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

<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="funct_1.html#NM1">Function</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/>



<b>assume </b><a NAME="E1:146"/><i><font color="Green">E83</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>1</sub></font> )
 ;<br/>

<b>then reconsider </b><font color="Maroon">c<sub>5</sub></font> =  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>6</sub></font> =  <a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>1</sub></font> as  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a>  <b>by </b><i><a class="ref" href="funct_1.html#T12">FUNCT_1:12</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>7</sub></font> = <font color="Maroon">c<sub>1</sub></font> as   <a href="funct_2.html#NM1">Function</a> of <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font> <b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a>, <a class="ref" href="relset_1.html#T11">RELSET_1:11</a></i>;<br/>
<a NAME="E4:146"/>
 <a href="relat_1.html#K2">rng</a> <span class="p1"><a href="finseq_1.html#K11">&lt;*</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span><a href="finseq_1.html#K11">*&gt;</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="enumset1.html#K1">{</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span><a href="enumset1.html#K1">}</a></span>
 
<b>by </b><i><a class="txt" href="finseq_2.html#E18"><i><font color="Green">Lemma12</font></i></a></i>;<br/>
<a NAME="E5:146"/><b>then </b>
(  <a href="relat_1.html#K2">rng</a> <span class="p1"><a href="finseq_1.html#K11">&lt;*</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span><a href="finseq_1.html#K11">*&gt;</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span><a href="tarski.html#K2">}</a></span> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>4</sub></font></span><a href="tarski.html#K1">}</a></span> &amp; <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span><a href="tarski.html#K2">}</a></span> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>5</sub></font> &amp; <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>4</sub></font></span><a href="tarski.html#K1">}</a></span> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>5</sub></font> )
 
<b>by </b><i><a class="txt" href="finseq_2.html#E1:146"><i><font color="Green">E83</font></i></a>, <a class="ref" href="enumset1.html#T43">ENUMSET1:43</a>, <a class="ref" href="zfmisc_1.html#T37">ZFMISC_1:37</a>, <a class="ref" href="zfmisc_1.html#T38">ZFMISC_1:38</a></i>;<br/>
<a NAME="E6:146"/><b>then </b>
 <a href="relat_1.html#K2">rng</a> <span class="p1"><a href="finseq_1.html#K11">&lt;*</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span><a href="finseq_1.html#K11">*&gt;</a></span> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T8">XBOOLE_1:8</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">c<sub>8</sub></font> = <span class="p1"><a href="finseq_1.html#K11">&lt;*</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span><a href="finseq_1.html#K11">*&gt;</a></span> as    <a href="finseq_1.html#M2">FinSequence</a> of <font color="Maroon">c<sub>5</sub></font> <b>by </b><i><a class="ref" href="finseq_1.html#D4">FINSEQ_1:def 4</a></i>;<br/>
<b>thus </b><font color="Maroon">c<sub>1</sub></font> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p1"><a href="finseq_1.html#K11">&lt;*</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span><a href="finseq_1.html#K11">*&gt;</a></span> = 
<font color="Maroon">c<sub>7</sub></font> <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font>

<br/>.= 
<span class="p1"><a href="finseq_1.html#K11">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span><a href="finseq_1.html#K11">*&gt;</a></span>
<b>by </b><i><a class="ref" href="finseq_2.html#T41" target="_self">Th41</a></i>
;<br/>


</div>
