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

<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>let </b><font color="Maroon">c<sub>2</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>3</sub></font>, <font color="Maroon">c<sub>4</sub></font> be   <a href="binop_1.html#NM2">BinOp</a> of <font color="Maroon">c<sub>2</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>5</sub></font> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">c<sub>2</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>6</sub></font>, <font color="Maroon">c<sub>7</sub></font> be    <a href="finseq_2.html#M2">Element</a> of <font color="Maroon">c<sub>1</sub></font> <a href="finseq_2.html#K4">-tuples_on</a> <font color="Maroon">c<sub>2</sub></font>;<br/>













<b>assume </b><a NAME="E1:25"/><i><font color="Green">E19</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="binop_1.html#R6">is_distributive_wrt</a> <font color="Maroon">c<sub>4</sub></font>
 ;<br/>

<i><font color="Green">E20</font></i>: <font color="Maroon">c<sub>3</sub></font> <a href="finseqop.html#K3">[;]</a> <font color="Maroon">c<sub>5</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="prvect_1.html#K1" target="_self">.:</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span>)</span> = 
<font color="Maroon">c<sub>3</sub></font> <a href="funcop_1.html#K5">[;]</a> <font color="Maroon">c<sub>5</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p2"><a href="funct_3.html#K13">&lt;:</a><span class="default"><font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span><a href="funct_3.html#K13">:&gt;</a></span></span>)</span>
<b>by </b><i><a class="ref" href="funcop_1.html#D3">FUNCOP_1:def 3</a></i>
<br/>.= 
<font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p1"><a href="funct_3.html#K13">&lt;:</a><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="funct_1.html#NK3" target="_self">*</a> <span class="p5"><a href="funct_3.html#K13">&lt;:</a><span class="default"><font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span><a href="funct_3.html#K13">:&gt;</a></span></span>)</span></span>)</span> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p3"><a href="funct_3.html#K13">&lt;:</a><span class="default"><font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span><a href="funct_3.html#K13">:&gt;</a></span></span>)</span></span><a href="funct_3.html#K13">:&gt;</a></span>
<b>by </b><i><a class="ref" href="funcop_1.html#D5">FUNCOP_1:def 5</a></i>
;<br/>
<b>set </b><font color="Maroon">c<sub>8</sub></font> = <font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p1"><a href="funct_3.html#K13">&lt;:</a><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="funct_1.html#NK3" target="_self">*</a> <span class="p5"><a href="funct_3.html#K13">&lt;:</a><span class="default"><font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span><a href="funct_3.html#K13">:&gt;</a></span></span>)</span></span>)</span> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p3"><a href="funct_3.html#K13">&lt;:</a><span class="default"><font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span><a href="funct_3.html#K13">:&gt;</a></span></span>)</span></span><a href="funct_3.html#K13">:&gt;</a></span>;<br/>
<i><font color="Green">E21</font></i>: <font color="Maroon">c<sub>4</sub></font> <a href="finseqop.html#K1">.:</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="finseqop.html#K3">[;]</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="finseqop.html#K3">[;]</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>7</sub></font></span>)</span> = 
<font color="Maroon">c<sub>4</sub></font> <a href="funcop_1.html#K3">.:</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p2"><a href="funct_3.html#K13">&lt;:</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>,<font color="Maroon">c<sub>6</sub></font></span><a href="funct_3.html#K13">:&gt;</a></span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="finseqop.html#K3">[;]</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>7</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="funcop_1.html#D5">FUNCOP_1:def 5</a></i>
<br/>.= 
<font color="Maroon">c<sub>4</sub></font> <a href="funcop_1.html#K3">.:</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p2"><a href="funct_3.html#K13">&lt;:</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>,<font color="Maroon">c<sub>6</sub></font></span><a href="funct_3.html#K13">:&gt;</a></span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p2"><a href="funct_3.html#K13">&lt;:</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>,<font color="Maroon">c<sub>7</sub></font></span><a href="funct_3.html#K13">:&gt;</a></span></span>)</span>
<b>by </b><i><a class="ref" href="funcop_1.html#D5">FUNCOP_1:def 5</a></i>
<br/>.= 
<font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p1"><a href="funct_3.html#K13">&lt;:</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p3"><a href="funct_3.html#K13">&lt;:</a><span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>,<font color="Maroon">c<sub>6</sub></font></span><a href="funct_3.html#K13">:&gt;</a></span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p3"><a href="funct_3.html#K13">&lt;:</a><span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>,<font color="Maroon">c<sub>7</sub></font></span><a href="funct_3.html#K13">:&gt;</a></span></span>)</span></span><a href="funct_3.html#K13">:&gt;</a></span>
<b>by </b><i><a class="ref" href="funcop_1.html#D3">FUNCOP_1:def 3</a></i>
;<br/>
<a NAME="E4:25"/><i><font color="Green">E22</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p2"><a href="funct_3.html#K13">&lt;:</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p0"><a href="funct_3.html#K13">&lt;:</a><span class="default"><font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span><a href="funct_3.html#K13">:&gt;</a></span></span>)</span></span>)</span> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p4"><a href="funct_3.html#K13">&lt;:</a><span class="default"><font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span><a href="funct_3.html#K13">:&gt;</a></span></span>)</span></span><a href="funct_3.html#K13">:&gt;</a></span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">c<sub>1</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="25_3"><b>proof </b></a><div class="add">

<i><font color="Green">E23</font></i>:  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>6</sub></font> = 
 <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>
<br/>.= 
 <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">c<sub>1</sub></font>
<b>by </b><i><a class="ref" href="finseq_2.html#T109">FINSEQ_2:109</a></i>
;<br/>
 <a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>7</sub></font> = 
 <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>7</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>
<br/>.= 
 <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">c<sub>1</sub></font>
<b>by </b><i><a class="ref" href="finseq_2.html#T109">FINSEQ_2:109</a></i>
;<br/>
<a NAME="E3:25_3"/><b>then </b><i><font color="Green">E24</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1"><a href="funct_3.html#K13">&lt;:</a><span class="default"><font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span><a href="funct_3.html#K13">:&gt;</a></span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="txt" href="prvect_1.html#E1:25_3"><i><font color="Green">E23</font></i></a>, <a class="ref" href="funct_3.html#T70">FUNCT_3:70</a></i>;<br/>
<a NAME="E4:25_3"/>
(  <a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>6</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>2</sub></font> &amp;  <a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>7</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>2</sub></font> )
 
<b>by </b><i><a class="ref" href="finseq_1.html#D4">FINSEQ_1:def 4</a></i>;<br/>
<a NAME="E5:25_3"/><b>then </b><i><font color="Green">E25</font></i>: 
<span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>6</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span>
 
<b>by </b><i><a class="ref" href="zfmisc_1.html#T119">ZFMISC_1:119</a></i>;<br/>
<a NAME="E6:25_3"/>
 <a href="relat_1.html#K2">rng</a> <span class="p1"><a href="funct_3.html#K13">&lt;:</a><span class="default"><font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span><a href="funct_3.html#K13">:&gt;</a></span> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>6</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span>
 
