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

<b>consider </b><font color="Maroon">c<sub>1</sub></font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E2:14_1"/><i><font color="Green">E18</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  holds <br/>( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font> iff ( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">F<sub>1</sub></font>() &amp; <font color="Maroon">P<sub>1</sub></font>[<font color="Olive">b<sub>1</sub></font>] ) )
 <b>from </b><i><a class="ref" href="xboole_0.html#S1">XBOOLE_0:sch 1</a>();<br/></i>
<b>consider </b><font color="Maroon">c<sub>2</sub></font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E4:14_1"/><i><font color="Green">E19</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  holds <br/>( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> iff ( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">F<sub>1</sub></font>() &amp; <font color="Maroon">P<sub>2</sub></font>[<font color="Olive">b<sub>1</sub></font>] ) )
 <b>from </b><i><a class="ref" href="xboole_0.html#S1">XBOOLE_0:sch 1</a>();<br/></i>
<b>consider </b><font color="Maroon">c<sub>3</sub></font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E6:14_1"/><i><font color="Green">E20</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  holds <br/>( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>3</sub></font> iff ( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">F<sub>1</sub></font>() &amp; <font color="Maroon">P<sub>3</sub></font>[<font color="Olive">b<sub>1</sub></font>] ) )
 <b>from </b><i><a class="ref" href="xboole_0.html#S1">XBOOLE_0:sch 1</a>();<br/></i>
<b>consider </b><font color="Maroon">c<sub>4</sub></font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E8:14_1"/><i><font color="Green">E21</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  holds <br/>( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>4</sub></font> iff ( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">F<sub>1</sub></font>() &amp; <font color="Maroon">P<sub>4</sub></font>[<font color="Olive">b<sub>1</sub></font>] ) )
 <b>from </b><i><a class="ref" href="xboole_0.html#S1">XBOOLE_0:sch 1</a>();<br/></i>
<b>consider </b><font color="Maroon">c<sub>5</sub></font> being   <a href="funct_1.html#NM1">Function</a><b> such that </b><br/><a NAME="E10:14_1"/><i><font color="Green">E22</font></i>: 
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font>
 <b>and </b><br/><a NAME="E11:14_1"/><i><font color="Green">E23</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>1</sub></font> holds <br/><font color="Maroon">c<sub>5</sub></font> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">F<sub>2</sub></font>(<font color="Olive">b<sub>1</sub></font>)
 <b>from </b><i><a class="ref" href="funct_1.html#S3">FUNCT_1:sch 3</a>();<br/></i>
<b>consider </b><font color="Maroon">c<sub>6</sub></font> being   <a href="funct_1.html#NM1">Function</a><b> such that </b><br/><a NAME="E13:14_1"/><i><font color="Green">E24</font></i>: 
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font>
 <b>and </b><br/><a NAME="E14:14_1"/><i><font color="Green">E25</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> holds <br/><font color="Maroon">c<sub>6</sub></font> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">F<sub>3</sub></font>(<font color="Olive">b<sub>1</sub></font>)
 <b>from </b><i><a class="ref" href="funct_1.html#S3">FUNCT_1:sch 3</a>();<br/></i>
<b>consider </b><font color="Maroon">c<sub>7</sub></font> being   <a href="funct_1.html#NM1">Function</a><b> such that </b><br/><a NAME="E16:14_1"/><i><font color="Green">E26</font></i>: 
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font>
 <b>and </b><br/><a NAME="E17:14_1"/><i><font color="Green">E27</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>3</sub></font> holds <br/><font color="Maroon">c<sub>7</sub></font> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">F<sub>4</sub></font>(<font color="Olive">b<sub>1</sub></font>)
 <b>from </b><i><a class="ref" href="funct_1.html#S3">FUNCT_1:sch 3</a>();<br/></i>
<b>consider </b><font color="Maroon">c<sub>8</sub></font> being   <a href="funct_1.html#NM1">Function</a><b> such that </b><br/><a NAME="E19:14_1"/><i><font color="Green">E28</font></i>: 
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font>
 <b>and </b><br/><a NAME="E20:14_1"/><i><font color="Green">E29</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>4</sub></font> holds <br/><font color="Maroon">c<sub>8</sub></font> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">F<sub>5</sub></font>(<font color="Olive">b<sub>1</sub></font>)
 <b>from </b><i><a class="ref" href="funct_1.html#S3">FUNCT_1:sch 3</a>();<br/></i>
<b>set </b><font color="Maroon">c<sub>9</sub></font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="funct_4.html#K1">+*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="funct_4.html#K1">+*</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="funct_4.html#K1">+*</a> <font color="Maroon">c<sub>8</sub></font>;<br/>
<b>take </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="funct_4.html#K1">+*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="funct_4.html#K1">+*</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="funct_4.html#K1">+*</a> <font color="Maroon">c<sub>8</sub></font>
;<br/>

