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

<b>set </b><font color="Maroon">C</font> =  <a href="zfmisc_1.html#K1">bool</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">U0</font>;<br/>
<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[   <a href="hidden.html#M1">set</a> ] <b>means </b>( <font color="Maroon">A</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">a<sub>1</sub></font> &amp;  <a href="unialg_2.html#K6" target="_self">Constants</a> <font color="Maroon">U0</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">a<sub>1</sub></font> &amp; ( for <font color="Olive">B</font> being non <a href="xboole_0.html#V1">empty</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">U0</font>  st <font color="Olive">B</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a<sub>1</sub></font> holds <br/><font color="Olive">B</font> is <a href="unialg_2.html#V1" target="_self">opers_closed</a> ) );<br/>
<b>consider </b><font color="Maroon">X</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E2:37_1_1"/><i><font color="Green">E26</font></i>: 
for <font color="Olive">x</font> being   <a href="hidden.html#M1">set</a>  holds <br/> ( <font color="Olive">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font> iff ( <font color="Olive">x</font> <a href="hidden.html#R2">in</a>  <a href="zfmisc_1.html#K1">bool</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">U0</font> &amp; <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">x</font>] ) )
 <b>from </b><i><a class="ref" href="xboole_0.html#S1">XBOOLE_0:sch 1</a>();<br/></i>
<b>set </b><font color="Maroon">P</font> =  <a href="setfam_1.html#K1">meet</a> <font color="Maroon">X</font>;<br/>
<a NAME="E3:37_1_1"/><i><font color="Green">E29</font></i>: 
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">U0</font> <a href="hidden.html#R2">in</a>  <a href="zfmisc_1.html#K1">bool</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">U0</font>
 
<b>by </b><i><a class="ref" href="zfmisc_1.html#D1">ZFMISC_1:def 1</a></i>;<br/>
<a NAME="E4:37_1_1"/>
for <font color="Olive">B</font> being non <a href="xboole_0.html#V1">empty</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">U0</font>  st <font color="Olive">B</font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">U0</font> holds <br/><font color="Olive">B</font> is <a href="unialg_2.html#V1" target="_self">opers_closed</a>
 
<b>by </b><i/>;<br/>
<a NAME="E5:37_1_1"/><b>then </b><i><font color="Green">E30</font></i>: 
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">U0</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font>
 
<b>by </b><i>, </i>;<br/>
<a NAME="E6:37_1_1"/><i><font color="Green">E51</font></i>: 
 <a href="setfam_1.html#K1">meet</a> <font color="Maroon">X</font> <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">U0</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="37_1_1_1"><b>proof </b></a><div class="add">

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

<b>assume </b><a NAME="E1:37_1_1_1"/>
<font color="Maroon">t</font> <a href="hidden.html#R2">in</a>  <a href="setfam_1.html#K1">meet</a> <font color="Maroon">X</font>
 ;<br/>

<b>hence </b><a NAME="E2:37_1_1_1"/>
<font color="Maroon">t</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">U0</font>
 <b>by </b><i><a class="txt" href="unialg_2.html#E2:37_1_1"><i><font color="Green">E26</font></i></a>, <a class="ref" href="setfam_1.html#D1">SETFAM_1:def 1</a></i>;<br/>


</div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="37_1_1_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:37_1_1_2"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font>
 ;<br/><a NAME="E2:37_1_1_2"/><b>then </b>
( <font color="Maroon">A</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">x</font> &amp;  <a href="unialg_2.html#K6" target="_self">Constants</a> <font color="Maroon">U0</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">x</font> )
 <b>by </b><i/>;<br/><b>hence </b><a NAME="E3:37_1_1_2"/>
<font color="Maroon">A</font> <a href="subset_1.html#K4">\/</a> <span class="p1">(<span class="default"><a href="unialg_2.html#K6" target="_self">Constants</a> <font color="Maroon">U0</font></span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">x</font>
 <b>by </b><i><a class="ref" href="xboole_1.html#T8">XBOOLE_1:8</a></i>;<br/></div><b>end;</b></div>
<a NAME="E8:37_1_1"/><b>then </b><i><font color="Green">E52</font></i>: 
<font color="Maroon">A</font> <a href="subset_1.html#K4">\/</a> <span class="p1">(<span class="default"><a href="unialg_2.html#K6" target="_self">Constants</a> <font color="Maroon">U0</font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="setfam_1.html#K1">meet</a> <font color="Maroon">X</font>
 
