<?xml version="1.0"?>
<div class="add">

<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>, <font color="Maroon">c<sub>7</sub></font> be    <a href="eqrel_1.html#M1">a_partition</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>













<b>assume </b><a NAME="E1:21"/><i><font color="Green">E14</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="enumset1.html#K3">{</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>,<font color="Maroon">c<sub>7</sub></font></span><a href="enumset1.html#K3">}</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>3</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>7</sub></font> )
 ;<br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="21_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:21_1"/>
( <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> or <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font> or <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font> or <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font> or <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font> or <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font> or ( <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>4</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>7</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; <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>7</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>7</sub></font> ) )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="21_1_1"><b>suppose </b></a><a NAME="E1:21_1_1"/><i><font color="Green">E15</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font>
 ;<br/><div class="add"><b>then </b><font color="Maroon">c<sub>2</sub></font> = 
<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>4</sub></font>,<font color="Maroon">c<sub>6</sub></font></span><a href="enumset1.html#K2">}</a></span> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="bvfunc_2.html#K4">{</a><span class="default"><font color="Maroon">c<sub>7</sub></font></span><a href="bvfunc_2.html#K4">}</a></span>
<b>by </b><i><a class="txt" href="bvfunc14.html#E1:21"><i><font color="Green">E14</font></i></a>, <a class="ref" href="enumset1.html#T50">ENUMSET1:50</a></i>
<br/>.= 
<span class="p1"><a href="enumset1.html#K2">{</a><span class="default"><font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font></span><a href="enumset1.html#K2">}</a></span> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="bvfunc_2.html#K4">{</a><span class="default"><font color="Maroon">c<sub>7</sub></font></span><a href="bvfunc_2.html#K4">}</a></span>
<b>by </b><i><a class="ref" href="enumset1.html#T110">ENUMSET1:110</a></i>
<br/>.= 
<span class="p1"><a href="enumset1.html#K3">{</a><span class="default"><font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span><a href="enumset1.html#K3">}</a></span>
<b>by </b><i><a class="ref" href="enumset1.html#T50">ENUMSET1:50</a></i>
<br/>.= 
<span class="p1"><a href="enumset1.html#K2">{</a><span class="default"><font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span><a href="enumset1.html#K2">}</a></span>
<b>by </b><i><a class="ref" href="enumset1.html#T72">ENUMSET1:72</a></i>
<br/>.= 
<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>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span><a href="enumset1.html#K2">}</a></span>
<b>by </b><i><a class="ref" href="enumset1.html#T108">ENUMSET1:108</a></i>
;<br/><b>hence </b> <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 class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="txt" href="bvfunc14.html#E1:21"><i><font color="Green">E14</font></i></a>, <a class="ref" href="bvfunc14.html#T7" target="_self">Th7</a></i>
<br/>.= 
<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="partit1.html#K2">'/\'</a> <font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="txt" href="bvfunc14.html#E1:21_1_1"><i><font color="Green">E15</font></i></a>, <a class="ref" href="partit1.html#T15">PARTIT1:15</a></i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="21_1_2"><b>suppose </b></a><a NAME="E1:21_1_2"/><i><font color="Green">E15</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font>
 ;<br/><div class="add"><b>then </b><font color="Maroon">c<sub>2</sub></font> = 
<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>4</sub></font></span><a href="enumset1.html#K2">}</a></span> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="bvfunc_2.html#K4">{</a><span class="default"><font color="Maroon">c<sub>7</sub></font></span><a href="bvfunc_2.html#K4">}</a></span>
<b>by </b><i><a class="txt" href="bvfunc14.html#E1:21"><i><font color="Green">E14</font></i></a>, <a class="ref" href="enumset1.html#T50">ENUMSET1:50</a></i>
<br/>.= 
<span class="p1"><a href="enumset1.html#K2">{</a><span class="default"><font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font></span><a href="enumset1.html#K2">}</a></span> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="bvfunc_2.html#K4">{</a><span class="default"><font color="Maroon">c<sub>7</sub></font></span><a href="bvfunc_2.html#K4">}</a></span>
<b>by </b><i><a class="ref" href="enumset1.html#T112">ENUMSET1:112</a></i>
<br/>.= 
<span class="p1"><a href="enumset1.html#K3">{</a><span class="default"><font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>7</sub></font></span><a href="enumset1.html#K3">}</a></span>
<b>by </b><i><a class="ref" href="enumset1.html#T50">ENUMSET1:50</a></i>
<br/>.= 
<span class="p1"><a href="enumset1.html#K2">{</a><span class="default"><font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>7</sub></font></span><a href="enumset1.html#K2">}</a></span>
<b>by </b><i><a class="ref" href="enumset1.html#T72">ENUMSET1:72</a></i>
<br/>.= 
<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>7</sub></font></span><a href="enumset1.html#K2">}</a></span>
<b>by </b><i><a class="ref" href="enumset1.html#T108">ENUMSET1:108</a></i>
;<br/><b>hence </b> <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 class="p1">(<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>7</sub></font>
<b>by </b><i><a class="txt" href="bvfunc14.html#E1:21"><i><font color="Green">E14</font></i></a>, <a class="ref" href="bvfunc14.html#T7" target="_self">Th7</a></i>
<br/>.= 
<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>6</sub></font></span>)</span> <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>7</sub></font>
<b>by </b><i><a class="txt" href="bvfunc14.html#E1:21_1_2"><i><font color="Green">E15</font></i></a>, <a class="ref" href="partit1.html#T15">PARTIT1:15</a></i>
<br/>.= 
<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="partit1.html#K2">'/\'</a> <font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="ref" href="partit1.html#T16">PARTIT1:16</a></i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="21_1_3"><b>suppose </b></a><a NAME="E1:21_1_3"/><i><font color="Green">E15</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font>
 ;<br/><div class="add"><b>then </b><font color="Maroon">c<sub>2</sub></font> = 
<span class="p1"><a href="bvfunc_2.html#K4">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="bvfunc_2.html#K4">}</a></span> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="enumset1.html#K2">{</a><span class="default"><font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font></span><a href="enumset1.html#K2">}</a></span>
<b>by </b><i><a class="txt" href="bvfunc14.html#E1:21"><i><font color="Green">E14</font></i></a>, <a class="ref" href="enumset1.html#T47">ENUMSET1:47</a></i>
<br/>.= 
<span class="p1"><a href="bvfunc_2.html#K4">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="bvfunc_2.html#K4">}</a></span> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="enumset1.html#K2">{</a><span class="default"><font color="Maroon">c<sub>4</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>
<b>by </b><i><a class="ref" href="enumset1.html#T105">ENUMSET1:105</a></i>
<br/>.= 
<span class="p1"><a href="bvfunc_2.html#K4">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="bvfunc_2.html#K4">}</a></span> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="enumset1.html#K1">{</a><span class="default"><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#K1">}</a></span>
<b>by </b><i><a class="ref" href="enumset1.html#T71">ENUMSET1:71</a></i>
<br/>.= 
<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>
<b>by </b><i><a class="ref" href="enumset1.html#T44">ENUMSET1:44</a></i>
;<br/><b>hence </b> <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 class="p1">(<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>
<b>by </b><i><a class="txt" href="bvfunc14.html#E1:21"><i><font color="Green">E14</font></i></a>, <a class="ref" href="bvfunc14.html#T7" target="_self">Th7</a></i>
<br/>.= 
<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>7</sub></font></span>)</span> <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="txt" href="bvfunc14.html#E1:21_1_3"><i><font color="Green">E15</font></i></a>, <a class="ref" href="partit1.html#T15">PARTIT1:15</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <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>
<b>by </b><i><a class="ref" href="partit1.html#T16">PARTIT1:16</a></i>
<br/>.= 
<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> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="ref" href="partit1.html#T16">PARTIT1:16</a></i>
<br/>.= 
<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="partit1.html#K2">'/\'</a> <font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="ref" href="partit1.html#T16">PARTIT1:16</a></i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="21_1_4"><b>suppose </b></a><a NAME="E1:21_1_4"/><i><font color="Green">E15</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font>
 ;<br/><div class="add"><b>then </b><font color="Maroon">c<sub>2</sub></font> = 
<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>5</sub></font></span><a href="enumset1.html#K2">}</a></span> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="bvfunc_2.html#K4">{</a><span class="default"><font color="Maroon">c<sub>7</sub></font></span><a href="bvfunc_2.html#K4">}</a></span>
<b>by </b><i><a class="txt" href="bvfunc14.html#E1:21"><i><font color="Green">E14</font></i></a>, <a class="ref" href="enumset1.html#T50">ENUMSET1:50</a></i>
<br/>.= 
<span class="p1"><a href="enumset1.html#K2">{</a><span class="default"><font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span><a href="enumset1.html#K2">}</a></span> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="bvfunc_2.html#K4">{</a><span class="default"><font color="Maroon">c<sub>7</sub></font></span><a href="bvfunc_2.html#K4">}</a></span>
<b>by </b><i><a class="ref" href="enumset1.html#T118">ENUMSET1:118</a></i>
<br/>.= 
<span class="p1"><a href="enumset1.html#K1">{</a><span class="default"><font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span><a href="enumset1.html#K1">}</a></span> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="bvfunc_2.html#K4">{</a><span class="default"><font color="Maroon">c<sub>7</sub></font></span><a href="bvfunc_2.html#K4">}</a></span>
<b>by </b><i><a class="ref" href="enumset1.html#T71">ENUMSET1:71</a></i>
<br/>.= 
<span class="p1"><a href="enumset1.html#K2">{</a><span class="default"><font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>7</sub></font></span><a href="enumset1.html#K2">}</a></span>
<b>by </b><i><a class="ref" href="enumset1.html#T46">ENUMSET1:46</a></i>
<br/>.= 
<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>7</sub></font></span><a href="enumset1.html#K2">}</a></span>
<b>by </b><i><a class="ref" href="enumset1.html#T110">ENUMSET1:110</a></i>
;<br/><b>hence </b> <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 class="p1">(<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>7</sub></font>
<b>by </b><i><a class="txt" href="bvfunc14.html#E1:21"><i><font color="Green">E14</font></i></a>, <a class="ref" href="bvfunc14.html#T7" target="_self">Th7</a></i>
<br/>.= 
<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> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="txt" href="bvfunc14.html#E1:21_1_4"><i><font color="Green">E15</font></i></a>, <a class="ref" href="partit1.html#T15">PARTIT1:15</a></i>
<br/>.= 
<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="partit1.html#K2">'/\'</a> <font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="ref" href="partit1.html#T16">PARTIT1:16</a></i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="21_1_5"><b>suppose </b></a><a NAME="E1:21_1_5"/><i><font color="Green">E15</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font>
 ;<br/><div class="add"><b>then </b><font color="Maroon">c<sub>2</sub></font> = 
<span class="p1"><a href="bvfunc_2.html#K4">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="bvfunc_2.html#K4">}</a></span> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="enumset1.html#K2">{</a><span class="default"><font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>5</sub></font></span><a href="enumset1.html#K2">}</a></span>
<b>by </b><i><a class="txt" href="bvfunc14.html#E1:21"><i><font color="Green">E14</font></i></a>, <a class="ref" href="enumset1.html#T47">ENUMSET1:47</a></i>
<br/>.= 
<span class="p1"><a href="bvfunc_2.html#K4">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="bvfunc_2.html#K4">}</a></span> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="enumset1.html#K2">{</a><span class="default"><font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>6</sub></font></span><a href="enumset1.html#K2">}</a></span>
<b>by </b><i><a class="ref" href="enumset1.html#T117">ENUMSET1:117</a></i>
<br/>.= 
<span class="p1"><a href="bvfunc_2.html#K4">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="bvfunc_2.html#K4">}</a></span> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="enumset1.html#K1">{</a><span class="default"><font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>6</sub></font></span><a href="enumset1.html#K1">}</a></span>
<b>by </b><i><a class="ref" href="enumset1.html#T71">ENUMSET1:71</a></i>
<br/>.= 
<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>5</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>6</sub></font></span><a href="enumset1.html#K2">}</a></span>
<b>by </b><i><a class="ref" href="enumset1.html#T44">ENUMSET1:44</a></i>
<br/>.= 
<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>
<b>by </b><i><a class="ref" href="enumset1.html#T104">ENUMSET1:104</a></i>
;<br/><b>hence </b> <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 class="p1">(<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>
<b>by </b><i><a class="txt" href="bvfunc14.html#E1:21"><i><font color="Green">E14</font></i></a>, <a class="ref" href="bvfunc14.html#T7" target="_self">Th7</a></i>
<br/>.= 
<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>7</sub></font></span>)</span></span>)</span> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">c<sub>6</sub></font>
<b>by </b><i><a class="txt" href="bvfunc14.html#E1:21_1_5"><i><font color="Green">E15</font></i></a>, <a class="ref" href="partit1.html#T15">PARTIT1:15</a></i>
<br/>.= 
<font color="Maroon">c<sub>4</sub></font> <a href="partit1.html#K2">'/\'</a> <span class="p1">(<span class="default"><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>7</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="ref" href="partit1.html#T16">PARTIT1:16</a></i>
<br/>.= 
<font color="Maroon">c<sub>4</sub></font> <a href="partit1.html#K2">'/\'</a> <span class="p1">(<span class="default"><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> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">c<sub>7</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="partit1.html#T16">PARTIT1:16</a></i>
<br/>.= 
<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> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="ref" href="partit1.html#T16">PARTIT1:16</a></i>
<br/>.= 
<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="partit1.html#K2">'/\'</a> <font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="ref" href="partit1.html#T16">PARTIT1:16</a></i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="21_1_6"><b>suppose </b></a><a NAME="E1:21_1_6"/><i><font color="Green">E15</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font>