<b>by </b><i><a class="ref" href="funct_3.html#T71">FUNCT_3:71</a></i>;<br/>
<a NAME="E7:25_3"/><b>then </b>
 <a href="relat_1.html#K2">rng</a> <span class="p1"><a href="funct_3.html#K13">&lt;:</a><span class="default"><font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span><a href="funct_3.html#K13">:&gt;</a></span> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span>
 
<b>by </b><i><a class="txt" href="prvect_1.html#E5:25_3"><i><font color="Green">E25</font></i></a>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>
<a NAME="E8:25_3"/><b>then </b>
 <a href="relat_1.html#K2">rng</a> <span class="p1"><a href="funct_3.html#K13">&lt;:</a><span class="default"><font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span><a href="funct_3.html#K13">:&gt;</a></span> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<a NAME="E9:25_3"/><b>then </b><i><font color="Green">E26</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="funct_1.html#NK3" target="_self">*</a> <span class="p2"><a href="funct_3.html#K13">&lt;:</a><span class="default"><font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span><a href="funct_3.html#K13">:&gt;</a></span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="txt" href="prvect_1.html#E3:25_3"><i><font color="Green">E24</font></i></a>, <a class="ref" href="relat_1.html#T46">RELAT_1:46</a></i>;<br/>
<a NAME="E10:25_3"/><b>then </b>
 <a href="relat_1.html#K1">dom</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="funct_1.html#NK3" target="_self">*</a> <span class="p4"><a href="funct_3.html#K13">&lt;:</a><span class="default"><font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span><a href="funct_3.html#K13">:&gt;</a></span></span>)</span></span>)</span> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="funcop_1.html#T19">FUNCOP_1:19</a></i>;<br/>
<a NAME="E11:25_3"/><b>then </b><i><font color="Green">E27</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1"><a href="funct_3.html#K13">&lt;:</a><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="funct_1.html#NK3" target="_self">*</a> <span class="p5"><a href="funct_3.html#K13">&lt;:</a><span class="default"><font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span><a href="funct_3.html#K13">:&gt;</a></span></span>)</span></span>)</span> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p3"><a href="funct_3.html#K13">&lt;:</a><span class="default"><font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span><a href="funct_3.html#K13">:&gt;</a></span></span>)</span></span><a href="funct_3.html#K13">:&gt;</a></span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="txt" href="prvect_1.html#E9:25_3"><i><font color="Green">E26</font></i></a>, <a class="ref" href="funct_3.html#T70">FUNCT_3:70</a></i>;<br/>
<a NAME="E12:25_3"/>
 <a href="relat_1.html#K2">rng</a> <span class="p1"><a href="funct_3.html#K13">&lt;:</a><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="funct_1.html#NK3" target="_self">*</a> <span class="p5"><a href="funct_3.html#K13">&lt;:</a><span class="default"><font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span><a href="funct_3.html#K13">:&gt;</a></span></span>)</span></span>)</span> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p3"><a href="funct_3.html#K13">&lt;:</a><span class="default"><font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span><a href="funct_3.html#K13">:&gt;</a></span></span>)</span></span><a href="funct_3.html#K13">:&gt;</a></span> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>3</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="25_3_3"><b>proof </b></a><div class="add">

<a NAME="E1:25_3_3"/><i><font color="Green">E28</font></i>: 
 <a href="relat_1.html#K2">rng</a> <span class="p1"><a href="funct_3.html#K13">&lt;:</a><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="funct_1.html#NK3" target="_self">*</a> <span class="p5"><a href="funct_3.html#K13">&lt;:</a><span class="default"><font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span><a href="funct_3.html#K13">:&gt;</a></span></span>)</span></span>)</span> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p3"><a href="funct_3.html#K13">&lt;:</a><span class="default"><font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span><a href="funct_3.html#K13">:&gt;</a></span></span>)</span></span><a href="funct_3.html#K13">:&gt;</a></span> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K2">rng</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p0"><a href="funct_3.html#K13">&lt;:</a><span class="default"><font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span><a href="funct_3.html#K13">:&gt;</a></span></span>)</span></span>)</span> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="relat_1.html#K2">rng</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p4"><a href="funct_3.html#K13">&lt;:</a><span class="default"><font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span><a href="funct_3.html#K13">:&gt;</a></span></span>)</span></span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span>
 
<b>by </b><i><a class="ref" href="funct_3.html#T71">FUNCT_3:71</a></i>;<br/>
<a NAME="E2:25_3_3"/>
(  <a href="relat_1.html#K2">rng</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="funct_1.html#NK3" target="_self">*</a> <span class="p4"><a href="funct_3.html#K13">&lt;:</a><span class="default"><font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span><a href="funct_3.html#K13">:&gt;</a></span></span>)</span></span>)</span> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>5</sub></font></span><a href="tarski.html#K1">}</a></span> &amp; <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>5</sub></font></span><a href="tarski.html#K1">}</a></span> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>2</sub></font> )
 
<b>by </b><i><a class="ref" href="funcop_1.html#T19">FUNCOP_1:19</a>, <a class="ref" href="zfmisc_1.html#T37">ZFMISC_1:37</a></i>;<br/>
<a NAME="E3:25_3_3"/><b>then </b><i><font color="Green">E29</font></i>: 
 <a href="relat_1.html#K2">rng</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="funct_1.html#NK3" target="_self">*</a> <span class="p4"><a href="funct_3.html#K13">&lt;:</a><span class="default"><font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span><a href="funct_3.html#K13">:&gt;</a></span></span>)</span></span>)</span> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>
<a NAME="E4:25_3_3"/><i><font color="Green">E30</font></i>: 
 <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p2"><a href="funct_3.html#K13">&lt;:</a><span class="default"><font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span><a href="funct_3.html#K13">:&gt;</a></span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="ref" href="relat_1.html#T45">RELAT_1:45</a></i>;<br/>
<a NAME="E5:25_3_3"/>
 <a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>4</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="relset_1.html#T12">RELSET_1:12</a></i>;<br/>
<a NAME="E6:25_3_3"/><b>then </b>
 <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p2"><a href="funct_3.html#K13">&lt;:</a><span class="default"><font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span><a href="funct_3.html#K13">:&gt;</a></span></span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="prvect_1.html#E4:25_3_3"><i><font color="Green">E30</font></i></a>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>
<a NAME="E7:25_3_3"/><b>then </b>
<span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K2">rng</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p0"><a href="funct_3.html#K13">&lt;:</a><span class="default"><font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span><a href="funct_3.html#K13">:&gt;</a></span></span>)</span></span>)</span> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="relat_1.html#K2">rng</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p4"><a href="funct_3.html#K13">&lt;:</a><span class="default"><font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span><a href="funct_3.html#K13">:&gt;</a></span></span>)</span></span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span>
 