<i><font color="Green">E30</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"><font color="Maroon">c<sub>5</sub></font> <a href="funct_4.html#K1">+*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="funct_4.html#K1">+*</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="funct_4.html#K1">+*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> = 
<span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="funct_4.html#K1">+*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="funct_4.html#K1">+*</a> <font color="Maroon">c<sub>7</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> <font color="Maroon">c<sub>8</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="funct_4.html#D1">FUNCT_4:def 1</a></i>
<br/>.= 
<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>5</sub></font> <a href="funct_4.html#K1">+*</a> <font color="Maroon">c<sub>6</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> <font color="Maroon">c<sub>7</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> <font color="Maroon">c<sub>8</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="funct_4.html#D1">FUNCT_4:def 1</a></i>
<br/>.= 
<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> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p3">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>6</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> <font color="Maroon">c<sub>7</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> <font color="Maroon">c<sub>8</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="funct_4.html#D1">FUNCT_4:def 1</a></i>
;<br/>
<b>thus </b><a NAME="E22:14_1"/>
 <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>5</sub></font> <a href="funct_4.html#K1">+*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="funct_4.html#K1">+*</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="funct_4.html#K1">+*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">F<sub>1</sub></font>()
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_1_2"><b>proof </b></a><div class="add">

<a NAME="E1:14_1_2"/><i><font color="Green">E31</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">F<sub>1</sub></font>()
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_1_2_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>10</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>thus </b><a NAME="E1:14_1_2_1"/>
(  not <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font> or <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">F<sub>1</sub></font>() )
 <b>by </b><i><a class="txt" href="recdef_2.html#E2:14_1"><i><font color="Green">E18</font></i></a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E2:14_1_2"/>
<font color="Maroon">c<sub>2</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">F<sub>1</sub></font>()
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_1_2_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>10</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>thus </b><a NAME="E1:14_1_2_2"/>
(  not <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> or <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">F<sub>1</sub></font>() )
 <b>by </b><i><a class="txt" href="recdef_2.html#E4:14_1"><i><font color="Green">E19</font></i></a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E3:14_1_2"/><b>then </b><i><font color="Green">E32</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">c<sub>2</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">F<sub>1</sub></font>()
 
<b>by </b><i><a class="txt" href="recdef_2.html#E1:14_1_2"><i><font color="Green">E31</font></i></a>, <a class="ref" href="xboole_1.html#T8">XBOOLE_1:8</a></i>;<br/>
<a NAME="E4:14_1_2"/>
<font color="Maroon">c<sub>3</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">F<sub>1</sub></font>()
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_1_2_3"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>10</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>thus </b><a NAME="E1:14_1_2_3"/>
(  not <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>3</sub></font> or <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">F<sub>1</sub></font>() )
 <b>by </b><i><a class="txt" href="recdef_2.html#E6:14_1"><i><font color="Green">E20</font></i></a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E5:14_1_2"/><b>then </b><i><font color="Green">E33</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">c<sub>3</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">F<sub>1</sub></font>()
 
