class="default"><a href="bvfunc_2.html#K5">CompF</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="t_1topsp.html#D1">T_1TOPSP:def 1</a></i>;<br/>
<a NAME="E49:19"/>
<font color="Maroon">c<sub>3</sub></font> <a href="partit1.html#K2">'/\'</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">c<sub>6</sub></font>
 
<b>by </b><i><a class="ref" href="partit1.html#T16">PARTIT1:16</a></i>;<br/>
<a NAME="E50:19"/><b>then </b>
<span class="p1">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>16</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="hidden.html#R2">in</a>  <a href="bvfunc_2.html#K5">CompF</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="bvfunc14.html#E2:19"><i><font color="Green">E14</font></i></a>, <a class="txt" href="bvfunc14.html#E38:19"><i><font color="Green">E32</font></i></a>, <a class="ref" href="partit1.html#D4">PARTIT1:def 4</a></i>;<br/>
<a NAME="E51:19"/><b>then </b>
( <span class="p1">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>16</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>7</sub></font>,<span class="p1">(<span class="default"><a href="bvfunc_2.html#K5">CompF</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> or <span class="p1">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>16</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="xboole_0.html#R1">misses</a>  <a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>7</sub></font>,<span class="p1">(<span class="default"><a href="bvfunc_2.html#K5">CompF</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> )
 
<b>by </b><i><a class="ref" href="eqrel_1.html#D6">EQREL_1:def 6</a></i>;<br/>
<a NAME="E52:19"/><b>then </b>
<font color="Maroon">c<sub>16</sub></font> <a href="hidden.html#R2">in</a>  <a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>7</sub></font>,<span class="p1">(<span class="default"><a href="bvfunc_2.html#K5">CompF</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="bvfunc14.html#E34:19"><i><font color="Green">E30</font></i></a>, <a class="txt" href="bvfunc14.html#E35:19"><i><font color="Green">E31</font></i></a>, <a class="txt" href="bvfunc14.html#E47:19"><i><font color="Green">E36</font></i></a>, <a class="txt" href="bvfunc14.html#E48:19"><i><font color="Green">E37</font></i></a>, <a class="ref" href="xboole_0.html#T3">XBOOLE_0:3</a>, <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/>
<a NAME="E53:19"/><b>then </b>
<font color="Maroon">c<sub>16</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>7</sub></font>,<span class="p2">(<span class="default"><a href="bvfunc_2.html#K5">CompF</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="bvfunc14.html#E41:19"><i><font color="Green">E34</font></i></a>, <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/>
<a NAME="E54:19"/><b>then </b>
 <a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="xboole_0.html#NR5" target="_self">meets</a>  <a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>7</sub></font>,<span class="p1">(<span class="default"><a href="bvfunc_2.html#K5">CompF</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="xboole_0.html#T4">XBOOLE_0:4</a></i>;<br/>
<b>hence </b><a NAME="E55:19"/>
 <a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>8</sub></font>,<span class="p1">(<span class="default"><a href="bvfunc_2.html#K5">CompF</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xboole_0.html#NR5" target="_self">meets</a>  <a href="bvfunc_1.html#K22">EqClass</a> <font color="Maroon">c<sub>7</sub></font>,<span class="p1">(<span class="default"><a href="bvfunc_2.html#K5">CompF</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="bvfunc14.html#E1:19"><i><font color="Green">E13</font></i></a>, <a class="ref" href="bvfunc14.html#T7" target="_self">Th7</a></i>;<br/>


</div>