<b>by </b><i><a class="txt" href="prvect_1.html#E3:25_3_3"><i><font color="Green">E29</font></i></a>, <a class="ref" href="zfmisc_1.html#T119">ZFMISC_1:119</a></i>;<br/>
<a NAME="E8:25_3_3"/><b>then </b>
(  <a href="relat_1.html#K2">rng</a> <span class="p1"><a href="funct_3.html#K13">&lt;:</a><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="funct_1.html#NK3" target="_self">*</a> <span class="p5"><a href="funct_3.html#K13">&lt;:</a><span class="default"><font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span><a href="funct_3.html#K13">:&gt;</a></span></span>)</span></span>)</span> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p3"><a href="funct_3.html#K13">&lt;:</a><span class="default"><font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span><a href="funct_3.html#K13">:&gt;</a></span></span>)</span></span><a href="funct_3.html#K13">:&gt;</a></span> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span> &amp;  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span> )
 
<b>by </b><i><a class="txt" href="prvect_1.html#E1:25_3_3"><i><font color="Green">E28</font></i></a>, <a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>
<b>hence </b><a NAME="E9:25_3_3"/>
 <a href="relat_1.html#K2">rng</a> <span class="p1"><a href="funct_3.html#K13">&lt;:</a><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="funct_1.html#NK3" target="_self">*</a> <span class="p5"><a href="funct_3.html#K13">&lt;:</a><span class="default"><font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span><a href="funct_3.html#K13">:&gt;</a></span></span>)</span></span>)</span> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p3"><a href="funct_3.html#K13">&lt;:</a><span class="default"><font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span><a href="funct_3.html#K13">:&gt;</a></span></span>)</span></span><a href="funct_3.html#K13">:&gt;</a></span> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E13:25_3"/>
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p2"><a href="funct_3.html#K13">&lt;:</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p0"><a href="funct_3.html#K13">&lt;:</a><span class="default"><font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span><a href="funct_3.html#K13">:&gt;</a></span></span>)</span></span>)</span> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p4"><a href="funct_3.html#K13">&lt;:</a><span class="default"><font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span><a href="funct_3.html#K13">:&gt;</a></span></span>)</span></span><a href="funct_3.html#K13">:&gt;</a></span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="prvect_1.html#E11:25_3"><i><font color="Green">E27</font></i></a>, <a class="ref" href="relat_1.html#T46">RELAT_1:46</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E5:25"/><i><font color="Green">E23</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="funct_1.html#NK3" target="_self">*</a> <span class="p2"><a href="funct_3.html#K13">&lt;:</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p4"><a href="funct_3.html#K13">&lt;:</a><span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>,<font color="Maroon">c<sub>6</sub></font></span><a href="funct_3.html#K13">:&gt;</a></span></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p4"><a href="funct_3.html#K13">&lt;:</a><span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>,<font color="Maroon">c<sub>7</sub></font></span><a href="funct_3.html#K13">:&gt;</a></span></span>)</span></span><a href="funct_3.html#K13">:&gt;</a></span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">c<sub>1</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="25_4"><b>proof </b></a><div class="add">

<a NAME="E1:25_4"/><i><font color="Green">E24</font></i>: 
 <a href="relat_1.html#K2">rng</a> <span class="p1"><a href="funct_3.html#K13">&lt;:</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p3"><a href="funct_3.html#K13">&lt;:</a><span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>,<font color="Maroon">c<sub>6</sub></font></span><a href="funct_3.html#K13">:&gt;</a></span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p3"><a href="funct_3.html#K13">&lt;:</a><span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>,<font color="Maroon">c<sub>7</sub></font></span><a href="funct_3.html#K13">:&gt;</a></span></span>)</span></span><a href="funct_3.html#K13">:&gt;</a></span> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>4</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="25_4_1"><b>proof </b></a><div class="add">

<a NAME="E1:25_4_1"/>
(  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p2"><a href="funct_3.html#K13">&lt;:</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>,<font color="Maroon">c<sub>6</sub></font></span><a href="funct_3.html#K13">:&gt;</a></span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>3</sub></font> &amp;  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p2"><a href="funct_3.html#K13">&lt;:</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>,<font color="Maroon">c<sub>7</sub></font></span><a href="funct_3.html#K13">:&gt;</a></span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>3</sub></font> )
 
<b>by </b><i><a class="ref" href="relat_1.html#T45">RELAT_1:45</a></i>;<br/>
<a NAME="E2:25_4_1"/><b>then </b><i><font color="Green">E25</font></i>: 
(  <a href="relat_1.html#K2">rng</a> <span class="p1"><a href="funct_3.html#K13">&lt;:</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p3"><a href="funct_3.html#K13">&lt;:</a><span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>,<font color="Maroon">c<sub>6</sub></font></span><a href="funct_3.html#K13">:&gt;</a></span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p3"><a href="funct_3.html#K13">&lt;:</a><span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>,<font color="Maroon">c<sub>7</sub></font></span><a href="funct_3.html#K13">:&gt;</a></span></span>)</span></span><a href="funct_3.html#K13">:&gt;</a></span> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K2">rng</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p4"><a href="funct_3.html#K13">&lt;:</a><span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>,<font color="Maroon">c<sub>6</sub></font></span><a href="funct_3.html#K13">:&gt;</a></span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="relat_1.html#K2">rng</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p4"><a href="funct_3.html#K13">&lt;:</a><span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>,<font color="Maroon">c<sub>7</sub></font></span><a href="funct_3.html#K13">:&gt;</a></span></span>)</span></span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span> &amp; <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K2">rng</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p4"><a href="funct_3.html#K13">&lt;:</a><span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>,<font color="Maroon">c<sub>6</sub></font></span><a href="funct_3.html#K13">:&gt;</a></span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="relat_1.html#K2">rng</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p4"><a href="funct_3.html#K13">&lt;:</a><span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>,<font color="Maroon">c<sub>7</sub></font></span><a href="funct_3.html#K13">:&gt;</a></span></span>)</span></span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span> )
 
<b>by </b><i><a class="ref" href="funct_3.html#T71">FUNCT_3:71</a>, <a class="ref" href="zfmisc_1.html#T119">ZFMISC_1:119</a></i>;<br/>
<a NAME="E3:25_4_1"/>
 <a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>3</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="relset_1.html#T12">RELSET_1:12</a></i>;<br/>
<a NAME="E4:25_4_1"/><b>then </b>
(  <a href="relat_1.html#K2">rng</a> <span class="p1"><a href="funct_3.html#K13">&lt;:</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p3"><a href="funct_3.html#K13">&lt;:</a><span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>,<font color="Maroon">c<sub>6</sub></font></span><a href="funct_3.html#K13">:&gt;</a></span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p3"><a href="funct_3.html#K13">&lt;:</a><span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>,<font color="Maroon">c<sub>7</sub></font></span><a href="funct_3.html#K13">:&gt;</a></span></span>)</span></span><a href="funct_3.html#K13">:&gt;</a></span> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span> &amp; <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span> )
 
<b>by </b><i><a class="txt" href="prvect_1.html#E2:25_4_1"><i><font color="Green">E25</font></i></a>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a>, <a class="ref" href="zfmisc_1.html#T119">ZFMISC_1:119</a></i>;<br/>
<a NAME="E5:25_4_1"/><b>then </b>
(  <a href="relat_1.html#K2">rng</a> <span class="p1"><a href="funct_3.html#K13">&lt;:</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p3"><a href="funct_3.html#K13">&lt;:</a><span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>,<font color="Maroon">c<sub>6</sub></font></span><a href="funct_3.html#K13">:&gt;</a></span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p3"><a href="funct_3.html#K13">&lt;:</a><span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>,<font color="Maroon">c<sub>7</sub></font></span><a href="funct_3.html#K13">:&gt;</a></span></span>)</span></span><a href="funct_3.html#K13">:&gt;</a></span> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span> &amp;  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span> )
 