<b>by </b><i><a class="txt" href="recdef_2.html#E3:14_1_2"><i><font color="Green">E32</font></i></a>, <a class="ref" href="xboole_1.html#T8">XBOOLE_1:8</a></i>;<br/>
<a NAME="E6:14_1_2"/>
<font color="Maroon">c<sub>4</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">F<sub>1</sub></font>()
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_1_2_4"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>10</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>thus </b><a NAME="E1:14_1_2_4"/>
(  not <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>4</sub></font> or <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">F<sub>1</sub></font>() )
 <b>by </b><i><a class="txt" href="recdef_2.html#E8:14_1"><i><font color="Green">E21</font></i></a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E7:14_1_2"/>
 <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>5</sub></font> <a href="funct_4.html#K1">+*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="funct_4.html#K1">+*</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="funct_4.html#K1">+*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">F<sub>1</sub></font>()
 <b>by </b><i><a class="txt" href="recdef_2.html#E10:14_1"><i><font color="Green">E22</font></i></a>, <a class="txt" href="recdef_2.html#E13:14_1"><i><font color="Green">E24</font></i></a>, <a class="txt" href="recdef_2.html#E16:14_1"><i><font color="Green">E26</font></i></a>, <a class="txt" href="recdef_2.html#E19:14_1"><i><font color="Green">E28</font></i></a>, <a class="txt" href="recdef_2.html#E21:14_1"><i><font color="Green">E30</font></i></a>, <a class="txt" href="recdef_2.html#E5:14_1_2"><i><font color="Green">E33</font></i></a>, <a class="ref" href="xboole_1.html#T8">XBOOLE_1:8</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a><br/>

<b>let </b><font color="Maroon">c<sub>10</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="E8:14_1_2"/><i><font color="Green">E34</font></i>: 
<font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">F<sub>1</sub></font>()
 ;<br/>

<a NAME="E9:14_1_2"/><b>then </b>
( <font color="Maroon">P<sub>1</sub></font>[<font color="Maroon">c<sub>10</sub></font>] or <font color="Maroon">P<sub>2</sub></font>[<font color="Maroon">c<sub>10</sub></font>] or <font color="Maroon">P<sub>3</sub></font>[<font color="Maroon">c<sub>10</sub></font>] or <font color="Maroon">P<sub>4</sub></font>[<font color="Maroon">c<sub>10</sub></font>] )
 
<b>by </b><i><a class="txt" href="recdef_2.html#E2:14"><i><font color="Green">E17</font></i></a></i>;<br/>
<a NAME="E10:14_1_2"/><b>then </b>
( <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font> or <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> or <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>3</sub></font> or <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>4</sub></font> )
 
<b>by </b><i><a class="txt" href="recdef_2.html#E2:14_1"><i><font color="Green">E18</font></i></a>, <a class="txt" href="recdef_2.html#E4:14_1"><i><font color="Green">E19</font></i></a>, <a class="txt" href="recdef_2.html#E6:14_1"><i><font color="Green">E20</font></i></a>, <a class="txt" href="recdef_2.html#E8:14_1"><i><font color="Green">E21</font></i></a>, <a class="txt" href="recdef_2.html#E8:14_1_2"><i><font color="Green">E34</font></i></a></i>;<br/>
<a NAME="E11:14_1_2"/><b>then </b>
( <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">c<sub>2</sub></font> or <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>3</sub></font> or <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>4</sub></font> )
 
<b>by </b><i><a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/>
<a NAME="E12:14_1_2"/><b>then </b>
( <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">c<sub>3</sub></font> or <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>4</sub></font> )
 
<b>by </b><i><a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/>
<b>hence </b><a NAME="E13:14_1_2"/>
<font color="Maroon">c<sub>10</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"><font color="Maroon">c<sub>5</sub></font> <a href="funct_4.html#K1">+*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="funct_4.html#K1">+*</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="funct_4.html#K1">+*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="recdef_2.html#E10:14_1"><i><font color="Green">E22</font></i></a>, <a class="txt" href="recdef_2.html#E13:14_1"><i><font color="Green">E24</font></i></a>, <a class="txt" href="recdef_2.html#E16:14_1"><i><font color="Green">E26</font></i></a>, <a class="txt" href="recdef_2.html#E19:14_1"><i><font color="Green">E28</font></i></a>, <a class="txt" href="recdef_2.html#E21:14_1"><i><font color="Green">E30</font></i></a>, <a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/>