 ;<br/><div class="add"><b>then </b><font color="Maroon">c<sub>2</sub></font> = 
<span class="p1"><a href="bvfunc_2.html#K4">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="bvfunc_2.html#K4">}</a></span> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="enumset1.html#K2">{</a><span class="default"><font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>6</sub></font></span><a href="enumset1.html#K2">}</a></span>
<b>by </b><i><a class="txt" href="bvfunc14.html#E1:21"><i><font color="Green">E14</font></i></a>, <a class="ref" href="enumset1.html#T47">ENUMSET1:47</a></i>
<br/>.= 
<span class="p1"><a href="bvfunc_2.html#K4">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="bvfunc_2.html#K4">}</a></span> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="enumset1.html#K2">{</a><span class="default"><font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span><a href="enumset1.html#K2">}</a></span>
<b>by </b><i><a class="ref" href="enumset1.html#T118">ENUMSET1:118</a></i>
<br/>.= 
<span class="p1"><a href="bvfunc_2.html#K4">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="bvfunc_2.html#K4">}</a></span> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="enumset1.html#K1">{</a><span class="default"><font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span><a href="enumset1.html#K1">}</a></span>
<b>by </b><i><a class="ref" href="enumset1.html#T71">ENUMSET1:71</a></i>
<br/>.= 
<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>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span><a href="enumset1.html#K2">}</a></span>
<b>by </b><i><a class="ref" href="enumset1.html#T44">ENUMSET1:44</a></i>
<br/>.= 
<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>
<b>by </b><i><a class="ref" href="enumset1.html#T105">ENUMSET1:105</a></i>
;<br/><b>hence </b> <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 class="p1">(<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>
<b>by </b><i><a class="txt" href="bvfunc14.html#E1:21"><i><font color="Green">E14</font></i></a>, <a class="ref" href="bvfunc14.html#T7" target="_self">Th7</a></i>
<br/>.= 
<span class="p1">(<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> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">c<sub>7</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="bvfunc14.html#E1:21_1_6"><i><font color="Green">E15</font></i></a>, <a class="ref" href="partit1.html#T15">PARTIT1:15</a></i>
<br/>.= 
<font color="Maroon">c<sub>4</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> <span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="partit1.html#T16">PARTIT1:16</a></i>
<br/>.= 
<font color="Maroon">c<sub>4</sub></font> <a href="partit1.html#K2">'/\'</a> <span class="p1">(<span class="default"><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> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">c<sub>7</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="partit1.html#T16">PARTIT1:16</a></i>
<br/>.= 
<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> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="ref" href="partit1.html#T16">PARTIT1:16</a></i>
<br/>.= 
<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="partit1.html#K2">'/\'</a> <font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="ref" href="partit1.html#T16">PARTIT1:16</a></i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="21_1_7"><b>suppose </b></a><a NAME="E1:21_1_7"/><i><font color="Green">E15</font></i>: 
( <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>4</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>7</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; <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>7</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>7</sub></font> )
 ;<br/><div class="add"><a NAME="E2:21_1_7"/>
<font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="bvfunc_2.html#K4">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="bvfunc_2.html#K4">}</a></span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2"><a href="bvfunc_2.html#K4">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="bvfunc_2.html#K4">}</a></span> <a href="xboole_0.html#K2">\/</a> <span class="p2"><a href="enumset1.html#K2">{</a><span class="default"><font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span><a href="enumset1.html#K2">}</a></span></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p1"><a href="bvfunc_2.html#K4">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="bvfunc_2.html#K4">}</a></span>
 <b>by </b><i><a class="txt" href="bvfunc14.html#E1:21"><i><font color="Green">E14</font></i></a>, <a class="ref" href="enumset1.html#T47">ENUMSET1:47</a></i>;<br/><a NAME="E3:21_1_7"/><b>then </b><i><font color="Green">E16</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="bvfunc_2.html#K4">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="bvfunc_2.html#K4">}</a></span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2"><a href="bvfunc_2.html#K4">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="bvfunc_2.html#K4">}</a></span> <a href="subset_1.html#K7">\</a> <span class="p2"><a href="bvfunc_2.html#K4">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="bvfunc_2.html#K4">}</a></span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><span class="p2"><a href="enumset1.html#K2">{</a><span class="default"><font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span><a href="enumset1.html#K2">}</a></span> <a href="subset_1.html#K6">\</a> <span class="p2"><a href="bvfunc_2.html#K4">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="bvfunc_2.html#K4">}</a></span></span>)</span>
 <b>by </b><i><a class="ref" href="xboole_1.html#T42">XBOOLE_1:42</a></i>;<br/><a NAME="E4:21_1_7"/><i><font color="Green">E17</font></i>: 
not <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="bvfunc_2.html#K4">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="bvfunc_2.html#K4">}</a></span>
 <b>by </b><i><a class="txt" href="bvfunc14.html#E1:21"><i><font color="Green">E14</font></i></a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><a NAME="E5:21_1_7"/><i><font color="Green">E18</font></i>: 
not <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="bvfunc_2.html#K4">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="bvfunc_2.html#K4">}</a></span>
 <b>by </b><i><a class="txt" href="bvfunc14.html#E1:21"><i><font color="Green">E14</font></i></a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><a NAME="E6:21_1_7"/><i><font color="Green">E19</font></i>: 
not <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="bvfunc_2.html#K4">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="bvfunc_2.html#K4">}</a></span>
 <b>by </b><i><a class="txt" href="bvfunc14.html#E1:21"><i><font color="Green">E14</font></i></a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><a NAME="E7:21_1_7"/><i><font color="Green">E20</font></i>: 
not <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="bvfunc_2.html#K4">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="bvfunc_2.html#K4">}</a></span>
 <b>by </b><i><a class="txt" href="bvfunc14.html#E1:21"><i><font color="Green">E14</font></i></a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><span class="p1"><a href="enumset1.html#K2">{</a><span class="default"><font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span><a href="enumset1.html#K2">}</a></span> <a href="subset_1.html#K6">\</a> <span class="p1"><a href="bvfunc_2.html#K4">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="bvfunc_2.html#K4">}</a></span> = 
<span class="p1">(<span class="default"><span class="p2"><a href="bvfunc_2.html#K4">{</a><span class="default"><font color="Maroon">c<sub>4</sub></font></span><a href="bvfunc_2.html#K4">}</a></span> <a href="xboole_0.html#K2">\/</a> <span class="p2"><a href="enumset1.html#K1">{</a><span class="default"><font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span><a href="enumset1.html#K1">}</a></span></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p1"><a href="bvfunc_2.html#K4">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="bvfunc_2.html#K4">}</a></span>
<b>by </b><i><a class="ref" href="enumset1.html#T44">ENUMSET1:44</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2"><a href="bvfunc_2.html#K4">{</a><span class="default"><font color="Maroon">c<sub>4</sub></font></span><a href="bvfunc_2.html#K4">}</a></span> <a href="subset_1.html#K7">\</a> <span class="p2"><a href="bvfunc_2.html#K4">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="bvfunc_2.html#K4">}</a></span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><span class="p2"><a href="enumset1.html#K1">{</a><span class="default"><font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span><a href="enumset1.html#K1">}</a></span> <a href="subset_1.html#K6">\</a> <span class="p2"><a href="bvfunc_2.html#K4">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="bvfunc_2.html#K4">}</a></span></span>)</span>
<b>by </b><i><a class="ref" href="xboole_1.html#T42">XBOOLE_1:42</a></i>
<br/>.= 
<span class="p1"><a href="bvfunc_2.html#K4">{</a><span class="default"><font color="Maroon">c<sub>4</sub></font></span><a href="bvfunc_2.html#K4">}</a></span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><span class="p2"><a href="enumset1.html#K1">{</a><span class="default"><font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span><a href="enumset1.html#K1">}</a></span> <a href="subset_1.html#K6">\</a> <span class="p2"><a href="bvfunc_2.html#K4">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="bvfunc_2.html#K4">}</a></span></span>)</span>
<b>by </b><i><a class="txt" href="bvfunc14.html#E4:21_1_7"><i><font color="Green">E17</font></i></a>, <a class="ref" href="zfmisc_1.html#T67">ZFMISC_1:67</a></i>
<br/>.= 
<span class="p1"><a href="bvfunc_2.html#K4">{</a><span class="default"><font color="Maroon">c<sub>4</sub></font></span><a href="bvfunc_2.html#K4">}</a></span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="bvfunc_2.html#K4">{</a><span class="default"><font color="Maroon">c<sub>5</sub></font></span><a href="bvfunc_2.html#K4">}</a></span> <a href="xboole_0.html#K2">\/</a> <span class="p3"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span><a href="tarski.html#K2">}</a></span></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p2"><a href="bvfunc_2.html#K4">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="bvfunc_2.html#K4">}</a></span></span>)</span>
<b>by </b><i><a class="ref" href="enumset1.html#T42">ENUMSET1:42</a></i>
<br/>.= 
<span class="p1"><a href="bvfunc_2.html#K4">{</a><span class="default"><font color="Maroon">c<sub>4</sub></font></span><a href="bvfunc_2.html#K4">}</a></span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="bvfunc_2.html#K4">{</a><span class="default"><font color="Maroon">c<sub>5</sub></font></span><a href="bvfunc_2.html#K4">}</a></span> <a href="subset_1.html#K7">\</a> <span class="p3"><a href="bvfunc_2.html#K4">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="bvfunc_2.html#K4">}</a></span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p2">(<span class="default"><span class="p3"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span><a href="tarski.html#K2">}</a></span> <a href="subset_1.html#K6">\</a> <span class="p3"><a href="bvfunc_2.html#K4">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="bvfunc_2.html#K4">}</a></span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="xboole_1.html#T42">XBOOLE_1:42</a></i>
<br/>.= 
<span class="p1"><a href="bvfunc_2.html#K4">{</a><span class="default"><font color="Maroon">c<sub>4</sub></font></span><a href="bvfunc_2.html#K4">}</a></span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="bvfunc_2.html#K4">{</a><span class="default"><font color="Maroon">c<sub>5</sub></font></span><a href="bvfunc_2.html#K4">}</a></span> <a href="subset_1.html#K7">\</a> <span class="p3"><a href="bvfunc_2.html#K4">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="bvfunc_2.html#K4">}</a></span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p2"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span><a href="tarski.html#K2">}</a></span></span>)</span>
<b>by </b><i><a class="txt" href="bvfunc14.html#E6:21_1_7"><i><font color="Green">E19</font></i></a>, <a class="txt" href="bvfunc14.html#E7:21_1_7"><i><font color="Green">E20</font></i></a>, <a class="ref" href="zfmisc_1.html#T72">ZFMISC_1:72</a></i>
<br/>.= 
<span class="p1"><a href="bvfunc_2.html#K4">{</a><span class="default"><font color="Maroon">c<sub>4</sub></font></span><a href="bvfunc_2.html#K4">}</a></span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><span class="p2"><a href="bvfunc_2.html#K4">{</a><span class="default"><font color="Maroon">c<sub>5</sub></font></span><a href="bvfunc_2.html#K4">}</a></span> <a href="xboole_0.html#K2">\/</a> <span class="p2"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span><a href="tarski.html#K2">}</a></span></span>)</span>
<b>by </b><i><a class="txt" href="bvfunc14.html#E5:21_1_7"><i><font color="Green">E18</font></i></a>, <a class="ref" href="zfmisc_1.html#T67">ZFMISC_1:67</a></i>
<br/>.= 
<span class="p1"><a href="bvfunc_2.html#K4">{</a><span class="default"><font color="Maroon">c<sub>4</sub></font></span><a href="bvfunc_2.html#K4">}</a></span> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="enumset1.html#K1">{</a><span class="default"><font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span><a href="enumset1.html#K1">}</a></span>
<b>by </b><i><a class="ref" href="enumset1.html#T42">ENUMSET1:42</a></i>
;<br/><a NAME="E9:21_1_7"/><b>then </b><i><font color="Green">E21</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="bvfunc_2.html#K4">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="bvfunc_2.html#K4">}</a></span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2"><a href="bvfunc_2.html#K4">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="bvfunc_2.html#K4">}</a></span> <a href="subset_1.html#K7">\</a> <span class="p2"><a href="bvfunc_2.html#K4">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="bvfunc_2.html#K4">}</a></span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="enumset1.html#K2">{</a><span class="default"><font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span><a href="enumset1.html#K2">}</a></span>
 <b>by </b><i><a class="txt" href="bvfunc14.html#E3:21_1_7"><i><font color="Green">E16</font></i></a>, <a class="ref" href="enumset1.html#T44">ENUMSET1:44</a></i>;<br/><a NAME="E10:21_1_7"/>
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="bvfunc_2.html#K4">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="bvfunc_2.html#K4">}</a></span>
 <b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><a NAME="E11:21_1_7"/><b>then </b><i><font color="Green">E22</font></i>: 
<span class="p1"><a href="bvfunc_2.html#K4">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="bvfunc_2.html#K4">}</a></span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="bvfunc_2.html#K4">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="bvfunc_2.html#K4">}</a></span> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 <b>by </b><i><a class="ref" href="zfmisc_1.html#T68">ZFMISC_1:68</a></i>;<br/><a NAME="E12:21_1_7"/><i><font color="Green">E23</font></i>: 
<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="partit1.html#K2">'/\'</a> <font color="Maroon">c<sub>7</sub></font> <a href="tarski.html#R1">c=</a>  <a href="bvfunc_2.html#K2">'/\'</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K7">\</a> <span class="p2"><a href="bvfunc_2.html#K4">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="bvfunc_2.html#K4">}</a></span></span>)</span>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="21_1_7_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>8</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="E1:21_1_7_2"/><i><font color="Green">E24</font></i>: 
<font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R2">in</a> <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="partit1.html#K2">'/\'</a> <font color="Maroon">c<sub>7</sub></font>
 ;<br/>