<b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>
<b>hence </b><a NAME="E6:25_4_1"/>
 <a href="relat_1.html#K2">rng</a> <span class="p1"><a href="funct_3.html#K13">&lt;:</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p3"><a href="funct_3.html#K13">&lt;:</a><span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>,<font color="Maroon">c<sub>6</sub></font></span><a href="funct_3.html#K13">:&gt;</a></span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p3"><a href="funct_3.html#K13">&lt;:</a><span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>,<font color="Maroon">c<sub>7</sub></font></span><a href="funct_3.html#K13">:&gt;</a></span></span>)</span></span><a href="funct_3.html#K13">:&gt;</a></span> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>4</sub></font>
 ;<br/>


</div><b>end;</b></div>
<a NAME="E2:25_4"/>
(  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p2"><a href="funct_3.html#K13">&lt;:</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>,<font color="Maroon">c<sub>6</sub></font></span><a href="funct_3.html#K13">:&gt;</a></span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">c<sub>1</sub></font> &amp;  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p2"><a href="funct_3.html#K13">&lt;:</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>,<font color="Maroon">c<sub>7</sub></font></span><a href="funct_3.html#K13">:&gt;</a></span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">c<sub>1</sub></font> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="25_4_2"><b>proof </b></a><div class="add">

<a NAME="E1:25_4_2"/>
 <a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>6</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="finseq_1.html#D4">FINSEQ_1:def 4</a></i>;<br/>
<a NAME="E2:25_4_2"/><b>then </b><i><font color="Green">E25</font></i>: 
(  <a href="relat_1.html#K2">rng</a> <span class="p1"><a href="funct_3.html#K13">&lt;:</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>,<font color="Maroon">c<sub>6</sub></font></span><a href="funct_3.html#K13">:&gt;</a></span> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K2">rng</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span> &amp; <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K2">rng</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K2">rng</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>2</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span> )
 
<b>by </b><i><a class="ref" href="funct_3.html#T71">FUNCT_3:71</a>, <a class="ref" href="zfmisc_1.html#T119">ZFMISC_1:119</a></i>;<br/>
<a NAME="E3:25_4_2"/>
 <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>5</sub></font></span><a href="tarski.html#K1">}</a></span>
 
<b>by </b><i><a class="ref" href="funcop_1.html#T19">FUNCOP_1:19</a></i>;<br/>
<a NAME="E4:25_4_2"/><b>then </b><i><font color="Green">E26</font></i>: 
(  <a href="relat_1.html#K2">rng</a> <span class="p1"><a href="funct_3.html#K13">&lt;:</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>,<font color="Maroon">c<sub>6</sub></font></span><a href="funct_3.html#K13">:&gt;</a></span> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K2">rng</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>2</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span> &amp; <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K2">rng</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>2</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>5</sub></font></span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">c<sub>2</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span> )
 
<b>by </b><i><a class="txt" href="prvect_1.html#E2:25_4_2"><i><font color="Green">E25</font></i></a>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a>, <a class="ref" href="zfmisc_1.html#T119">ZFMISC_1:119</a></i>;<br/>
<a NAME="E5:25_4_2"/>
<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>5</sub></font></span><a href="tarski.html#K1">}</a></span> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="zfmisc_1.html#T37">ZFMISC_1:37</a></i>;<br/>
<a NAME="E6:25_4_2"/><b>then </b><i><font color="Green">E27</font></i>: 
(  <a href="relat_1.html#K2">rng</a> <span class="p1"><a href="funct_3.html#K13">&lt;:</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>,<font color="Maroon">c<sub>6</sub></font></span><a href="funct_3.html#K13">:&gt;</a></span> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>5</sub></font></span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">c<sub>2</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span> &amp; <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>5</sub></font></span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">c<sub>2</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span> )
 
<b>by </b><i><a class="txt" href="prvect_1.html#E4:25_4_2"><i><font color="Green">E26</font></i></a>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a>, <a class="ref" href="zfmisc_1.html#T119">ZFMISC_1:119</a></i>;<br/>
<a NAME="E7:25_4_2"/>
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span>
 
<b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<a NAME="E8:25_4_2"/><b>then </b><i><font color="Green">E28</font></i>: 
 <a href="relat_1.html#K2">rng</a> <span class="p1"><a href="funct_3.html#K13">&lt;:</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>,<font color="Maroon">c<sub>6</sub></font></span><a href="funct_3.html#K13">:&gt;</a></span> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="txt" href="prvect_1.html#E6:25_4_2"><i><font color="Green">E27</font></i></a>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>
<i><font color="Green">E29</font></i>:  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> = 
 <a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>6</sub></font>
<b>by </b><i><a class="ref" href="funcop_1.html#T19">FUNCOP_1:19</a></i>
<br/>.= 
 <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>
<br/>.= 
 <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">c<sub>1</sub></font>
<b>by </b><i><a class="ref" href="finseq_2.html#T109">FINSEQ_2:109</a></i>
;<br/>
<i><font color="Green">E30</font></i>:  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>6</sub></font> = 
 <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>
<br/>.= 
 <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">c<sub>1</sub></font>
<b>by </b><i><a class="ref" href="finseq_2.html#T109">FINSEQ_2:109</a></i>
;<br/>
<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>3</sub></font> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p2"><a href="funct_3.html#K13">&lt;:</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>,<font color="Maroon">c<sub>6</sub></font></span><a href="funct_3.html#K13">:&gt;</a></span></span>)</span> = 
 <a href="relat_1.html#K1">dom</a> <span class="p1"><a href="funct_3.html#K13">&lt;:</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>,<font color="Maroon">c<sub>6</sub></font></span><a href="funct_3.html#K13">:&gt;</a></span>
<b>by </b><i><a class="txt" href="prvect_1.html#E8:25_4_2"><i><font color="Green">E28</font></i></a>, <a class="ref" href="relat_1.html#T46">RELAT_1:46</a></i>
<br/>.= 
 <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">c<sub>1</sub></font>
<b>by </b><i><a class="txt" href="prvect_1.html#E9:25_4_2"><i><font color="Green">E29</font></i></a>, <a class="txt" href="prvect_1.html#E10:25_4_2"><i><font color="Green">E30</font></i></a>, <a class="ref" href="funct_3.html#T70">FUNCT_3:70</a></i>
;<br/>
<a NAME="E12:25_4_2"/>
 <a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>7</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="finseq_1.html#D4">FINSEQ_1:def 4</a></i>;<br/>
<a NAME="E13:25_4_2"/><b>then </b><i><font color="Green">E32</font></i>: 
(  <a href="relat_1.html#K2">rng</a> <span class="p1"><a href="funct_3.html#K13">&lt;:</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>,<font color="Maroon">c<sub>7</sub></font></span><a href="funct_3.html#K13">:&gt;</a></span> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K2">rng</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span> &amp; <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K2">rng</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K2">rng</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>2</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span> )
 