</div><b>end;</b></div>

<b>let </b><font color="Maroon">c<sub>10</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><a NAME="E23:14_1"/><i><font color="Green">E31</font></i>: 
<font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">F<sub>1</sub></font>()
 ;<br/>

<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:14_1_3"/><i><font color="Green">E32</font></i>: 
<font color="Maroon">P<sub>1</sub></font>[<font color="Maroon">c<sub>10</sub></font>]
 ;<br/><a NAME="E2:14_1_3"/><b>then </b><i><font color="Green">E33</font></i>: 
<font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="recdef_2.html#E2:14_1"><i><font color="Green">E18</font></i></a>, <a class="txt" href="recdef_2.html#E23:14_1"><i><font color="Green">E31</font></i></a></i>;<br/><a NAME="E3:14_1_3"/>
<font color="Maroon">P<sub>2</sub></font>[<font color="Maroon">c<sub>10</sub></font>]
 <b>by </b><i><a class="txt" href="recdef_2.html#E1:14"><i><font color="Green">E16</font></i></a>, <a class="txt" href="recdef_2.html#E23:14_1"><i><font color="Green">E31</font></i></a>, <a class="txt" href="recdef_2.html#E1:14_1_3"><i><font color="Green">E32</font></i></a></i>;<br/><a NAME="E4:14_1_3"/><b>then </b><i><font color="Green">E34</font></i>: 
not <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="recdef_2.html#E4:14_1"><i><font color="Green">E19</font></i></a></i>;<br/><a NAME="E5:14_1_3"/>
<font color="Maroon">P<sub>3</sub></font>[<font color="Maroon">c<sub>10</sub></font>]
 <b>by </b><i><a class="txt" href="recdef_2.html#E1:14"><i><font color="Green">E16</font></i></a>, <a class="txt" href="recdef_2.html#E23:14_1"><i><font color="Green">E31</font></i></a>, <a class="txt" href="recdef_2.html#E1:14_1_3"><i><font color="Green">E32</font></i></a></i>;<br/><a NAME="E6:14_1_3"/><b>then </b><i><font color="Green">E35</font></i>: 
not <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="recdef_2.html#E6:14_1"><i><font color="Green">E20</font></i></a></i>;<br/><a NAME="E7:14_1_3"/>
<font color="Maroon">P<sub>4</sub></font>[<font color="Maroon">c<sub>10</sub></font>]
 <b>by </b><i><a class="txt" href="recdef_2.html#E1:14"><i><font color="Green">E16</font></i></a>, <a class="txt" href="recdef_2.html#E23:14_1"><i><font color="Green">E31</font></i></a>, <a class="txt" href="recdef_2.html#E1:14_1_3"><i><font color="Green">E32</font></i></a></i>;<br/><a NAME="E8:14_1_3"/><b>then </b>
not <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="txt" href="recdef_2.html#E8:14_1"><i><font color="Green">E21</font></i></a></i>;<br/><b>hence </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="funct_4.html#K1">+*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="funct_4.html#K1">+*</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="funct_4.html#K1">+*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>10</sub></font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="funct_4.html#K1">+*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="funct_4.html#K1">+*</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>10</sub></font>
<b>by </b><i><a class="txt" href="recdef_2.html#E19:14_1"><i><font color="Green">E28</font></i></a>, <a class="ref" href="funct_4.html#T12">FUNCT_4:12</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="funct_4.html#K1">+*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>10</sub></font>
<b>by </b><i><a class="txt" href="recdef_2.html#E16:14_1"><i><font color="Green">E26</font></i></a>, <a class="txt" href="recdef_2.html#E6:14_1_3"><i><font color="Green">E35</font></i></a>, <a class="ref" href="funct_4.html#T12">FUNCT_4:12</a></i>
<br/>.= 
<font color="Maroon">c<sub>5</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>10</sub></font>
<b>by </b><i><a class="txt" href="recdef_2.html#E13:14_1"><i><font color="Green">E24</font></i></a>, <a class="txt" href="recdef_2.html#E4:14_1_3"><i><font color="Green">E34</font></i></a>, <a class="ref" href="funct_4.html#T12">FUNCT_4:12</a></i>
<br/>.= 
<font color="Maroon">F<sub>2</sub></font>(<font color="Maroon">c<sub>10</sub></font>)
<b>by </b><i><a class="txt" href="recdef_2.html#E11:14_1"><i><font color="Green">E23</font></i></a>, <a class="txt" href="recdef_2.html#E2:14_1_3"><i><font color="Green">E33</font></i></a></i>
;<br/><br/></div>
<b>end;</b></div>