<a NAME="E2:21_1_7_2"/><b>then </b>
<font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="setfam_1.html#K3">INTERSECTION</a> <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>,<font color="Maroon">c<sub>7</sub></font></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="partit1.html#D4">PARTIT1:def 4</a></i>;<br/>
<a NAME="E3:21_1_7_2"/><b>then </b>
( <font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R2">in</a>  <a href="setfam_1.html#K3">INTERSECTION</a> <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>,<font color="Maroon">c<sub>7</sub></font> &amp; not <font color="Maroon">c<sub>8</sub></font> <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="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/>
<b>then consider </b><font color="Maroon">c<sub>9</sub></font>, <font color="Maroon">c<sub>10</sub></font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E5:21_1_7_2"/><i><font color="Green">E25</font></i>: 
( <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">(<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> &amp; <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>7</sub></font> &amp; <font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>9</sub></font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">c<sub>10</sub></font> )
 <b>by </b><i><a class="ref" href="setfam_1.html#D5">SETFAM_1:def 5</a></i>;<br/>
<a NAME="E6:21_1_7_2"/>
<font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="setfam_1.html#K3">INTERSECTION</a> <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>,<font color="Maroon">c<sub>6</sub></font></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="txt" href="bvfunc14.html#E5:21_1_7_2"><i><font color="Green">E25</font></i></a>, <a class="ref" href="partit1.html#D4">PARTIT1:def 4</a></i>;<br/>
<a NAME="E7:21_1_7_2"/><b>then </b>
( <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R2">in</a>  <a href="setfam_1.html#K3">INTERSECTION</a> <span class="p1">(<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>,<font color="Maroon">c<sub>6</sub></font> &amp; not <font color="Maroon">c<sub>9</sub></font> <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="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/>
<b>then consider </b><font color="Maroon">c<sub>11</sub></font>, <font color="Maroon">c<sub>12</sub></font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E9:21_1_7_2"/><i><font color="Green">E26</font></i>: 
( <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>4</sub></font> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>11</sub></font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">c<sub>12</sub></font> )
 <b>by </b><i><a class="ref" href="setfam_1.html#D5">SETFAM_1:def 5</a></i>;<br/>
<a NAME="E10:21_1_7_2"/>
<font color="Maroon">c<sub>11</sub></font> <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>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></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="txt" href="bvfunc14.html#E9:21_1_7_2"><i><font color="Green">E26</font></i></a>, <a class="ref" href="partit1.html#D4">PARTIT1:def 4</a></i>;<br/>
<a NAME="E11:21_1_7_2"/><b>then </b>
( <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R2">in</a>  <a href="setfam_1.html#K3">INTERSECTION</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> &amp; not <font color="Maroon">c<sub>11</sub></font> <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="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/>
<b>then consider </b><font color="Maroon">c<sub>13</sub></font>, <font color="Maroon">c<sub>14</sub></font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E13:21_1_7_2"/><i><font color="Green">E27</font></i>: 
( <font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#R2">in</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> <font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>13</sub></font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">c<sub>14</sub></font> )
 <b>by </b><i><a class="ref" href="setfam_1.html#D5">SETFAM_1:def 5</a></i>;<br/>
<b>set </b><font color="Maroon">c<sub>15</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> <font color="Maroon">c<sub>13</sub></font></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> <font color="Maroon">c<sub>14</sub></font></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> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>10</sub></font></span>)</span>;<br/>
<a NAME="E14:21_1_7_2"/>
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>13</sub></font></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>14</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>13</sub></font></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>14</sub></font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_4.html#D1">FUNCT_4:def 1</a></i>;<br/>
<a NAME="E15:21_1_7_2"/><b>then </b>
 <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"><font color="Maroon">c<sub>4</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>13</sub></font></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> <font color="Maroon">c<sub>14</sub></font></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> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>13</sub></font></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>14</sub></font></span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_4.html#D1">FUNCT_4:def 1</a></i>;<br/>
<a NAME="E16:21_1_7_2"/><b>then </b><i><font color="Green">E28</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> <font color="Maroon">c<sub>13</sub></font></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> <font color="Maroon">c<sub>14</sub></font></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> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>13</sub></font></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p3">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>14</sub></font></span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_4.html#D1">FUNCT_4:def 1</a></i>;<br/>
<a NAME="E17:21_1_7_2"/><i><font color="Green">E29</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>13</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="bvfunc_2.html#K4">{</a><span class="default"><font color="Maroon">c<sub>4</sub></font></span><a href="bvfunc_2.html#K4">}</a></span>
 
<b>by </b><i><a class="ref" href="cqc_lang.html#T5">CQC_LANG:5</a></i>;<br/>
<a NAME="E18:21_1_7_2"/><i><font color="Green">E30</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="bvfunc_2.html#K4">{</a><span class="default"><font color="Maroon">c<sub>5</sub></font></span><a href="bvfunc_2.html#K4">}</a></span>
 
<b>by </b><i><a class="ref" href="cqc_lang.html#T5">CQC_LANG:5</a></i>;<br/>
<a NAME="E19:21_1_7_2"/><i><font color="Green">E31</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>12</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="bvfunc_2.html#K4">{</a><span class="default"><font color="Maroon">c<sub>6</sub></font></span><a href="bvfunc_2.html#K4">}</a></span>
 
<b>by </b><i><a class="ref" href="cqc_lang.html#T5">CQC_LANG:5</a></i>;<br/>
<a NAME="E20:21_1_7_2"/><i><font color="Green">E32</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="bvfunc_2.html#K4">{</a><span class="default"><font color="Maroon">c<sub>7</sub></font></span><a href="bvfunc_2.html#K4">}</a></span>
 
<b>by </b><i><a class="ref" href="cqc_lang.html#T5">CQC_LANG:5</a></i>;<br/>
<i><font color="Green">E33</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> <font color="Maroon">c<sub>13</sub></font></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> <font color="Maroon">c<sub>14</sub></font></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> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="bvfunc_2.html#K4">{</a><span class="default"><font color="Maroon">c<sub>4</sub></font></span><a href="bvfunc_2.html#K4">}</a></span> <a href="subset_1.html#K4">\/</a> <span class="p3"><a href="bvfunc_2.html#K4">{</a><span class="default"><font color="Maroon">c<sub>5</sub></font></span><a href="bvfunc_2.html#K4">}</a></span></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p2"><a href="bvfunc_2.html#K4">{</a><span class="default"><font color="Maroon">c<sub>6</sub></font></span><a href="bvfunc_2.html#K4">}</a></span></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1"><a href="bvfunc_2.html#K4">{</a><span class="default"><font color="Maroon">c<sub>7</sub></font></span><a href="bvfunc_2.html#K4">}</a></span>
<b>by </b><i><a class="txt" href="bvfunc14.html#E16:21_1_7_2"><i><font color="Green">E28</font></i></a>, <a class="txt" href="bvfunc14.html#E17:21_1_7_2"><i><font color="Green">E29</font></i></a>, <a class="txt" href="bvfunc14.html#E18:21_1_7_2"><i><font color="Green">E30</font></i></a>, <a class="txt" href="bvfunc14.html#E19:21_1_7_2"><i><font color="Green">E31</font></i></a>, <a class="ref" href="cqc_lang.html#T5">CQC_LANG:5</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span><a href="tarski.html#K2">}</a></span> <a href="xboole_0.html#K2">\/</a> <span class="p2"><a href="bvfunc_2.html#K4">{</a><span class="default"><font color="Maroon">c<sub>6</sub></font></span><a href="bvfunc_2.html#K4">}</a></span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="bvfunc_2.html#K4">{</a><span class="default"><font color="Maroon">c<sub>7</sub></font></span><a href="bvfunc_2.html#K4">}</a></span>
<b>by </b><i><a class="ref" href="enumset1.html#T41">ENUMSET1:41</a></i>
<br/>.= 
<span class="p1"><a href="enumset1.html#K1">{</a><span class="default"><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#K1">}</a></span> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="bvfunc_2.html#K4">{</a><span class="default"><font color="Maroon">c<sub>7</sub></font></span><a href="bvfunc_2.html#K4">}</a></span>
<b>by </b><i><a class="ref" href="enumset1.html#T43">ENUMSET1:43</a></i>
<br/>.= 
<span class="p1"><a href="enumset1.html#K2">{</a><span class="default"><font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span><a href="enumset1.html#K2">}</a></span>
<b>by </b><i><a class="ref" href="enumset1.html#T46">ENUMSET1:46</a></i>
;<br/>
<a NAME="E22:21_1_7_2"/><i><font color="Green">E34</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> <font color="Maroon">c<sub>13</sub></font></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> <font color="Maroon">c<sub>14</sub></font></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> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>10</sub></font></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> <font color="Maroon">c<sub>12</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="21_1_7_2_2"><b>proof </b></a><div class="add">

<a NAME="E1:21_1_7_2_2"/>
not <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"><font color="Maroon">c<sub>7</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>10</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="bvfunc14.html#E1:21_1_7"><i><font color="Green">E15</font></i></a>, <a class="txt" href="bvfunc14.html#E20:21_1_7_2"><i><font color="Green">E32</font></i></a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<a NAME="E2:21_1_7_2_2"/><b>then </b><i><font color="Green">E35</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> <font color="Maroon">c<sub>13</sub></font></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> <font color="Maroon">c<sub>14</sub></font></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> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>10</sub></font></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> <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> <font color="Maroon">c<sub>13</sub></font></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> <font color="Maroon">c<sub>14</sub></font></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> <font color="Maroon">c<sub>12</sub></font></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="ref" href="funct_4.html#T12">FUNCT_4:12</a></i>;<br/>
<a NAME="E3:21_1_7_2_2"/>
<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"><font color="Maroon">c<sub>6</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>12</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="bvfunc14.html#E19:21_1_7_2"><i><font color="Green">E31</font></i></a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<a NAME="E4:21_1_7_2_2"/><b>then </b>
<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> <font color="Maroon">c<sub>13</sub></font></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> <font color="Maroon">c<sub>14</sub></font></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> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>10</sub></font></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> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>12</sub></font></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#E2:21_1_7_2_2"><i><font color="Green">E35</font></i></a>, <a class="ref" href="funct_4.html#T14">FUNCT_4:14</a></i>;<br/>
<b>hence </b><a NAME="E5:21_1_7_2_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> <font color="Maroon">c<sub>13</sub></font></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> <font color="Maroon">c<sub>14</sub></font></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> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>10</sub></font></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> <font color="Maroon">c<sub>12</sub></font>
 <b>by </b><i><a class="ref" href="cqc_lang.html#T6">CQC_LANG:6</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E23:21_1_7_2"/><i><font color="Green">E35</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> <font color="Maroon">c<sub>13</sub></font></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> <font color="Maroon">c<sub>14</sub></font></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> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>10</sub></font></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> <font color="Maroon">c<sub>13</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="21_1_7_2_3"><b>proof </b></a><div class="add">