<b>by </b><i><a class="ref" href="funct_3.html#T71">FUNCT_3:71</a>, <a class="ref" href="zfmisc_1.html#T119">ZFMISC_1:119</a></i>;<br/>
<a NAME="E14:25_4_2"/>
 <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>5</sub></font></span><a href="tarski.html#K1">}</a></span>
 
<b>by </b><i><a class="ref" href="funcop_1.html#T19">FUNCOP_1:19</a></i>;<br/>
<a NAME="E15:25_4_2"/><b>then </b><i><font color="Green">E33</font></i>: 
(  <a href="relat_1.html#K2">rng</a> <span class="p1"><a href="funct_3.html#K13">&lt;:</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>,<font color="Maroon">c<sub>7</sub></font></span><a href="funct_3.html#K13">:&gt;</a></span> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K2">rng</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>2</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span> &amp; <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K2">rng</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>2</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>5</sub></font></span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">c<sub>2</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span> )
 
<b>by </b><i><a class="txt" href="prvect_1.html#E13:25_4_2"><i><font color="Green">E32</font></i></a>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a>, <a class="ref" href="zfmisc_1.html#T119">ZFMISC_1:119</a></i>;<br/>
<a NAME="E16:25_4_2"/>
<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>5</sub></font></span><a href="tarski.html#K1">}</a></span> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="zfmisc_1.html#T37">ZFMISC_1:37</a></i>;<br/>
<a NAME="E17:25_4_2"/><b>then </b><i><font color="Green">E34</font></i>: 
(  <a href="relat_1.html#K2">rng</a> <span class="p1"><a href="funct_3.html#K13">&lt;:</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>,<font color="Maroon">c<sub>7</sub></font></span><a href="funct_3.html#K13">:&gt;</a></span> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>5</sub></font></span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">c<sub>2</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span> &amp; <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>5</sub></font></span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">c<sub>2</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span> )
 
<b>by </b><i><a class="txt" href="prvect_1.html#E15:25_4_2"><i><font color="Green">E33</font></i></a>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a>, <a class="ref" href="zfmisc_1.html#T119">ZFMISC_1:119</a></i>;<br/>
<a NAME="E18:25_4_2"/>
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span>
 
<b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<a NAME="E19:25_4_2"/><b>then </b><i><font color="Green">E35</font></i>: 
 <a href="relat_1.html#K2">rng</a> <span class="p1"><a href="funct_3.html#K13">&lt;:</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>,<font color="Maroon">c<sub>7</sub></font></span><a href="funct_3.html#K13">:&gt;</a></span> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="txt" href="prvect_1.html#E17:25_4_2"><i><font color="Green">E34</font></i></a>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>
<i><font color="Green">E36</font></i>:  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> = 
 <a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="ref" href="funcop_1.html#T19">FUNCOP_1:19</a></i>
<br/>.= 
 <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>7</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>
<br/>.= 
 <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">c<sub>1</sub></font>
<b>by </b><i><a class="ref" href="finseq_2.html#T109">FINSEQ_2:109</a></i>
;<br/>
<i><font color="Green">E37</font></i>:  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>7</sub></font> = 
 <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>7</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>
<br/>.= 
 <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">c<sub>1</sub></font>
<b>by </b><i><a class="ref" href="finseq_2.html#T109">FINSEQ_2:109</a></i>
;<br/>
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p2"><a href="funct_3.html#K13">&lt;:</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>,<font color="Maroon">c<sub>7</sub></font></span><a href="funct_3.html#K13">:&gt;</a></span></span>)</span> = 
 <a href="relat_1.html#K1">dom</a> <span class="p1"><a href="funct_3.html#K13">&lt;:</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>,<font color="Maroon">c<sub>7</sub></font></span><a href="funct_3.html#K13">:&gt;</a></span>
<b>by </b><i><a class="txt" href="prvect_1.html#E19:25_4_2"><i><font color="Green">E35</font></i></a>, <a class="ref" href="relat_1.html#T46">RELAT_1:46</a></i>
<br/>.= 
 <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">c<sub>1</sub></font>
<b>by </b><i><a class="txt" href="prvect_1.html#E20:25_4_2"><i><font color="Green">E36</font></i></a>, <a class="txt" href="prvect_1.html#E21:25_4_2"><i><font color="Green">E37</font></i></a>, <a class="ref" href="funct_3.html#T70">FUNCT_3:70</a></i>
;<br/>
<b>hence </b><a NAME="E23:25_4_2"/>
(  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p2"><a href="funct_3.html#K13">&lt;:</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>,<font color="Maroon">c<sub>6</sub></font></span><a href="funct_3.html#K13">:&gt;</a></span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">c<sub>1</sub></font> &amp;  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p2"><a href="funct_3.html#K13">&lt;:</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>,<font color="Maroon">c<sub>7</sub></font></span><a href="funct_3.html#K13">:&gt;</a></span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">c<sub>1</sub></font> )
 <b>by </b><i><a class="txt" href="prvect_1.html#E11:25_4_2"><i><font color="Green">E31</font></i></a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E3:25_4"/><b>then </b>
 <a href="relat_1.html#K1">dom</a> <span class="p1"><a href="funct_3.html#K13">&lt;:</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p3"><a href="funct_3.html#K13">&lt;:</a><span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>,<font color="Maroon">c<sub>6</sub></font></span><a href="funct_3.html#K13">:&gt;</a></span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p3"><a href="funct_3.html#K13">&lt;:</a><span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>,<font color="Maroon">c<sub>7</sub></font></span><a href="funct_3.html#K13">:&gt;</a></span></span>)</span></span><a href="funct_3.html#K13">:&gt;</a></span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="funct_3.html#T70">FUNCT_3:70</a></i>;<br/>
<b>hence </b><a NAME="E4:25_4"/>
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p2"><a href="funct_3.html#K13">&lt;:</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p4"><a href="funct_3.html#K13">&lt;:</a><span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>,<font color="Maroon">c<sub>6</sub></font></span><a href="funct_3.html#K13">:&gt;</a></span></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p4"><a href="funct_3.html#K13">&lt;:</a><span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>,<font color="Maroon">c<sub>7</sub></font></span><a href="funct_3.html#K13">:&gt;</a></span></span>)</span></span><a href="funct_3.html#K13">:&gt;</a></span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="prvect_1.html#E1:25_4"><i><font color="Green">E24</font></i></a>, <a class="ref" href="relat_1.html#T46">RELAT_1:46</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E6:25"/>
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#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p2"><a href="funct_3.html#K13">&lt;:</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p0"><a href="funct_3.html#K13">&lt;:</a><span class="default"><font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span><a href="funct_3.html#K13">:&gt;</a></span></span>)</span></span>)</span> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p4"><a href="funct_3.html#K13">&lt;:</a><span class="default"><font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span><a href="funct_3.html#K13">:&gt;</a></span></span>)</span></span><a href="funct_3.html#K13">:&gt;</a></span></span>)</span> holds <br/><span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="finseqop.html#K3">[;]</a> <font color="Maroon">c<sub>5</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="prvect_1.html#K1" target="_self">.:</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</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#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="finseqop.html#K1">.:</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="finseqop.html#K3">[;]</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="finseqop.html#K3">[;]</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="25_5"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>9</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><a NAME="E1:25_5"/><i><font color="Green">E24</font></i>: 
<font color="Maroon">c<sub>9</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>3</sub></font> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p2"><a href="funct_3.html#K13">&lt;:</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p0"><a href="funct_3.html#K13">&lt;:</a><span class="default"><font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span><a href="funct_3.html#K13">:&gt;</a></span></span>)</span></span>)</span> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p4"><a href="funct_3.html#K13">&lt;:</a><span class="default"><font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span><a href="funct_3.html#K13">:&gt;</a></span></span>)</span></span><a href="funct_3.html#K13">:&gt;</a></span></span>)</span>
 ;<br/>