<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:14_1_4"/><i><font color="Green">E32</font></i>: 
<font color="Maroon">P<sub>2</sub></font>[<font color="Maroon">c<sub>10</sub></font>]
 ;<br/><a NAME="E2:14_1_4"/><b>then </b><i><font color="Green">E33</font></i>: 
<font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="recdef_2.html#E4:14_1"><i><font color="Green">E19</font></i></a>, <a class="txt" href="recdef_2.html#E23:14_1"><i><font color="Green">E31</font></i></a></i>;<br/><a NAME="E3:14_1_4"/>
<font color="Maroon">P<sub>3</sub></font>[<font color="Maroon">c<sub>10</sub></font>]
 <b>by </b><i><a class="txt" href="recdef_2.html#E1:14"><i><font color="Green">E16</font></i></a>, <a class="txt" href="recdef_2.html#E23:14_1"><i><font color="Green">E31</font></i></a>, <a class="txt" href="recdef_2.html#E1:14_1_4"><i><font color="Green">E32</font></i></a></i>;<br/><a NAME="E4:14_1_4"/><b>then </b><i><font color="Green">E34</font></i>: 
not <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="recdef_2.html#E6:14_1"><i><font color="Green">E20</font></i></a></i>;<br/><a NAME="E5:14_1_4"/>
<font color="Maroon">P<sub>4</sub></font>[<font color="Maroon">c<sub>10</sub></font>]
 <b>by </b><i><a class="txt" href="recdef_2.html#E1:14"><i><font color="Green">E16</font></i></a>, <a class="txt" href="recdef_2.html#E23:14_1"><i><font color="Green">E31</font></i></a>, <a class="txt" href="recdef_2.html#E1:14_1_4"><i><font color="Green">E32</font></i></a></i>;<br/><a NAME="E6:14_1_4"/><b>then </b>
not <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="txt" href="recdef_2.html#E8:14_1"><i><font color="Green">E21</font></i></a></i>;<br/><b>hence </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="funct_4.html#K1">+*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="funct_4.html#K1">+*</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="funct_4.html#K1">+*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>10</sub></font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="funct_4.html#K1">+*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="funct_4.html#K1">+*</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>10</sub></font>
<b>by </b><i><a class="txt" href="recdef_2.html#E19:14_1"><i><font color="Green">E28</font></i></a>, <a class="ref" href="funct_4.html#T12">FUNCT_4:12</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="funct_4.html#K1">+*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>10</sub></font>
<b>by </b><i><a class="txt" href="recdef_2.html#E16:14_1"><i><font color="Green">E26</font></i></a>, <a class="txt" href="recdef_2.html#E4:14_1_4"><i><font color="Green">E34</font></i></a>, <a class="ref" href="funct_4.html#T12">FUNCT_4:12</a></i>
<br/>.= 
<font color="Maroon">c<sub>6</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>10</sub></font>
<b>by </b><i><a class="txt" href="recdef_2.html#E13:14_1"><i><font color="Green">E24</font></i></a>, <a class="txt" href="recdef_2.html#E2:14_1_4"><i><font color="Green">E33</font></i></a>, <a class="ref" href="funct_4.html#T14">FUNCT_4:14</a></i>
<br/>.= 
<font color="Maroon">F<sub>3</sub></font>(<font color="Maroon">c<sub>10</sub></font>)
<b>by </b><i><a class="txt" href="recdef_2.html#E14:14_1"><i><font color="Green">E25</font></i></a>, <a class="txt" href="recdef_2.html#E2:14_1_4"><i><font color="Green">E33</font></i></a></i>
;<br/><br/></div>
<b>end;</b></div>