<a NAME="E1:21_1_7_2_3"/><i><font color="Green">E36</font></i>: 
not <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"><font color="Maroon">c<sub>6</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>12</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="bvfunc14.html#E1:21_1_7"><i><font color="Green">E15</font></i></a>, <a class="txt" href="bvfunc14.html#E19:21_1_7_2"><i><font color="Green">E31</font></i></a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<a NAME="E2:21_1_7_2_3"/>
not <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"><font color="Maroon">c<sub>7</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>10</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="bvfunc14.html#E1:21_1_7"><i><font color="Green">E15</font></i></a>, <a class="txt" href="bvfunc14.html#E20:21_1_7_2"><i><font color="Green">E32</font></i></a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<a NAME="E3:21_1_7_2_3"/><b>then </b>
<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> <font color="Maroon">c<sub>13</sub></font></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> <font color="Maroon">c<sub>14</sub></font></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> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>10</sub></font></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> <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> <font color="Maroon">c<sub>13</sub></font></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> <font color="Maroon">c<sub>14</sub></font></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> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="ref" href="funct_4.html#T12">FUNCT_4:12</a></i>;<br/>
<a NAME="E4:21_1_7_2_3"/><b>then </b><i><font color="Green">E37</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> <font color="Maroon">c<sub>13</sub></font></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> <font color="Maroon">c<sub>14</sub></font></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> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>10</sub></font></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> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>13</sub></font></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>14</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="txt" href="bvfunc14.html#E1:21_1_7_2_3"><i><font color="Green">E36</font></i></a>, <a class="ref" href="funct_4.html#T12">FUNCT_4:12</a></i>;<br/>
<a NAME="E5:21_1_7_2_3"/>
not <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"><font color="Maroon">c<sub>5</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>14</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="bvfunc14.html#E1:21_1_7"><i><font color="Green">E15</font></i></a>, <a class="txt" href="bvfunc14.html#E18:21_1_7_2"><i><font color="Green">E30</font></i></a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<a NAME="E6:21_1_7_2_3"/><b>then </b>
<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> <font color="Maroon">c<sub>13</sub></font></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> <font color="Maroon">c<sub>14</sub></font></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> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>10</sub></font></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> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>13</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="txt" href="bvfunc14.html#E4:21_1_7_2_3"><i><font color="Green">E37</font></i></a>, <a class="ref" href="funct_4.html#T12">FUNCT_4:12</a></i>;<br/>
<b>hence </b><a NAME="E7:21_1_7_2_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> <font color="Maroon">c<sub>13</sub></font></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> <font color="Maroon">c<sub>14</sub></font></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> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>10</sub></font></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> <font color="Maroon">c<sub>13</sub></font>
 <b>by </b><i><a class="ref" href="cqc_lang.html#T6">CQC_LANG:6</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E24:21_1_7_2"/><i><font color="Green">E36</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> <font color="Maroon">c<sub>13</sub></font></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> <font color="Maroon">c<sub>14</sub></font></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> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>10</sub></font></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> <font color="Maroon">c<sub>14</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="21_1_7_2_4"><b>proof </b></a><div class="add">

<a NAME="E1:21_1_7_2_4"/><i><font color="Green">E37</font></i>: 
not <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"><font color="Maroon">c<sub>6</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>12</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="bvfunc14.html#E1:21_1_7"><i><font color="Green">E15</font></i></a>, <a class="txt" href="bvfunc14.html#E19:21_1_7_2"><i><font color="Green">E31</font></i></a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<a NAME="E2:21_1_7_2_4"/>
not <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"><font color="Maroon">c<sub>7</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>10</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="bvfunc14.html#E1:21_1_7"><i><font color="Green">E15</font></i></a>, <a class="txt" href="bvfunc14.html#E20:21_1_7_2"><i><font color="Green">E32</font></i></a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<a NAME="E3:21_1_7_2_4"/><b>then </b>
<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> <font color="Maroon">c<sub>13</sub></font></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> <font color="Maroon">c<sub>14</sub></font></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> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>10</sub></font></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> <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> <font color="Maroon">c<sub>13</sub></font></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> <font color="Maroon">c<sub>14</sub></font></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> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="ref" href="funct_4.html#T12">FUNCT_4:12</a></i>;<br/>
<a NAME="E4:21_1_7_2_4"/><b>then </b><i><font color="Green">E38</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> <font color="Maroon">c<sub>13</sub></font></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> <font color="Maroon">c<sub>14</sub></font></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> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>10</sub></font></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> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>13</sub></font></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>14</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="txt" href="bvfunc14.html#E1:21_1_7_2_4"><i><font color="Green">E37</font></i></a>, <a class="ref" href="funct_4.html#T12">FUNCT_4:12</a></i>;<br/>
<a NAME="E5:21_1_7_2_4"/>
<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"><font color="Maroon">c<sub>5</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>14</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="bvfunc14.html#E18:21_1_7_2"><i><font color="Green">E30</font></i></a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<a NAME="E6:21_1_7_2_4"/><b>then </b>
<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> <font color="Maroon">c<sub>13</sub></font></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> <font color="Maroon">c<sub>14</sub></font></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> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>10</sub></font></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> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="txt" href="bvfunc14.html#E4:21_1_7_2_4"><i><font color="Green">E38</font></i></a>, <a class="ref" href="funct_4.html#T14">FUNCT_4:14</a></i>;<br/>
<b>hence </b><a NAME="E7:21_1_7_2_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> <font color="Maroon">c<sub>13</sub></font></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> <font color="Maroon">c<sub>14</sub></font></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> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>10</sub></font></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> <font color="Maroon">c<sub>14</sub></font>
 <b>by </b><i><a class="ref" href="cqc_lang.html#T6">CQC_LANG:6</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E25:21_1_7_2"/><i><font color="Green">E37</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> <font color="Maroon">c<sub>13</sub></font></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> <font color="Maroon">c<sub>14</sub></font></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> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>10</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="21_1_7_2_5"><b>proof </b></a><div class="add">

<a NAME="E1:21_1_7_2_5"/>
<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>10</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="bvfunc14.html#E20:21_1_7_2"><i><font color="Green">E32</font></i></a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<a NAME="E2:21_1_7_2_5"/><b>then </b>
<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> <font color="Maroon">c<sub>13</sub></font></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> <font color="Maroon">c<sub>14</sub></font></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> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>7</sub></font>
 
<b>by </b><i><a class="ref" href="funct_4.html#T14">FUNCT_4:14</a></i>;<br/>
<b>hence </b><a NAME="E3:21_1_7_2_5"/>
<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> <font color="Maroon">c<sub>13</sub></font></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> <font color="Maroon">c<sub>14</sub></font></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> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>10</sub></font>
 <b>by </b><i><a class="ref" href="cqc_lang.html#T6">CQC_LANG:6</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E26:21_1_7_2"/><i><font color="Green">E38</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> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="bvfunc_2.html#K4">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="bvfunc_2.html#K4">}</a></span> 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> <font color="Maroon">c<sub>13</sub></font></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> <font color="Maroon">c<sub>14</sub></font></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> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>10</sub></font></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="21_1_7_2_6"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>16</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><a NAME="E1:21_1_7_2_6"/><i><font color="Green">E39</font></i>: 
<font color="Maroon">c<sub>16</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="bvfunc_2.html#K4">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="bvfunc_2.html#K4">}</a></span>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="21_1_7_2_6_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="21_1_7_2_6_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:21_1_7_2_6_1_1"/>
( <font color="Maroon">c<sub>16</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font> or <font color="Maroon">c<sub>16</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> or <font color="Maroon">c<sub>16</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> or <font color="Maroon">c<sub>16</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font> )
 </span><b>by </b><i><a class="txt" href="bvfunc14.html#E9:21_1_7"><i><font color="Green">E21</font></i></a>, <a class="txt" href="bvfunc14.html#E11:21_1_7"><i><font color="Green">E22</font></i></a>, <a class="txt" href="bvfunc14.html#E1:21_1_7_2_6"><i><font color="Green">E39</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="21_1_7_2_6_1_1_1"><b>case </b></a><a NAME="E1:21_1_7_2_6_1_1_1"/>
<font color="Maroon">c<sub>16</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:21_1_7_2_6_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> <font color="Maroon">c<sub>13</sub></font></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> <font color="Maroon">c<sub>14</sub></font></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> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>16</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>16</sub></font>
 <b>by </b><i><a class="txt" href="bvfunc14.html#E9:21_1_7_2"><i><font color="Green">E26</font></i></a>, <a class="txt" href="bvfunc14.html#E22:21_1_7_2"><i><font color="Green">E34</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="21_1_7_2_6_1_1_2"><b>case </b></a><a NAME="E1:21_1_7_2_6_1_1_2"/>
<font color="Maroon">c<sub>16</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:21_1_7_2_6_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> <font color="Maroon">c<sub>13</sub></font></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> <font color="Maroon">c<sub>14</sub></font></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> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>16</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>16</sub></font>
 <b>by </b><i><a class="txt" href="bvfunc14.html#E13:21_1_7_2"><i><font color="Green">E27</font></i></a>, <a class="txt" href="bvfunc14.html#E23:21_1_7_2"><i><font color="Green">E35</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="21_1_7_2_6_1_1_3"><b>case </b></a><a NAME="E1:21_1_7_2_6_1_1_3"/>
<font color="Maroon">c<sub>16</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:21_1_7_2_6_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> <font color="Maroon">c<sub>13</sub></font></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> <font color="Maroon">c<sub>14</sub></font></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> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>16</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>16</sub></font>
 <b>by </b><i><a class="txt" href="bvfunc14.html#E13:21_1_7_2"><i><font color="Green">E27</font></i></a>, <a class="txt" href="bvfunc14.html#E24:21_1_7_2"><i><font color="Green">E36</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="21_1_7_2_6_1_1_4"><b>case </b></a><a NAME="E1:21_1_7_2_6_1_1_4"/>
<font color="Maroon">c<sub>16</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:21_1_7_2_6_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> <font color="Maroon">c<sub>13</sub></font></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> <font color="Maroon">c<sub>14</sub></font></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> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>16</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>16</sub></font>
 <b>by </b><i><a class="txt" href="bvfunc14.html#E5:21_1_7_2"><i><font color="Green">E25</font></i></a>, <a class="txt" href="bvfunc14.html#E25:21_1_7_2"><i><font color="Green">E37</font></i></a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E3:21_1_7_2_6"/>
<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> <font color="Maroon">c<sub>13</sub></font></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> <font color="Maroon">c<sub>14</sub></font></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> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>16</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>16</sub></font>
 ;<br/>


</div><b>end;</b></div>
<a NAME="E27:21_1_7_2"/><i><font color="Green">E39</font></i>: 
<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> <font color="Maroon">c<sub>13</sub></font></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> <font color="Maroon">c<sub>14</sub></font></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> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="bvfunc14.html#E21:21_1_7_2"><i><font color="Green">E33</font></i></a>, <a class="ref" href="enumset1.html#D2">ENUMSET1:def 2</a></i>;<br/>
<a NAME="E28:21_1_7_2"/><i><font color="Green">E40</font></i>: 
<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> <font color="Maroon">c<sub>13</sub></font></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> <font color="Maroon">c<sub>14</sub></font></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> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="bvfunc14.html#E21:21_1_7_2"><i><font color="Green">E33</font></i></a>, <a class="ref" href="enumset1.html#D2">ENUMSET1:def 2</a></i>;<br/>
<a NAME="E29:21_1_7_2"/><i><font color="Green">E41</font></i>: 
<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> <font color="Maroon">c<sub>13</sub></font></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> <font color="Maroon">c<sub>14</sub></font></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> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="bvfunc14.html#E21:21_1_7_2"><i><font color="Green">E33</font></i></a>, <a class="ref" href="enumset1.html#D2">ENUMSET1:def 2</a></i>;<br/>
<a NAME="E30:21_1_7_2"/><i><font color="Green">E42</font></i>: 
<font color="Maroon">c<sub>7</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> <font color="Maroon">c<sub>13</sub></font></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> <font color="Maroon">c<sub>14</sub></font></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> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="bvfunc14.html#E21:21_1_7_2"><i><font color="Green">E33</font></i></a>, <a class="ref" href="enumset1.html#D2">ENUMSET1:def 2</a></i>;<br/>
<a NAME="E31:21_1_7_2"/><i><font color="Green">E43</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> <font color="Maroon">c<sub>13</sub></font></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> <font color="Maroon">c<sub>14</sub></font></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> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span> <a href="tarski.html#R1">c=</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> <font color="Maroon">c<sub>13</sub></font></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> <font color="Maroon">c<sub>14</sub></font></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> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>6</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> <font color="Maroon">c<sub>13</sub></font></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> <font color="Maroon">c<sub>14</sub></font></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> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>10</sub></font></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> <font color="Maroon">c<sub>13</sub></font></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> <font color="Maroon">c<sub>14</sub></font></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> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>10</sub></font></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> <font color="Maroon">c<sub>13</sub></font></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> <font color="Maroon">c<sub>14</sub></font></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> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="enumset1.html#K2">}</a></span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="21_1_7_2_7"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>16</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="E1:21_1_7_2_7"/>
<font color="Maroon">c<sub>16</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> <font color="Maroon">c<sub>13</sub></font></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> <font color="Maroon">c<sub>14</sub></font></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> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span>
 ;<br/>