<a NAME="E2:25_5"/><b>then </b>
<font color="Maroon">c<sub>9</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>3</sub></font> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p2"><a href="funct_3.html#K13">&lt;:</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K4">dom</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="prvect_1.html#K1" target="_self">.:</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="prvect_1.html#K1" target="_self">.:</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="funct_3.html#K13">:&gt;</a></span></span>)</span>
 
<b>by </b><i><a class="txt" href="prvect_1.html#E2:25"><i><font color="Green">E20</font></i></a>, <a class="ref" href="funcop_1.html#D5">FUNCOP_1:def 5</a></i>;<br/>
<a NAME="E3:25_5"/><b>then </b><i><font color="Green">E25</font></i>: 
<font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1"><a href="funct_3.html#K13">&lt;:</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K4">dom</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="prvect_1.html#K1" target="_self">.:</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="prvect_1.html#K1" target="_self">.:</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="funct_3.html#K13">:&gt;</a></span>
 
<b>by </b><i><a class="ref" href="funct_1.html#T21">FUNCT_1:21</a></i>;<br/>
<a NAME="E4:25_5"/>
 <a href="relat_1.html#K1">dom</a> <span class="p1"><a href="funct_3.html#K13">&lt;:</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K4">dom</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="prvect_1.html#K1" target="_self">.:</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="prvect_1.html#K1" target="_self">.:</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="funct_3.html#K13">:&gt;</a></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"><span class="p3">(<span class="default"><a href="finseq_1.html#K4">dom</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="prvect_1.html#K1" target="_self">.:</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K4">dom</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="prvect_1.html#K1" target="_self">.:</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_3.html#D8">FUNCT_3:def 8</a></i>;<br/>
<a NAME="E5:25_5"/><b>then </b><i><font color="Green">E26</font></i>: 
<font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="prvect_1.html#K1" target="_self">.:</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="prvect_1.html#E3:25_5"><i><font color="Green">E25</font></i></a>, <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/>
<a NAME="E6:25_5"/><i><font color="Green">E27</font></i>: 
( <font color="Maroon">c<sub>6</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>7</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="25_5_1"><b>proof </b></a><div class="add">

<i><font color="Green">E28</font></i>:  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>6</sub></font> = 
 <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>
<br/>.= 
 <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">c<sub>1</sub></font>
<b>by </b><i><a class="ref" href="finseq_2.html#T109">FINSEQ_2:109</a></i>
;<br/>
<a NAME="E2:25_5_1"/><i><font color="Green">E29</font></i>: 
 <a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>6</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="finseq_1.html#D4">FINSEQ_1:def 4</a></i>;<br/>
<a NAME="E3:25_5_1"/><i><font color="Green">E30</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>6</sub></font>
 
<b>by </b><i><a class="txt" href="prvect_1.html#E4:25"><i><font color="Green">E22</font></i></a>, <a class="txt" href="prvect_1.html#E1:25_5"><i><font color="Green">E24</font></i></a>, <a class="txt" href="prvect_1.html#E1:25_5_1"><i><font color="Green">E28</font></i></a>, <a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/>
<i><font color="Green">E31</font></i>:  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>7</sub></font> = 
 <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>7</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>
<br/>.= 
 <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">c<sub>1</sub></font>
<b>by </b><i><a class="ref" href="finseq_2.html#T109">FINSEQ_2:109</a></i>
;<br/>
<a NAME="E5:25_5_1"/><i><font color="Green">E32</font></i>: 
 <a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>7</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="finseq_1.html#D4">FINSEQ_1:def 4</a></i>;<br/>
<a NAME="E6:25_5_1"/>
<font color="Maroon">c<sub>7</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>7</sub></font>
 
<b>by </b><i><a class="txt" href="prvect_1.html#E4:25"><i><font color="Green">E22</font></i></a>, <a class="txt" href="prvect_1.html#E1:25_5"><i><font color="Green">E24</font></i></a>, <a class="txt" href="prvect_1.html#E4:25_5_1"><i><font color="Green">E31</font></i></a>, <a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/>
<b>hence </b><a NAME="E7:25_5_1"/>
( <font color="Maroon">c<sub>6</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>7</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>9</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="prvect_1.html#E2:25_5_1"><i><font color="Green">E29</font></i></a>, <a class="txt" href="prvect_1.html#E3:25_5_1"><i><font color="Green">E30</font></i></a>, <a class="txt" href="prvect_1.html#E5:25_5_1"><i><font color="Green">E32</font></i></a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E7:25_5"/><i><font color="Green">E28</font></i>: 
( <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="finseqop.html#K3">[;]</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> &amp; <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="finseqop.html#K3">[;]</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>7</sub></font></span>)</span> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="25_5_2"><b>proof </b></a><div class="add">

<a NAME="E1:25_5_2"/>
(  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p2"><a href="funct_3.html#K13">&lt;:</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>,<font color="Maroon">c<sub>6</sub></font></span><a href="funct_3.html#K13">:&gt;</a></span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">c<sub>1</sub></font> &amp;  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p2"><a href="funct_3.html#K13">&lt;:</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>,<font color="Maroon">c<sub>7</sub></font></span><a href="funct_3.html#K13">:&gt;</a></span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">c<sub>1</sub></font> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="25_5_2_1"><b>proof </b></a><div class="add">

<a NAME="E1:25_5_2_1"/>
 <a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>6</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="finseq_1.html#D4">FINSEQ_1:def 4</a></i>;<br/>
<a NAME="E2:25_5_2_1"/><b>then </b><i><font color="Green">E29</font></i>: 
(  <a href="relat_1.html#K2">rng</a> <span class="p1"><a href="funct_3.html#K13">&lt;:</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>,<font color="Maroon">c<sub>6</sub></font></span><a href="funct_3.html#K13">:&gt;</a></span> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K2">rng</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span> &amp; <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K2">rng</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K2">rng</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>2</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span> )
 
<b>by </b><i><a class="ref" href="funct_3.html#T71">FUNCT_3:71</a>, <a class="ref" href="zfmisc_1.html#T119">ZFMISC_1:119</a></i>;<br/>
<a NAME="E3:25_5_2_1"/>
 <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>5</sub></font></span><a href="tarski.html#K1">}</a></span>
 