<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:14_1_5"/><i><font color="Green">E32</font></i>: 
<font color="Maroon">P<sub>3</sub></font>[<font color="Maroon">c<sub>10</sub></font>]
 ;<br/><a NAME="E2:14_1_5"/><b>then </b><i><font color="Green">E33</font></i>: 
<font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="recdef_2.html#E6:14_1"><i><font color="Green">E20</font></i></a>, <a class="txt" href="recdef_2.html#E23:14_1"><i><font color="Green">E31</font></i></a></i>;<br/><a NAME="E3:14_1_5"/>
<font color="Maroon">P<sub>4</sub></font>[<font color="Maroon">c<sub>10</sub></font>]
 <b>by </b><i><a class="txt" href="recdef_2.html#E1:14"><i><font color="Green">E16</font></i></a>, <a class="txt" href="recdef_2.html#E23:14_1"><i><font color="Green">E31</font></i></a>, <a class="txt" href="recdef_2.html#E1:14_1_5"><i><font color="Green">E32</font></i></a></i>;<br/><a NAME="E4:14_1_5"/><b>then </b>
not <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="txt" href="recdef_2.html#E8:14_1"><i><font color="Green">E21</font></i></a></i>;<br/><b>hence </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="funct_4.html#K1">+*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="funct_4.html#K1">+*</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="funct_4.html#K1">+*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>10</sub></font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="funct_4.html#K1">+*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="funct_4.html#K1">+*</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>10</sub></font>
<b>by </b><i><a class="txt" href="recdef_2.html#E19:14_1"><i><font color="Green">E28</font></i></a>, <a class="ref" href="funct_4.html#T12">FUNCT_4:12</a></i>
<br/>.= 
<font color="Maroon">c<sub>7</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>10</sub></font>
<b>by </b><i><a class="txt" href="recdef_2.html#E16:14_1"><i><font color="Green">E26</font></i></a>, <a class="txt" href="recdef_2.html#E2:14_1_5"><i><font color="Green">E33</font></i></a>, <a class="ref" href="funct_4.html#T14">FUNCT_4:14</a></i>
<br/>.= 
<font color="Maroon">F<sub>4</sub></font>(<font color="Maroon">c<sub>10</sub></font>)
<b>by </b><i><a class="txt" href="recdef_2.html#E17:14_1"><i><font color="Green">E27</font></i></a>, <a class="txt" href="recdef_2.html#E2:14_1_5"><i><font color="Green">E33</font></i></a></i>
;<br/><br/></div>
<b>end;</b></div>

<b>assume </b><a NAME="E27:14_1"/>
<font color="Maroon">P<sub>4</sub></font>[<font color="Maroon">c<sub>10</sub></font>]
 ;<br/>

<a NAME="E28:14_1"/><b>then </b><i><font color="Green">E32</font></i>: 
<font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="txt" href="recdef_2.html#E8:14_1"><i><font color="Green">E21</font></i></a>, <a class="txt" href="recdef_2.html#E23:14_1"><i><font color="Green">E31</font></i></a></i>;<br/>
<b>hence </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="funct_4.html#K1">+*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="funct_4.html#K1">+*</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="funct_4.html#K1">+*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>10</sub></font> = 
<font color="Maroon">c<sub>8</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>10</sub></font>
<b>by </b><i><a class="txt" href="recdef_2.html#E19:14_1"><i><font color="Green">E28</font></i></a>, <a class="ref" href="funct_4.html#T14">FUNCT_4:14</a></i>
<br/>.= 
<font color="Maroon">F<sub>5</sub></font>(<font color="Maroon">c<sub>10</sub></font>)
<b>by </b><i><a class="txt" href="recdef_2.html#E20:14_1"><i><font color="Green">E29</font></i></a>, <a class="txt" href="recdef_2.html#E28:14_1"><i><font color="Green">E32</font></i></a></i>
;<br/><br/>


</div>