<b>then consider </b><font color="Maroon">c<sub>17</sub></font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E3:21_1_7_2_7"/><i><font color="Green">E44</font></i>: 
( <font color="Maroon">c<sub>17</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> <font color="Maroon">c<sub>13</sub></font></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> <font color="Maroon">c<sub>14</sub></font></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> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span> &amp; <font color="Maroon">c<sub>16</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> <font color="Maroon">c<sub>13</sub></font></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> <font color="Maroon">c<sub>14</sub></font></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> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>17</sub></font> )
 <b>by </b><i><a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="21_1_7_2_7_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="21_1_7_2_7_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:21_1_7_2_7_1_1"/>
( <font color="Maroon">c<sub>17</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font> or <font color="Maroon">c<sub>17</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> or <font color="Maroon">c<sub>17</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> or <font color="Maroon">c<sub>17</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font> )
 </span><b>by </b><i><a class="txt" href="bvfunc14.html#E21:21_1_7_2"><i><font color="Green">E33</font></i></a>, <a class="txt" href="bvfunc14.html#E3:21_1_7_2_7"><i><font color="Green">E44</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="21_1_7_2_7_1_1_1"><b>case </b></a><a NAME="E1:21_1_7_2_7_1_1_1"/>
<font color="Maroon">c<sub>17</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:21_1_7_2_7_1_1_1"/>
<font color="Maroon">c<sub>16</sub></font> <a href="hidden.html#R2">in</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> <font color="Maroon">c<sub>13</sub></font></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> <font color="Maroon">c<sub>14</sub></font></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> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>6</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> <font color="Maroon">c<sub>13</sub></font></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> <font color="Maroon">c<sub>14</sub></font></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> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>10</sub></font></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> <font color="Maroon">c<sub>13</sub></font></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> <font color="Maroon">c<sub>14</sub></font></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> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>10</sub></font></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> <font color="Maroon">c<sub>13</sub></font></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> <font color="Maroon">c<sub>14</sub></font></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> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="enumset1.html#K2">}</a></span>
 <b>by </b><i><a class="txt" href="bvfunc14.html#E3:21_1_7_2_7"><i><font color="Green">E44</font></i></a>, <a class="ref" href="enumset1.html#D2">ENUMSET1:def 2</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="21_1_7_2_7_1_1_2"><b>case </b></a><a NAME="E1:21_1_7_2_7_1_1_2"/>
<font color="Maroon">c<sub>17</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:21_1_7_2_7_1_1_2"/>
<font color="Maroon">c<sub>16</sub></font> <a href="hidden.html#R2">in</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> <font color="Maroon">c<sub>13</sub></font></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> <font color="Maroon">c<sub>14</sub></font></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> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>6</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> <font color="Maroon">c<sub>13</sub></font></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> <font color="Maroon">c<sub>14</sub></font></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> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>10</sub></font></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> <font color="Maroon">c<sub>13</sub></font></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> <font color="Maroon">c<sub>14</sub></font></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> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>10</sub></font></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> <font color="Maroon">c<sub>13</sub></font></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> <font color="Maroon">c<sub>14</sub></font></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> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="enumset1.html#K2">}</a></span>
 <b>by </b><i><a class="txt" href="bvfunc14.html#E3:21_1_7_2_7"><i><font color="Green">E44</font></i></a>, <a class="ref" href="enumset1.html#D2">ENUMSET1:def 2</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="21_1_7_2_7_1_1_3"><b>case </b></a><a NAME="E1:21_1_7_2_7_1_1_3"/>
<font color="Maroon">c<sub>17</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:21_1_7_2_7_1_1_3"/>
<font color="Maroon">c<sub>16</sub></font> <a href="hidden.html#R2">in</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> <font color="Maroon">c<sub>13</sub></font></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> <font color="Maroon">c<sub>14</sub></font></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> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>6</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> <font color="Maroon">c<sub>13</sub></font></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> <font color="Maroon">c<sub>14</sub></font></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> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>10</sub></font></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> <font color="Maroon">c<sub>13</sub></font></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> <font color="Maroon">c<sub>14</sub></font></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> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>10</sub></font></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> <font color="Maroon">c<sub>13</sub></font></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> <font color="Maroon">c<sub>14</sub></font></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> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="enumset1.html#K2">}</a></span>
 <b>by </b><i><a class="txt" href="bvfunc14.html#E3:21_1_7_2_7"><i><font color="Green">E44</font></i></a>, <a class="ref" href="enumset1.html#D2">ENUMSET1:def 2</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="21_1_7_2_7_1_1_4"><b>case </b></a><a NAME="E1:21_1_7_2_7_1_1_4"/>
<font color="Maroon">c<sub>17</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:21_1_7_2_7_1_1_4"/>
<font color="Maroon">c<sub>16</sub></font> <a href="hidden.html#R2">in</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> <font color="Maroon">c<sub>13</sub></font></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> <font color="Maroon">c<sub>14</sub></font></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> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>6</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> <font color="Maroon">c<sub>13</sub></font></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> <font color="Maroon">c<sub>14</sub></font></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> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>10</sub></font></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> <font color="Maroon">c<sub>13</sub></font></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> <font color="Maroon">c<sub>14</sub></font></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> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>10</sub></font></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> <font color="Maroon">c<sub>13</sub></font></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> <font color="Maroon">c<sub>14</sub></font></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> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="enumset1.html#K2">}</a></span>
 <b>by </b><i><a class="txt" href="bvfunc14.html#E3:21_1_7_2_7"><i><font color="Green">E44</font></i></a>, <a class="ref" href="enumset1.html#D2">ENUMSET1:def 2</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E5:21_1_7_2_7"/>
<font color="Maroon">c<sub>16</sub></font> <a href="hidden.html#R2">in</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> <font color="Maroon">c<sub>13</sub></font></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> <font color="Maroon">c<sub>14</sub></font></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> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>6</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> <font color="Maroon">c<sub>13</sub></font></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> <font color="Maroon">c<sub>14</sub></font></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> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>10</sub></font></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> <font color="Maroon">c<sub>13</sub></font></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> <font color="Maroon">c<sub>14</sub></font></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> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>10</sub></font></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> <font color="Maroon">c<sub>13</sub></font></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> <font color="Maroon">c<sub>14</sub></font></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> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="enumset1.html#K2">}</a></span>
 ;<br/>


</div><b>end;</b></div>
<a NAME="E32:21_1_7_2"/><i><font color="Green">E44</font></i>: 
<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> <font color="Maroon">c<sub>13</sub></font></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> <font color="Maroon">c<sub>14</sub></font></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> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>6</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> <font color="Maroon">c<sub>13</sub></font></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> <font color="Maroon">c<sub>14</sub></font></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> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>10</sub></font></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> <font color="Maroon">c<sub>13</sub></font></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> <font color="Maroon">c<sub>14</sub></font></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> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>10</sub></font></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> <font color="Maroon">c<sub>13</sub></font></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> <font color="Maroon">c<sub>14</sub></font></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> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="enumset1.html#K2">}</a></span> <a href="tarski.html#R1">c=</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> <font color="Maroon">c<sub>13</sub></font></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> <font color="Maroon">c<sub>14</sub></font></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> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="21_1_7_2_8"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>16</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="E1:21_1_7_2_8"/><i><font color="Green">E45</font></i>: 
<font color="Maroon">c<sub>16</sub></font> <a href="hidden.html#R2">in</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> <font color="Maroon">c<sub>13</sub></font></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> <font color="Maroon">c<sub>14</sub></font></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> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>6</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> <font color="Maroon">c<sub>13</sub></font></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> <font color="Maroon">c<sub>14</sub></font></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> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>10</sub></font></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> <font color="Maroon">c<sub>13</sub></font></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> <font color="Maroon">c<sub>14</sub></font></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> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>10</sub></font></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> <font color="Maroon">c<sub>13</sub></font></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> <font color="Maroon">c<sub>14</sub></font></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> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="enumset1.html#K2">}</a></span>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="21_1_7_2_8_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="21_1_7_2_8_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:21_1_7_2_8_1_1"/>
( <font color="Maroon">c<sub>16</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> <font color="Maroon">c<sub>13</sub></font></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> <font color="Maroon">c<sub>14</sub></font></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> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>6</sub></font> or <font color="Maroon">c<sub>16</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> <font color="Maroon">c<sub>13</sub></font></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> <font color="Maroon">c<sub>14</sub></font></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> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>10</sub></font></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>16</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> <font color="Maroon">c<sub>13</sub></font></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> <font color="Maroon">c<sub>14</sub></font></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> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>10</sub></font></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>16</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> <font color="Maroon">c<sub>13</sub></font></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> <font color="Maroon">c<sub>14</sub></font></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> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>7</sub></font> )
 </span><b>by </b><i><a class="txt" href="bvfunc14.html#E1:21_1_7_2_8"><i><font color="Green">E45</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="21_1_7_2_8_1_1_1"><b>case </b></a><a NAME="E1:21_1_7_2_8_1_1_1"/>
<font color="Maroon">c<sub>16</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> <font color="Maroon">c<sub>13</sub></font></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> <font color="Maroon">c<sub>14</sub></font></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> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>6</sub></font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:21_1_7_2_8_1_1_1"/>
<font color="Maroon">c<sub>16</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> <font color="Maroon">c<sub>13</sub></font></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> <font color="Maroon">c<sub>14</sub></font></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> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="bvfunc14.html#E27:21_1_7_2"><i><font color="Green">E39</font></i></a>, <a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="21_1_7_2_8_1_1_2"><b>case </b></a><a NAME="E1:21_1_7_2_8_1_1_2"/>
<font color="Maroon">c<sub>16</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> <font color="Maroon">c<sub>13</sub></font></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> <font color="Maroon">c<sub>14</sub></font></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> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>4</sub></font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:21_1_7_2_8_1_1_2"/>
<font color="Maroon">c<sub>16</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> <font color="Maroon">c<sub>13</sub></font></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> <font color="Maroon">c<sub>14</sub></font></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> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="bvfunc14.html#E28:21_1_7_2"><i><font color="Green">E40</font></i></a>, <a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="21_1_7_2_8_1_1_3"><b>case </b></a><a NAME="E1:21_1_7_2_8_1_1_3"/>
<font color="Maroon">c<sub>16</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> <font color="Maroon">c<sub>13</sub></font></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> <font color="Maroon">c<sub>14</sub></font></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> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>5</sub></font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:21_1_7_2_8_1_1_3"/>
<font color="Maroon">c<sub>16</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> <font color="Maroon">c<sub>13</sub></font></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> <font color="Maroon">c<sub>14</sub></font></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> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="bvfunc14.html#E29:21_1_7_2"><i><font color="Green">E41</font></i></a>, <a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="21_1_7_2_8_1_1_4"><b>case </b></a><a NAME="E1:21_1_7_2_8_1_1_4"/>
<font color="Maroon">c<sub>16</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> <font color="Maroon">c<sub>13</sub></font></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> <font color="Maroon">c<sub>14</sub></font></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> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>7</sub></font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:21_1_7_2_8_1_1_4"/>
<font color="Maroon">c<sub>16</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> <font color="Maroon">c<sub>13</sub></font></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> <font color="Maroon">c<sub>14</sub></font></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> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="bvfunc14.html#E30:21_1_7_2"><i><font color="Green">E42</font></i></a>, <a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E3:21_1_7_2_8"/>
<font color="Maroon">c<sub>16</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> <font color="Maroon">c<sub>13</sub></font></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> <font color="Maroon">c<sub>14</sub></font></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> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span>
 ;<br/>