<b>by </b><i><a class="ref" href="funcop_1.html#T19">FUNCOP_1:19</a></i>;<br/>
<a NAME="E4:25_5_2_1"/><b>then </b><i><font color="Green">E30</font></i>: 
(  <a href="relat_1.html#K2">rng</a> <span class="p1"><a href="funct_3.html#K13">&lt;:</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>,<font color="Maroon">c<sub>6</sub></font></span><a href="funct_3.html#K13">:&gt;</a></span> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K2">rng</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>2</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span> &amp; <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K2">rng</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>2</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>5</sub></font></span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">c<sub>2</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span> )
 
<b>by </b><i><a class="txt" href="prvect_1.html#E2:25_5_2_1"><i><font color="Green">E29</font></i></a>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a>, <a class="ref" href="zfmisc_1.html#T119">ZFMISC_1:119</a></i>;<br/>
<a NAME="E5:25_5_2_1"/>
<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>5</sub></font></span><a href="tarski.html#K1">}</a></span> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="zfmisc_1.html#T37">ZFMISC_1:37</a></i>;<br/>
<a NAME="E6:25_5_2_1"/><b>then </b><i><font color="Green">E31</font></i>: 
(  <a href="relat_1.html#K2">rng</a> <span class="p1"><a href="funct_3.html#K13">&lt;:</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>,<font color="Maroon">c<sub>6</sub></font></span><a href="funct_3.html#K13">:&gt;</a></span> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>5</sub></font></span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">c<sub>2</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span> &amp; <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>5</sub></font></span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">c<sub>2</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span> )
 
<b>by </b><i><a class="txt" href="prvect_1.html#E4:25_5_2_1"><i><font color="Green">E30</font></i></a>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a>, <a class="ref" href="zfmisc_1.html#T119">ZFMISC_1:119</a></i>;<br/>
<a NAME="E7:25_5_2_1"/>
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span>
 
<b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<a NAME="E8:25_5_2_1"/><b>then </b><i><font color="Green">E32</font></i>: 
 <a href="relat_1.html#K2">rng</a> <span class="p1"><a href="funct_3.html#K13">&lt;:</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>,<font color="Maroon">c<sub>6</sub></font></span><a href="funct_3.html#K13">:&gt;</a></span> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="txt" href="prvect_1.html#E6:25_5_2_1"><i><font color="Green">E31</font></i></a>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</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"><a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> = 
 <a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>6</sub></font>
<b>by </b><i><a class="ref" href="funcop_1.html#T19">FUNCOP_1:19</a></i>
<br/>.= 
 <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>
<br/>.= 
 <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">c<sub>1</sub></font>
<b>by </b><i><a class="ref" href="finseq_2.html#T109">FINSEQ_2:109</a></i>
;<br/>
<i><font color="Green">E34</font></i>:  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>6</sub></font> = 
 <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>
<br/>.= 
 <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">c<sub>1</sub></font>
<b>by </b><i><a class="ref" href="finseq_2.html#T109">FINSEQ_2:109</a></i>
;<br/>
<i><font color="Green">E35</font></i>:  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p2"><a href="funct_3.html#K13">&lt;:</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>,<font color="Maroon">c<sub>6</sub></font></span><a href="funct_3.html#K13">:&gt;</a></span></span>)</span> = 
 <a href="relat_1.html#K1">dom</a> <span class="p1"><a href="funct_3.html#K13">&lt;:</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>,<font color="Maroon">c<sub>6</sub></font></span><a href="funct_3.html#K13">:&gt;</a></span>
<b>by </b><i><a class="txt" href="prvect_1.html#E8:25_5_2_1"><i><font color="Green">E32</font></i></a>, <a class="ref" href="relat_1.html#T46">RELAT_1:46</a></i>
<br/>.= 
 <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">c<sub>1</sub></font>
<b>by </b><i><a class="txt" href="prvect_1.html#E9:25_5_2_1"><i><font color="Green">E33</font></i></a>, <a class="txt" href="prvect_1.html#E10:25_5_2_1"><i><font color="Green">E34</font></i></a>, <a class="ref" href="funct_3.html#T70">FUNCT_3:70</a></i>
;<br/>
<a NAME="E12:25_5_2_1"/>
 <a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>7</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="finseq_1.html#D4">FINSEQ_1:def 4</a></i>;<br/>
<a NAME="E13:25_5_2_1"/><b>then </b><i><font color="Green">E36</font></i>: 
(  <a href="relat_1.html#K2">rng</a> <span class="p1"><a href="funct_3.html#K13">&lt;:</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>,<font color="Maroon">c<sub>7</sub></font></span><a href="funct_3.html#K13">:&gt;</a></span> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K2">rng</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span> &amp; <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K2">rng</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K2">rng</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>2</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span> )
 
<b>by </b><i><a class="ref" href="funct_3.html#T71">FUNCT_3:71</a>, <a class="ref" href="zfmisc_1.html#T119">ZFMISC_1:119</a></i>;<br/>
<a NAME="E14:25_5_2_1"/>
 <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>5</sub></font></span><a href="tarski.html#K1">}</a></span>
 
<b>by </b><i><a class="ref" href="funcop_1.html#T19">FUNCOP_1:19</a></i>;<br/>
<a NAME="E15:25_5_2_1"/><b>then </b><i><font color="Green">E37</font></i>: 
(  <a href="relat_1.html#K2">rng</a> <span class="p1"><a href="funct_3.html#K13">&lt;:</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>,<font color="Maroon">c<sub>7</sub></font></span><a href="funct_3.html#K13">:&gt;</a></span> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K2">rng</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>2</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span> &amp; <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K2">rng</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>2</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>5</sub></font></span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">c<sub>2</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span> )
 
<b>by </b><i><a class="txt" href="prvect_1.html#E13:25_5_2_1"><i><font color="Green">E36</font></i></a>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a>, <a class="ref" href="zfmisc_1.html#T119">ZFMISC_1:119</a></i>;<br/>
<a NAME="E16:25_5_2_1"/>
<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>5</sub></font></span><a href="tarski.html#K1">}</a></span> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="zfmisc_1.html#T37">ZFMISC_1:37</a></i>;<br/>
<a NAME="E17:25_5_2_1"/><b>then </b><i><font color="Green">E38</font></i>: 
(  <a href="relat_1.html#K2">rng</a> <span class="p1"><a href="funct_3.html#K13">&lt;:</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>,<font color="Maroon">c<sub>7</sub></font></span><a href="funct_3.html#K13">:&gt;</a></span> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>5</sub></font></span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">c<sub>2</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span> &amp; <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>5</sub></font></span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">c<sub>2</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span> )
 
<b>by </b><i><a class="txt" href="prvect_1.html#E15:25_5_2_1"><i><font color="Green">E37</font></i></a>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a>, <a class="ref" href="zfmisc_1.html#T119">ZFMISC_1:119</a></i>;<br/>
<a NAME="E18:25_5_2_1"/>
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span>
 
<b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<a NAME="E19:25_5_2_1"/><b>then </b><i><font color="Green">E39</font></i>: 
 <a href="relat_1.html#K2">rng</a> <span class="p1"><a href="funct_3.html#K13">&lt;:</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>,<font color="Maroon">c<sub>7</sub></font></span><a href="funct_3.html#K13">:&gt;</a></span> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="txt" href="prvect_1.html#E17:25_5_2_1"><i><font color="Green">E38</font></i></a>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>
<i><font color="Green">E40</font></i>:  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> = 
 <a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="ref" href="funcop_1.html#T19">FUNCOP_1:19</a></i>
<br/>.= 
 <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>7</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>
<br/>.= 
 <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">c<sub>1</sub></font>
<b>by </b><i><a class="ref" href="finseq_2.html#T109">FINSEQ_2:109</a></i>
;<br/>
<i><font color="Green">E41</font></i>:  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>7</sub></font> = 
 <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>7</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>
<br/>.= 
 <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">c<sub>1</sub></font>
<b>by </b><i><a class="ref" href="finseq_2.html#T109">FINSEQ_2:109</a></i>
;<br/>
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p2"><a href="funct_3.html#K13">&lt;:</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>,<font color="Maroon">c<sub>7</sub></font></span><a href="funct_3.html#K13">:&gt;</a></span></span>)</span> = 
 <a href="relat_1.html#K1">dom</a> <span class="p1"><a href="funct_3.html#K13">&lt;:</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>,<font color="Maroon">c<sub>7</sub></font></span><a href="funct_3.html#K13">:&gt;</a></span>
<b>by </b><i><a class="txt" href="prvect_1.html#E19:25_5_2_1"><i><font color="Green">E39</font></i></a>, <a class="ref" href="relat_1.html#T46">RELAT_1:46</a></i>
<br/>.= 
 <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">c<sub>1</sub></font>
<b>by </b><i><a class="txt" href="prvect_1.html#E20:25_5_2_1"><i><font color="Green">E40</font></i></a>, <a class="txt" href="prvect_1.html#E21:25_5_2_1"><i><font color="Green">E41</font></i></a>, <a class="ref" href="funct_3.html#T70">FUNCT_3:70</a></i>
;<br/>
<b>hence </b><a NAME="E23:25_5_2_1"/>
(  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p2"><a href="funct_3.html#K13">&lt;:</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>,<font color="Maroon">c<sub>6</sub></font></span><a href="funct_3.html#K13">:&gt;</a></span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">c<sub>1</sub></font> &amp;  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p2"><a href="funct_3.html#K13">&lt;:</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>,<font color="Maroon">c<sub>7</sub></font></span><a href="funct_3.html#K13">:&gt;</a></span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">c<sub>1</sub></font> )
 <b>by </b><i><a class="txt" href="prvect_1.html#E11:25_5_2_1"><i><font color="Green">E35</font></i></a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E2:25_5_2"/>
( <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="finseqop.html#K3">[;]</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> &amp; <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="finseqop.html#K3">[;]</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>7</sub></font></span>)</span> )
 <b>by </b><i><a class="txt" href="prvect_1.html#E4:25"><i><font color="Green">E22</font></i></a>, <a class="txt" href="prvect_1.html#E1:25_5"><i><font color="Green">E24</font></i></a>, <a class="ref" href="funcop_1.html#D5">FUNCOP_1:def 5</a></i>;<br/>


</div><b>end;</b></div>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="finseqop.html#K3">[;]</a> <font color="Maroon">c<sub>5</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="prvect_1.html#K1" target="_self">.:</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>9</sub></font> = 
<font color="Maroon">c<sub>3</sub></font> <a href="binop_1.html#K1">.</a> <font color="Maroon">c<sub>5</sub></font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="prvect_1.html#K1" target="_self">.:</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="prvect_1.html#E2:25"><i><font color="Green">E20</font></i></a>, <a class="txt" href="prvect_1.html#E1:25_5"><i><font color="Green">E24</font></i></a>, <a class="ref" href="funcop_1.html#T42">FUNCOP_1:42</a></i>
<br/>.= 
<font color="Maroon">c<sub>3</sub></font> <a href="binop_1.html#K1">.</a> <font color="Maroon">c<sub>5</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="binop_1.html#K1">.</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="prvect_1.html#E5:25_5"><i><font color="Green">E26</font></i></a>, <a class="ref" href="funcop_1.html#T28">FUNCOP_1:28</a></i>
<br/>.= 
<font color="Maroon">c<sub>4</sub></font> <a href="binop_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="binop_1.html#K1">.</a> <font color="Maroon">c<sub>5</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="binop_1.html#K1">.</a> <font color="Maroon">c<sub>5</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="prvect_1.html#E1:25"><i><font color="Green">E19</font></i></a>, <a class="txt" href="prvect_1.html#E6:25_5"><i><font color="Green">E27</font></i></a>, <a class="ref" href="binop_1.html#T23">BINOP_1:23</a></i>
<br/>.= 
<font color="Maroon">c<sub>4</sub></font> <a href="binop_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="finseqop.html#K3">[;]</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="binop_1.html#K1">.</a> <font color="Maroon">c<sub>5</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="prvect_1.html#E7:25_5"><i><font color="Green">E28</font></i></a>, <a class="ref" href="funcop_1.html#T42">FUNCOP_1:42</a></i>
<br/>.= 
<font color="Maroon">c<sub>4</sub></font> <a href="binop_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="finseqop.html#K3">[;]</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="finseqop.html#K3">[;]</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="prvect_1.html#E7:25_5"><i><font color="Green">E28</font></i></a>, <a class="ref" href="funcop_1.html#T42">FUNCOP_1:42</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="finseqop.html#K1">.:</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="finseqop.html#K3">[;]</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="finseqop.html#K3">[;]</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>9</sub></font>
<b>by </b><i><a class="txt" href="prvect_1.html#E3:25"><i><font color="Green">E21</font></i></a>, <a class="txt" href="prvect_1.html#E4:25"><i><font color="Green">E22</font></i></a>, <a class="txt" href="prvect_1.html#E5:25"><i><font color="Green">E23</font></i></a>, <a class="txt" href="prvect_1.html#E1:25_5"><i><font color="Green">E24</font></i></a>, <a class="ref" href="funcop_1.html#T28">FUNCOP_1:28</a></i>
;<br/>
<b>hence </b><a NAME="E9:25_5"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="finseqop.html#K3">[;]</a> <font color="Maroon">c<sub>5</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="prvect_1.html#K1" target="_self">.:</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="finseqop.html#K1">.:</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="finseqop.html#K3">[;]</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="finseqop.html#K3">[;]</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>9</sub></font>
 ;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E7:25"/>
<font color="Maroon">c<sub>3</sub></font> <a href="finseqop.html#K3">[;]</a> <font color="Maroon">c<sub>5</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="prvect_1.html#K1" target="_self">.:</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="finseqop.html#K1">.:</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="finseqop.html#K3">[;]</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="finseqop.html#K3">[;]</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>7</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="prvect_1.html#E2:25"><i><font color="Green">E20</font></i></a>, <a class="txt" href="prvect_1.html#E3:25"><i><font color="Green">E21</font></i></a>, <a class="txt" href="prvect_1.html#E4:25"><i><font color="Green">E22</font></i></a>, <a class="txt" href="prvect_1.html#E5:25"><i><font color="Green">E23</font></i></a>, <a class="ref" href="funct_1.html#T9">FUNCT_1:9</a></i>;<br/>


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