</div><b>end;</b></div>
<a NAME="E33:21_1_7_2"/><b>then </b><i><font color="Green">E45</font></i>: 
<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> <font color="Maroon">c<sub>13</sub></font></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> <font color="Maroon">c<sub>14</sub></font></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> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>6</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> <font color="Maroon">c<sub>13</sub></font></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> <font color="Maroon">c<sub>14</sub></font></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> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>10</sub></font></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> <font color="Maroon">c<sub>13</sub></font></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> <font color="Maroon">c<sub>14</sub></font></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> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>10</sub></font></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> <font color="Maroon">c<sub>13</sub></font></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> <font color="Maroon">c<sub>14</sub></font></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> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="enumset1.html#K2">}</a></span> <a href="hidden.html#R1">=</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> <font color="Maroon">c<sub>13</sub></font></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> <font color="Maroon">c<sub>14</sub></font></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> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="bvfunc14.html#E31:21_1_7_2"><i><font color="Green">E43</font></i></a>, <a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a></i>;<br/>
<a NAME="E34:21_1_7_2"/>
 <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> <font color="Maroon">c<sub>13</sub></font></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> <font color="Maroon">c<sub>14</sub></font></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> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>10</sub></font></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="21_1_7_2_9"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>16</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="E1:21_1_7_2_9"/><i><font color="Green">E46</font></i>: 
<font color="Maroon">c<sub>16</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> <font color="Maroon">c<sub>13</sub></font></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> <font color="Maroon">c<sub>14</sub></font></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> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="21_1_7_2_9_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="21_1_7_2_9_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:21_1_7_2_9_1_1"/>
( <font color="Maroon">c<sub>16</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> <font color="Maroon">c<sub>13</sub></font></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> <font color="Maroon">c<sub>14</sub></font></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> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>6</sub></font> or <font color="Maroon">c<sub>16</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> <font color="Maroon">c<sub>13</sub></font></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> <font color="Maroon">c<sub>14</sub></font></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> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>10</sub></font></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>16</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> <font color="Maroon">c<sub>13</sub></font></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> <font color="Maroon">c<sub>14</sub></font></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> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>10</sub></font></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>16</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> <font color="Maroon">c<sub>13</sub></font></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> <font color="Maroon">c<sub>14</sub></font></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> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>7</sub></font> )
 </span><b>by </b><i><a class="txt" href="bvfunc14.html#E31:21_1_7_2"><i><font color="Green">E43</font></i></a>, <a class="txt" href="bvfunc14.html#E1:21_1_7_2_9"><i><font color="Green">E46</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="21_1_7_2_9_1_1_1"><b>case </b></a><a NAME="E1:21_1_7_2_9_1_1_1"/>
<font color="Maroon">c<sub>16</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> <font color="Maroon">c<sub>13</sub></font></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> <font color="Maroon">c<sub>14</sub></font></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> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>6</sub></font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:21_1_7_2_9_1_1_1"/>
<font color="Maroon">c<sub>16</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>
 <b>by </b><i><a class="txt" href="bvfunc14.html#E9:21_1_7_2"><i><font color="Green">E26</font></i></a>, <a class="txt" href="bvfunc14.html#E22:21_1_7_2"><i><font color="Green">E34</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="21_1_7_2_9_1_1_2"><b>case </b></a><a NAME="E1:21_1_7_2_9_1_1_2"/>
<font color="Maroon">c<sub>16</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> <font color="Maroon">c<sub>13</sub></font></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> <font color="Maroon">c<sub>14</sub></font></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> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>4</sub></font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:21_1_7_2_9_1_1_2"/>
<font color="Maroon">c<sub>16</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>
 <b>by </b><i><a class="txt" href="bvfunc14.html#E13:21_1_7_2"><i><font color="Green">E27</font></i></a>, <a class="txt" href="bvfunc14.html#E23:21_1_7_2"><i><font color="Green">E35</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="21_1_7_2_9_1_1_3"><b>case </b></a><a NAME="E1:21_1_7_2_9_1_1_3"/>
<font color="Maroon">c<sub>16</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> <font color="Maroon">c<sub>13</sub></font></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> <font color="Maroon">c<sub>14</sub></font></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> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>5</sub></font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:21_1_7_2_9_1_1_3"/>
<font color="Maroon">c<sub>16</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>
 <b>by </b><i><a class="txt" href="bvfunc14.html#E13:21_1_7_2"><i><font color="Green">E27</font></i></a>, <a class="txt" href="bvfunc14.html#E24:21_1_7_2"><i><font color="Green">E36</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="21_1_7_2_9_1_1_4"><b>case </b></a><a NAME="E1:21_1_7_2_9_1_1_4"/>
<font color="Maroon">c<sub>16</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> <font color="Maroon">c<sub>13</sub></font></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> <font color="Maroon">c<sub>14</sub></font></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> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>7</sub></font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:21_1_7_2_9_1_1_4"/>
<font color="Maroon">c<sub>16</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>
 <b>by </b><i><a class="txt" href="bvfunc14.html#E5:21_1_7_2"><i><font color="Green">E25</font></i></a>, <a class="txt" href="bvfunc14.html#E25:21_1_7_2"><i><font color="Green">E37</font></i></a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E3:21_1_7_2_9"/>
<font color="Maroon">c<sub>16</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>
<b>then reconsider </b><font color="Maroon">c<sub>16</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> <font color="Maroon">c<sub>13</sub></font></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> <font color="Maroon">c<sub>14</sub></font></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> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span> as   <a href="setfam_1.html#NM1">Subset-Family</a> of <font color="Maroon">c<sub>1</sub></font> ;<br/>
<b>reconsider </b><font color="Maroon">c<sub>17</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> <font color="Maroon">c<sub>13</sub></font></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> <font color="Maroon">c<sub>14</sub></font></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> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> as   <a href="funct_1.html#NM1">Function</a> ;<br/>
<a NAME="E37:21_1_7_2"/><i><font color="Green">E46</font></i>: 
 <a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>17</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#E27:21_1_7_2"><i><font color="Green">E39</font></i></a>, <a class="ref" href="funct_1.html#T12">FUNCT_1:12</a></i>;<br/>
<a NAME="E38:21_1_7_2"/><i><font color="Green">E47</font></i>: 
<font color="Maroon">c<sub>8</sub></font> <a href="tarski.html#R1">c=</a>  <a href="setfam_1.html#K8">Intersect</a> <font color="Maroon">c<sub>16</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="21_1_7_2_10"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>18</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="E1:21_1_7_2_10"/><i><font color="Green">E48</font></i>: 
<font color="Maroon">c<sub>18</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>8</sub></font>
 ;<br/>

<a NAME="E2:21_1_7_2_10"/><i><font color="Green">E49</font></i>: 
<font color="Maroon">c<sub>17</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="enumset1.html#K2">{</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>17</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>17</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>17</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>17</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="enumset1.html#K2">}</a></span>
 
<b>by </b><i><a class="ref" href="enumset1.html#D2">ENUMSET1:def 2</a></i>;<br/>
<a NAME="E3:21_1_7_2_10"/>
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>16</sub></font> holds <br/><font color="Maroon">c<sub>18</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="21_1_7_2_10_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>19</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><a NAME="E1:21_1_7_2_10_1"/><i><font color="Green">E50</font></i>: 
<font color="Maroon">c<sub>19</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>16</sub></font>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="21_1_7_2_10_1_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="21_1_7_2_10_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:21_1_7_2_10_1_1_1"/>
( <font color="Maroon">c<sub>19</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>17</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>6</sub></font> or <font color="Maroon">c<sub>19</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>17</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>4</sub></font> or <font color="Maroon">c<sub>19</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>17</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>5</sub></font> or <font color="Maroon">c<sub>19</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>17</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>7</sub></font> )
 </span><b>by </b><i><a class="txt" href="bvfunc14.html#E31:21_1_7_2"><i><font color="Green">E43</font></i></a>, <a class="txt" href="bvfunc14.html#E1:21_1_7_2_10_1"><i><font color="Green">E50</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="21_1_7_2_10_1_1_1_1"><b>case </b></a><a NAME="E1:21_1_7_2_10_1_1_1_1"/><i><font color="Green">E51</font></i>: 
<font color="Maroon">c<sub>19</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>17</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>6</sub></font>
 ;<br/><div class="add"><a NAME="E2:21_1_7_2_10_1_1_1_1"/>
<font color="Maroon">c<sub>18</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>12</sub></font> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>13</sub></font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">c<sub>10</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="bvfunc14.html#E5:21_1_7_2"><i><font color="Green">E25</font></i></a>, <a class="txt" href="bvfunc14.html#E9:21_1_7_2"><i><font color="Green">E26</font></i></a>, <a class="txt" href="bvfunc14.html#E13:21_1_7_2"><i><font color="Green">E27</font></i></a>, <a class="txt" href="bvfunc14.html#E1:21_1_7_2_10"><i><font color="Green">E48</font></i></a>, <a class="ref" href="xboole_1.html#T16">XBOOLE_1:16</a></i>;<br/><b>hence </b><a NAME="E3:21_1_7_2_10_1_1_1_1"/>
<font color="Maroon">c<sub>18</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>19</sub></font>
 <b>by </b><i><a class="txt" href="bvfunc14.html#E22:21_1_7_2"><i><font color="Green">E34</font></i></a>, <a class="txt" href="bvfunc14.html#E1:21_1_7_2_10_1_1_1_1"><i><font color="Green">E51</font></i></a>, <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="21_1_7_2_10_1_1_1_2"><b>case </b></a><a NAME="E1:21_1_7_2_10_1_1_1_2"/><i><font color="Green">E51</font></i>: 
<font color="Maroon">c<sub>19</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>17</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>4</sub></font>
 ;<br/><div class="add"><a NAME="E2:21_1_7_2_10_1_1_1_2"/>
<font color="Maroon">c<sub>18</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>14</sub></font> <a href="xboole_0.html#K3">/\</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>12</sub></font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">c<sub>13</sub></font></span>)</span></span>)</span> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">c<sub>10</sub></font>
 <b>by </b><i><a class="txt" href="bvfunc14.html#E5:21_1_7_2"><i><font color="Green">E25</font></i></a>, <a class="txt" href="bvfunc14.html#E9:21_1_7_2"><i><font color="Green">E26</font></i></a>, <a class="txt" href="bvfunc14.html#E13:21_1_7_2"><i><font color="Green">E27</font></i></a>, <a class="txt" href="bvfunc14.html#E1:21_1_7_2_10"><i><font color="Green">E48</font></i></a>, <a class="ref" href="xboole_1.html#T16">XBOOLE_1:16</a></i>;<br/><a NAME="E3:21_1_7_2_10_1_1_1_2"/><b>then </b>
<font color="Maroon">c<sub>18</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>14</sub></font> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>12</sub></font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">c<sub>13</sub></font></span>)</span> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">c<sub>10</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="xboole_1.html#T16">XBOOLE_1:16</a></i>;<br/><a NAME="E4:21_1_7_2_10_1_1_1_2"/><b>then </b>
<font color="Maroon">c<sub>18</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>14</sub></font> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>12</sub></font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">c<sub>13</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="xboole_1.html#T16">XBOOLE_1:16</a></i>;<br/><a NAME="E5:21_1_7_2_10_1_1_1_2"/><b>then </b>
<font color="Maroon">c<sub>18</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>14</sub></font> <a href="xboole_0.html#K3">/\</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>12</sub></font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">c<sub>13</sub></font>
 <b>by </b><i><a class="ref" href="xboole_1.html#T16">XBOOLE_1:16</a></i>;<br/><b>hence </b><a NAME="E6:21_1_7_2_10_1_1_1_2"/>
<font color="Maroon">c<sub>18</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>19</sub></font>
 <b>by </b><i><a class="txt" href="bvfunc14.html#E23:21_1_7_2"><i><font color="Green">E35</font></i></a>, <a class="txt" href="bvfunc14.html#E1:21_1_7_2_10_1_1_1_2"><i><font color="Green">E51</font></i></a>, <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="21_1_7_2_10_1_1_1_3"><b>case </b></a><a NAME="E1:21_1_7_2_10_1_1_1_3"/><i><font color="Green">E51</font></i>: 
<font color="Maroon">c<sub>19</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>17</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>5</sub></font>
 ;<br/><div class="add"><a NAME="E2:21_1_7_2_10_1_1_1_3"/>
<font color="Maroon">c<sub>18</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>14</sub></font> <a href="xboole_0.html#K3">/\</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>13</sub></font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">c<sub>10</sub></font>
 <b>by </b><i><a class="txt" href="bvfunc14.html#E5:21_1_7_2"><i><font color="Green">E25</font></i></a>, <a class="txt" href="bvfunc14.html#E9:21_1_7_2"><i><font color="Green">E26</font></i></a>, <a class="txt" href="bvfunc14.html#E13:21_1_7_2"><i><font color="Green">E27</font></i></a>, <a class="txt" href="bvfunc14.html#E1:21_1_7_2_10"><i><font color="Green">E48</font></i></a>, <a class="ref" href="xboole_1.html#T16">XBOOLE_1:16</a></i>;<br/><a NAME="E3:21_1_7_2_10_1_1_1_3"/><b>then </b>
<font color="Maroon">c<sub>18</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>14</sub></font> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>13</sub></font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">c<sub>12</sub></font></span>)</span> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">c<sub>10</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="xboole_1.html#T16">XBOOLE_1:16</a></i>;<br/><b>hence </b><a NAME="E4:21_1_7_2_10_1_1_1_3"/>
<font color="Maroon">c<sub>18</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>19</sub></font>
 <b>by </b><i><a class="txt" href="bvfunc14.html#E24:21_1_7_2"><i><font color="Green">E36</font></i></a>, <a class="txt" href="bvfunc14.html#E1:21_1_7_2_10_1_1_1_3"><i><font color="Green">E51</font></i></a>, <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="21_1_7_2_10_1_1_1_4"><b>case </b></a><a NAME="E1:21_1_7_2_10_1_1_1_4"/>
<font color="Maroon">c<sub>19</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>17</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>7</sub></font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:21_1_7_2_10_1_1_1_4"/>
<font color="Maroon">c<sub>18</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>19</sub></font>
 <b>by </b><i><a class="txt" href="bvfunc14.html#E5:21_1_7_2"><i><font color="Green">E25</font></i></a>, <a class="txt" href="bvfunc14.html#E25:21_1_7_2"><i><font color="Green">E37</font></i></a>, <a class="txt" href="bvfunc14.html#E1:21_1_7_2_10"><i><font color="Green">E48</font></i></a>, <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E3:21_1_7_2_10_1"/>
<font color="Maroon">c<sub>18</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>19</sub></font>
 ;<br/>


</div><b>end;</b></div>
<a NAME="E4:21_1_7_2_10"/><b>then </b>
<font color="Maroon">c<sub>18</sub></font> <a href="hidden.html#R2">in</a>  <a href="setfam_1.html#K6">meet</a> <font color="Maroon">c<sub>16</sub></font>
 
<b>by </b><i><a class="txt" href="bvfunc14.html#E32:21_1_7_2"><i><font color="Green">E44</font></i></a>, <a class="txt" href="bvfunc14.html#E2:21_1_7_2_10"><i><font color="Green">E49</font></i></a>, <a class="ref" href="setfam_1.html#D1">SETFAM_1:def 1</a></i>;<br/>
<b>hence </b><a NAME="E5:21_1_7_2_10"/>
<font color="Maroon">c<sub>18</sub></font> <a href="hidden.html#R2">in</a>  <a href="setfam_1.html#K8">Intersect</a> <font color="Maroon">c<sub>16</sub></font>
 <b>by </b><i><a class="txt" href="bvfunc14.html#E32:21_1_7_2"><i><font color="Green">E44</font></i></a>, <a class="txt" href="bvfunc14.html#E2:21_1_7_2_10"><i><font color="Green">E49</font></i></a>, <a class="ref" href="setfam_1.html#D10">SETFAM_1:def 10</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E39:21_1_7_2"/>
 <a href="setfam_1.html#K8">Intersect</a> <font color="Maroon">c<sub>16</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>8</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="21_1_7_2_11"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>18</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="E1:21_1_7_2_11"/>
<font color="Maroon">c<sub>18</sub></font> <a href="hidden.html#R2">in</a>  <a href="setfam_1.html#K8">Intersect</a> <font color="Maroon">c<sub>16</sub></font>
 ;<br/>

<a NAME="E2:21_1_7_2_11"/><b>then </b><i><font color="Green">E48</font></i>: 
<font color="Maroon">c<sub>18</sub></font> <a href="hidden.html#R2">in</a>  <a href="setfam_1.html#K1">meet</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>17</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="bvfunc14.html#E37:21_1_7_2"><i><font color="Green">E46</font></i></a>, <a class="ref" href="setfam_1.html#D10">SETFAM_1:def 10</a></i>;<br/>
<a NAME="E3:21_1_7_2_11"/>
( <font color="Maroon">c<sub>17</sub></font> <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> <font color="Maroon">c<sub>17</sub></font> &amp; <font color="Maroon">c<sub>17</sub></font> <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> <font color="Maroon">c<sub>17</sub></font> &amp; <font color="Maroon">c<sub>17</sub></font> <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> <font color="Maroon">c<sub>17</sub></font> &amp; <font color="Maroon">c<sub>17</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>17</sub></font> )
 
<b>by </b><i><a class="txt" href="bvfunc14.html#E33:21_1_7_2"><i><font color="Green">E45</font></i></a>, <a class="ref" href="enumset1.html#D2">ENUMSET1:def 2</a></i>;<br/>
<a NAME="E4:21_1_7_2_11"/><b>then </b><i><font color="Green">E49</font></i>: 
( <font color="Maroon">c<sub>18</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>17</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>4</sub></font> &amp; <font color="Maroon">c<sub>18</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>17</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>18</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>17</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>18</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>17</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>7</sub></font> )
 
<b>by </b><i><a class="txt" href="bvfunc14.html#E2:21_1_7_2_11"><i><font color="Green">E48</font></i></a>, <a class="ref" href="setfam_1.html#D1">SETFAM_1:def 1</a></i>;<br/>
<a NAME="E5:21_1_7_2_11"/><b>then </b>
<font color="Maroon">c<sub>18</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>13</sub></font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">c<sub>14</sub></font>
 
<b>by </b><i><a class="txt" href="bvfunc14.html#E23:21_1_7_2"><i><font color="Green">E35</font></i></a>, <a class="txt" href="bvfunc14.html#E24:21_1_7_2"><i><font color="Green">E36</font></i></a>, <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/>
<a NAME="E6:21_1_7_2_11"/><b>then </b>
<font color="Maroon">c<sub>18</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>13</sub></font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">c<sub>12</sub></font>
 
<b>by </b><i><a class="txt" href="bvfunc14.html#E22:21_1_7_2"><i><font color="Green">E34</font></i></a>, <a class="txt" href="bvfunc14.html#E4:21_1_7_2_11"><i><font color="Green">E49</font></i></a>, <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/>
<b>hence </b><a NAME="E7:21_1_7_2_11"/>
<font color="Maroon">c<sub>18</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>8</sub></font>
 <b>by </b><i><a class="txt" href="bvfunc14.html#E5:21_1_7_2"><i><font color="Green">E25</font></i></a>, <a class="txt" href="bvfunc14.html#E9:21_1_7_2"><i><font color="Green">E26</font></i></a>, <a class="txt" href="bvfunc14.html#E13:21_1_7_2"><i><font color="Green">E27</font></i></a>, <a class="txt" href="bvfunc14.html#E25:21_1_7_2"><i><font color="Green">E37</font></i></a>, <a class="txt" href="bvfunc14.html#E4:21_1_7_2_11"><i><font color="Green">E49</font></i></a>, <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E40:21_1_7_2"/><b>then </b><i><font color="Green">E48</font></i>: 
<font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R1">=</a>  <a href="setfam_1.html#K8">Intersect</a> <font color="Maroon">c<sub>16</sub></font>
 
<b>by </b><i><a class="txt" href="bvfunc14.html#E38:21_1_7_2"><i><font color="Green">E47</font></i></a>, <a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a></i>;<br/>
<a NAME="E41:21_1_7_2"/>
<font color="Maroon">c<sub>8</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#E1:21_1_7_2"><i><font color="Green">E24</font></i></a>, <a class="ref" href="eqrel_1.html#D6">EQREL_1:def 6</a></i>;<br/>
<b>hence </b><a NAME="E42:21_1_7_2"/>
<font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R2">in</a>  <a href="bvfunc_2.html#K2">'/\'</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K7">\</a> <span class="p2"><a href="bvfunc_2.html#K4">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="bvfunc_2.html#K4">}</a></span></span>)</span>
 <b>by </b><i><a class="txt" href="bvfunc14.html#E9:21_1_7"><i><font color="Green">E21</font></i></a>, <a class="txt" href="bvfunc14.html#E11:21_1_7"><i><font color="Green">E22</font></i></a>, <a class="txt" href="bvfunc14.html#E21:21_1_7_2"><i><font color="Green">E33</font></i></a>, <a class="txt" href="bvfunc14.html#E26:21_1_7_2"><i><font color="Green">E38</font></i></a>, <a class="txt" href="bvfunc14.html#E40:21_1_7_2"><i><font color="Green">E48</font></i></a>, <a class="ref" href="bvfunc_2.html#D1">BVFUNC_2:def 1</a></i>;<br/>


</div><b>end;</b></div><a NAME="E13:21_1_7"/>
 <a href="bvfunc_2.html#K2">'/\'</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K7">\</a> <span class="p2"><a href="bvfunc_2.html#K4">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="bvfunc_2.html#K4">}</a></span></span>)</span> <a href="tarski.html#R1">c=</a> <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="partit1.html#K2">'/\'</a> <font color="Maroon">c<sub>7</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="21_1_7_3"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>8</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="E1:21_1_7_3"/>
<font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R2">in</a>  <a href="bvfunc_2.html#K2">'/\'</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K7">\</a> <span class="p2"><a href="bvfunc_2.html#K4">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="bvfunc_2.html#K4">}</a></span></span>)</span>
 ;<br/>

<b>then consider </b><font color="Maroon">c<sub>9</sub></font> being   <a href="funct_1.html#NM1">Function</a>, <font color="Maroon">c<sub>10</sub></font> being   <a href="setfam_1.html#NM1">Subset-Family</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E3:21_1_7_3"/><i><font color="Green">E24</font></i>: 
(  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="bvfunc_2.html#K4">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="bvfunc_2.html#K4">}</a></span> &amp;  <a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>10</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> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="bvfunc_2.html#K4">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="bvfunc_2.html#K4">}</a></span> holds <br/><font color="Maroon">c<sub>9</sub></font> <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> ) &amp; <font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R1">=</a>  <a href="setfam_1.html#K8">Intersect</a> <font color="Maroon">c<sub>10</sub></font> &amp; <font color="Maroon">c<sub>8</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="ref" href="bvfunc_2.html#D1">BVFUNC_2:def 1</a></i>;<br/>
<a NAME="E4:21_1_7_3"/>
( <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="bvfunc_2.html#K4">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="bvfunc_2.html#K4">}</a></span> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="bvfunc_2.html#K4">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="bvfunc_2.html#K4">}</a></span> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="bvfunc_2.html#K4">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="bvfunc_2.html#K4">}</a></span> &amp; <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="bvfunc_2.html#K4">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="bvfunc_2.html#K4">}</a></span> )
 
<b>by </b><i><a class="txt" href="bvfunc14.html#E9:21_1_7"><i><font color="Green">E21</font></i></a>, <a class="txt" href="bvfunc14.html#E11:21_1_7"><i><font color="Green">E22</font></i></a>, <a class="ref" href="enumset1.html#D2">ENUMSET1:def 2</a></i>;<br/>
<a NAME="E5:21_1_7_3"/><b>then </b><i><font color="Green">E25</font></i>: 
( <font color="Maroon">c<sub>9</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>4</sub></font> &amp; <font color="Maroon">c<sub>9</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>9</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>9</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>7</sub></font> )
 
<b>by </b><i><a class="txt" href="bvfunc14.html#E3:21_1_7_3"><i><font color="Green">E24</font></i></a></i>;<br/>
<a NAME="E6:21_1_7_3"/>
( <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>9</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>9</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>9</sub></font> &amp; <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>9</sub></font> )
 
<b>by </b><i><a class="txt" href="bvfunc14.html#E9:21_1_7"><i><font color="Green">E21</font></i></a>, <a class="txt" href="bvfunc14.html#E11:21_1_7"><i><font color="Green">E22</font></i></a>, <a class="txt" href="bvfunc14.html#E3:21_1_7_3"><i><font color="Green">E24</font></i></a>, <a class="ref" href="enumset1.html#D2">ENUMSET1:def 2</a></i>;<br/>
<a NAME="E7:21_1_7_3"/><b>then </b><i><font color="Green">E26</font></i>: 
( <font color="Maroon">c<sub>9</sub></font> <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> <font color="Maroon">c<sub>9</sub></font> &amp; <font color="Maroon">c<sub>9</sub></font> <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> <font color="Maroon">c<sub>9</sub></font> &amp; <font color="Maroon">c<sub>9</sub></font> <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> <font color="Maroon">c<sub>9</sub></font> &amp; <font color="Maroon">c<sub>9</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>9</sub></font> )
 
<b>by </b><i><a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/>
<a NAME="E8:21_1_7_3"/><i><font color="Green">E27</font></i>: 
not <font color="Maroon">c<sub>8</sub></font> <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="txt" href="bvfunc14.html#E3:21_1_7_3"><i><font color="Green">E24</font></i></a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<a NAME="E9:21_1_7_3"/><i><font color="Green">E28</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>8</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="21_1_7_3_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>11</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="E1:21_1_7_3_1"/><i><font color="Green">E29</font></i>: 
<font color="Maroon">c<sub>11</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"><font color="Maroon">c<sub>9</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span>
 ;<br/>

<a NAME="E2:21_1_7_3_1"/><b>then </b><i><font color="Green">E30</font></i>: 
( <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> &amp; <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>9</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>7</sub></font> )
 
<b>by </b><i><a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/>
<a NAME="E3:21_1_7_3_1"/><b>then </b><i><font color="Green">E31</font></i>: 
( <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> &amp; <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>9</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>6</sub></font> )
 
<b>by </b><i><a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/>
<a NAME="E4:21_1_7_3_1"/><i><font color="Green">E32</font></i>: 
 <a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>9</sub></font> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="enumset1.html#K2">{</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="enumset1.html#K2">}</a></span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="21_1_7_3_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>12</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="E1:21_1_7_3_1_1"/>
<font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>9</sub></font>
 ;<br/>

<b>then consider </b><font color="Maroon">c<sub>13</sub></font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E3:21_1_7_3_1_1"/><i><font color="Green">E33</font></i>: 
( <font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>9</sub></font> &amp; <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>9</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>13</sub></font> )
 <b>by </b><i><a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="21_1_7_3_1_1_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="21_1_7_3_1_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:21_1_7_3_1_1_1_1"/>
( <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> or <font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font> )
 </span><b>by </b><i><a class="txt" href="bvfunc14.html#E9:21_1_7"><i><font color="Green">E21</font></i></a>, <a class="txt" href="bvfunc14.html#E11:21_1_7"><i><font color="Green">E22</font></i></a>, <a class="txt" href="bvfunc14.html#E3:21_1_7_3"><i><font color="Green">E24</font></i></a>, <a class="txt" href="bvfunc14.html#E3:21_1_7_3_1_1"><i><font color="Green">E33</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="21_1_7_3_1_1_1_1_1"><b>case </b></a><a NAME="E1:21_1_7_3_1_1_1_1_1"/>
<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"><b>hence </b><a NAME="E2:21_1_7_3_1_1_1_1_1"/>
<font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="enumset1.html#K2">{</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="enumset1.html#K2">}</a></span>
 <b>by </b><i><a class="txt" href="bvfunc14.html#E3:21_1_7_3_1_1"><i><font color="Green">E33</font></i></a>, <a class="ref" href="enumset1.html#D2">ENUMSET1:def 2</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="21_1_7_3_1_1_1_1_2"><b>case </b></a><a NAME="E1:21_1_7_3_1_1_1_1_2"/>
<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"><b>hence </b><a NAME="E2:21_1_7_3_1_1_1_1_2"/>
<font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="enumset1.html#K2">{</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="enumset1.html#K2">}</a></span>
 <b>by </b><i><a class="txt" href="bvfunc14.html#E3:21_1_7_3_1_1"><i><font color="Green">E33</font></i></a>, <a class="ref" href="enumset1.html#D2">ENUMSET1:def 2</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="21_1_7_3_1_1_1_1_3"><b>case </b></a><a NAME="E1:21_1_7_3_1_1_1_1_3"/>
<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"><b>hence </b><a NAME="E2:21_1_7_3_1_1_1_1_3"/>
<font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="enumset1.html#K2">{</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="enumset1.html#K2">}</a></span>
 <b>by </b><i><a class="txt" href="bvfunc14.html#E3:21_1_7_3_1_1"><i><font color="Green">E33</font></i></a>, <a class="ref" href="enumset1.html#D2">ENUMSET1:def 2</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="21_1_7_3_1_1_1_1_4"><b>case </b></a><a NAME="E1:21_1_7_3_1_1_1_1_4"/>
<font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:21_1_7_3_1_1_1_1_4"/>
<font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="enumset1.html#K2">{</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="enumset1.html#K2">}</a></span>
 <b>by </b><i><a class="txt" href="bvfunc14.html#E3:21_1_7_3_1_1"><i><font color="Green">E33</font></i></a>, <a class="ref" href="enumset1.html#D2">ENUMSET1:def 2</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E5:21_1_7_3_1_1"/>
<font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="enumset1.html#K2">{</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="enumset1.html#K2">}</a></span>
 ;<br/>


</div><b>end;</b></div>
<a NAME="E5:21_1_7_3_1"/>
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>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>9</sub></font> holds <br/><font color="Maroon">c<sub>11</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="21_1_7_3_1_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>12</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><a NAME="E1:21_1_7_3_1_2"/><i><font color="Green">E33</font></i>: 
<font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>9</sub></font>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="21_1_7_3_1_2_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="21_1_7_3_1_2_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:21_1_7_3_1_2_1_1"/>
( <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>9</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>4</sub></font> or <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>9</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>5</sub></font> or <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>9</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>6</sub></font> or <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>9</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>7</sub></font> )
 </span><b>by </b><i><a class="txt" href="bvfunc14.html#E4:21_1_7_3_1"><i><font color="Green">E32</font></i></a>, <a class="txt" href="bvfunc14.html#E1:21_1_7_3_1_2"><i><font color="Green">E33</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="21_1_7_3_1_2_1_1_1"><b>case </b></a><a NAME="E1:21_1_7_3_1_2_1_1_1"/>
<font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>9</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>4</sub></font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:21_1_7_3_1_2_1_1_1"/>
<font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>12</sub></font>
 <b>by </b><i><a class="txt" href="bvfunc14.html#E3:21_1_7_3_1"><i><font color="Green">E31</font></i></a>, <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="21_1_7_3_1_2_1_1_2"><b>case </b></a><a NAME="E1:21_1_7_3_1_2_1_1_2"/>
<font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>9</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>5</sub></font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:21_1_7_3_1_2_1_1_2"/>
<font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>12</sub></font>
 <b>by </b><i><a class="txt" href="bvfunc14.html#E3:21_1_7_3_1"><i><font color="Green">E31</font></i></a>, <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="21_1_7_3_1_2_1_1_3"><b>case </b></a><a NAME="E1:21_1_7_3_1_2_1_1_3"/>
<font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>9</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>6</sub></font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:21_1_7_3_1_2_1_1_3"/>
<font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>12</sub></font>
 <b>by </b><i><a class="txt" href="bvfunc14.html#E2:21_1_7_3_1"><i><font color="Green">E30</font></i></a>, <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="21_1_7_3_1_2_1_1_4"><b>case </b></a><a NAME="E1:21_1_7_3_1_2_1_1_4"/>
<font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>9</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>7</sub></font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:21_1_7_3_1_2_1_1_4"/>
<font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>12</sub></font>
 <b>by </b><i><a class="txt" href="bvfunc14.html#E1:21_1_7_3_1"><i><font color="Green">E29</font></i></a>, <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E3:21_1_7_3_1_2"/>
<font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>12</sub></font>
 ;<br/>


</div><b>end;</b></div>
<a NAME="E6:21_1_7_3_1"/><b>then </b>
<font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R2">in</a>  <a href="setfam_1.html#K1">meet</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>9</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="bvfunc14.html#E7:21_1_7_3"><i><font color="Green">E26</font></i></a>, <a class="ref" href="setfam_1.html#D1">SETFAM_1:def 1</a></i>;<br/>
<b>hence </b><a NAME="E7:21_1_7_3_1"/>
<font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>8</sub></font>
 <b>by </b><i><a class="txt" href="bvfunc14.html#E3:21_1_7_3"><i><font color="Green">E24</font></i></a>, <a class="txt" href="bvfunc14.html#E7:21_1_7_3"><i><font color="Green">E26</font></i></a>, <a class="ref" href="setfam_1.html#D10">SETFAM_1:def 10</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E10:21_1_7_3"/><i><font color="Green">E29</font></i>: 
<font color="Maroon">c<sub>8</sub></font> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="21_1_7_3_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>11</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="E1:21_1_7_3_2"/>
<font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>8</sub></font>
 ;<br/>

<a NAME="E2:21_1_7_3_2"/><b>then </b>
<font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R2">in</a>  <a href="setfam_1.html#K1">meet</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>9</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="bvfunc14.html#E3:21_1_7_3"><i><font color="Green">E24</font></i></a>, <a class="txt" href="bvfunc14.html#E7:21_1_7_3"><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="E3:21_1_7_3_2"/><b>then </b><i><font color="Green">E30</font></i>: 
( <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>9</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>4</sub></font> &amp; <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>9</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>9</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>9</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>7</sub></font> )
 
<b>by </b><i><a class="txt" href="bvfunc14.html#E7:21_1_7_3"><i><font color="Green">E26</font></i></a>, <a class="ref" href="setfam_1.html#D1">SETFAM_1:def 1</a></i>;<br/>
<a NAME="E4:21_1_7_3_2"/><b>then </b>
<font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/>
<a NAME="E5:21_1_7_3_2"/><b>then </b>
<font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="bvfunc14.html#E3:21_1_7_3_2"><i><font color="Green">E30</font></i></a>, <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/>
<b>hence </b><a NAME="E6:21_1_7_3_2"/>
<font color="Maroon">c<sub>11</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"><font color="Maroon">c<sub>9</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="bvfunc14.html#E3:21_1_7_3_2"><i><font color="Green">E30</font></i></a>, <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E11:21_1_7_3"/><b>then </b><i><font color="Green">E30</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>8</sub></font>
 
<b>by </b><i><a class="txt" href="bvfunc14.html#E9:21_1_7_3"><i><font color="Green">E28</font></i></a>, <a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a></i>;<br/>
<b>set </b><font color="Maroon">c<sub>11</sub></font> = <span class="p1">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>5</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"><font color="Maroon">c<sub>9</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span>;<br/>
<a NAME="E12:21_1_7_3"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>6</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#E3:21_1_7_3"><i><font color="Green">E24</font></i></a>, <a class="txt" href="bvfunc14.html#E9:21_1_7_3"><i><font color="Green">E28</font></i></a>, <a class="txt" href="bvfunc14.html#E10:21_1_7_3"><i><font color="Green">E29</font></i></a>, <a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a></i>;<br/>
<a NAME="E13:21_1_7_3"/><b>then </b><i><font color="Green">E31</font></i>: 
not <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>6</sub></font></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="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<a NAME="E14:21_1_7_3"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>5</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#E3:21_1_7_3"><i><font color="Green">E24</font></i></a>, <a class="txt" href="bvfunc14.html#E9:21_1_7_3"><i><font color="Green">E28</font></i></a>, <a class="txt" href="bvfunc14.html#E10:21_1_7_3"><i><font color="Green">E29</font></i></a>, <a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a></i>;<br/>
<a NAME="E15:21_1_7_3"/><b>then </b><i><font color="Green">E32</font></i>: 
not <span class="p1">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>5</sub></font></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="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<a NAME="E16:21_1_7_3"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="setfam_1.html#K3">INTERSECTION</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="txt" href="bvfunc14.html#E5:21_1_7_3"><i><font color="Green">E25</font></i></a>, <a class="ref" href="setfam_1.html#D5">SETFAM_1:def 5</a></i>;<br/>
<a NAME="E17:21_1_7_3"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>5</sub></font></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>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></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="txt" href="bvfunc14.html#E15:21_1_7_3"><i><font color="Green">E32</font></i></a>, <a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/>
<a NAME="E18:21_1_7_3"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>4</sub></font> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="ref" href="partit1.html#D4">PARTIT1:def 4</a></i>;<br/>
<a NAME="E19:21_1_7_3"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="setfam_1.html#K3">INTERSECTION</a> <span class="p1">(<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>,<font color="Maroon">c<sub>6</sub></font>
 
<b>by </b><i><a class="txt" href="bvfunc14.html#E5:21_1_7_3"><i><font color="Green">E25</font></i></a>, <a class="ref" href="setfam_1.html#D5">SETFAM_1:def 5</a></i>;<br/>
<a NAME="E20:21_1_7_3"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="setfam_1.html#K3">INTERSECTION</a> <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>,<font color="Maroon">c<sub>6</sub></font></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="txt" href="bvfunc14.html#E13:21_1_7_3"><i><font color="Green">E31</font></i></a>, <a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/>
<a NAME="E21:21_1_7_3"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="hidden.html#R2">in</a> <span class="p1">(<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>
 
<b>by </b><i><a class="ref" href="partit1.html#D4">PARTIT1:def 4</a></i>;<br/>
<a NAME="E22:21_1_7_3"/><b>then </b>
<font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R2">in</a>  <a href="setfam_1.html#K3">INTERSECTION</a> <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>,<font color="Maroon">c<sub>7</sub></font>
 
<b>by </b><i><a class="txt" href="bvfunc14.html#E5:21_1_7_3"><i><font color="Green">E25</font></i></a>, <a class="txt" href="bvfunc14.html#E11:21_1_7_3"><i><font color="Green">E30</font></i></a>, <a class="ref" href="setfam_1.html#D5">SETFAM_1:def 5</a></i>;<br/>
<a NAME="E23:21_1_7_3"/><b>then </b>
<font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="setfam_1.html#K3">INTERSECTION</a> <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>,<font color="Maroon">c<sub>7</sub></font></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="txt" href="bvfunc14.html#E8:21_1_7_3"><i><font color="Green">E27</font></i></a>, <a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/>
<b>hence </b><a NAME="E24:21_1_7_3"/>
<font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R2">in</a> <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="partit1.html#K2">'/\'</a> <font color="Maroon">c<sub>7</sub></font>
 <b>by </b><i><a class="ref" href="partit1.html#D4">PARTIT1:def 4</a></i>;<br/>


</div><b>end;</b></div><a NAME="E14:21_1_7"/><b>then </b>
 <a href="bvfunc_2.html#K2">'/\'</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K7">\</a> <span class="p2"><a href="bvfunc_2.html#K4">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="bvfunc_2.html#K4">}</a></span></span>)</span> <a href="hidden.html#R1">=</a> <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="partit1.html#K2">'/\'</a> <font color="Maroon">c<sub>7</sub></font>
 <b>by </b><i><a class="txt" href="bvfunc14.html#E12:21_1_7"><i><font color="Green">E23</font></i></a>, <a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a></i>;<br/><b>hence </b><a NAME="E15:21_1_7"/>
 <a href="bvfunc_2.html#K5">CompF</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <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="partit1.html#K2">'/\'</a> <font color="Maroon">c<sub>7</sub></font>
 <b>by </b><i><a class="ref" href="bvfunc_2.html#D7">BVFUNC_2:def 7</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div>