<b>by </b><i><a class="txt" href="unialg_2.html#E2:37_1_1"><i><font color="Green">E26</font></i></a>, <a class="ref" href="setfam_1.html#T6">SETFAM_1:6</a></i>;<br/>
<a NAME="E9:37_1_1"/><i><font color="Green">E53</font></i>: 
<font color="Maroon">A</font> <a href="subset_1.html#K4">\/</a> <span class="p1">(<span class="default"><a href="unialg_2.html#K6" target="_self">Constants</a> <font color="Maroon">U0</font></span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i>, <a class="ref" href="xboole_1.html#T15">XBOOLE_1:15</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">P</font> =  <a href="setfam_1.html#K1">meet</a> <font color="Maroon">X</font> as  non <a href="xboole_0.html#V1">empty</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">U0</font> <b>by </b><i>, , <a class="ref" href="xboole_1.html#T3">XBOOLE_1:3</a></i>;<br/>
<a NAME="E11:37_1_1"/><i><font color="Green">E55</font></i>: 
<font color="Maroon">P</font> is <a href="unialg_2.html#V1" target="_self">opers_closed</a>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="37_1_1_3"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">o</font> be   <a href="unialg_2.html#NM5">operation</a> of <font color="Maroon">U0</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="unialg_2.html#D5" target="_self">UNIALG_2:def 5</a><br/><b>let </b><font color="Maroon">s</font> be    <a href="finseq_1.html#M2">FinSequence</a> of <font color="Maroon">P</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="unialg_2.html#D4" target="_self">UNIALG_2:def 4</a><br/>



<b>assume </b><a NAME="E1:37_1_1_3"/><i><font color="Green">E56</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">s</font> <a href="hidden.html#R1">=</a>  <a href="unialg_1.html#K3">arity</a> <font color="Maroon">o</font>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="37_1_1_3_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">a</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:37_1_1_3_1"/><i><font color="Green">E57</font></i>: 
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font>
 ;<br/><b>then reconsider </b><font color="Maroon">a0</font> = <font color="Maroon">a</font> as   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">U0</font> <b>by </b><i/>;<br/><a NAME="E3:37_1_1_3_1"/>
( <font color="Maroon">A</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">a0</font> &amp;  <a href="unialg_2.html#K6" target="_self">Constants</a> <font color="Maroon">U0</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">a0</font> )
 <b>by </b><i>, </i>;<br/><a NAME="E4:37_1_1_3_1"/><b>then </b>
<font color="Maroon">A</font> <a href="subset_1.html#K4">\/</a> <span class="p1">(<span class="default"><a href="unialg_2.html#K6" target="_self">Constants</a> <font color="Maroon">U0</font></span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">a0</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">a0</font> = <font color="Maroon">a0</font> as  non <a href="xboole_0.html#V1">empty</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">U0</font> <b>by </b><i><a class="txt" href="unialg_2.html#E3:37_1_1"><i><font color="Green">E29</font></i></a>, <a class="ref" href="xboole_1.html#T3">XBOOLE_1:3</a></i>;<br/><a NAME="E6:37_1_1_3_1"/>
<font color="Maroon">a0</font> is <a href="unialg_2.html#V1" target="_self">opers_closed</a>
 <b>by </b><i>, </i>;<br/><a NAME="E7:37_1_1_3_1"/><b>then </b><i><font color="Green">E58</font></i>: 
<font color="Maroon">a0</font> <a href="unialg_2.html#R2" target="_self">is_closed_on</a> <font color="Maroon">o</font>
 <b>by </b><i/>;<br/><a NAME="E8:37_1_1_3_1"/>
( <font color="Maroon">P</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">a0</font> &amp;  <a href="relat_1.html#K2">rng</a> <font color="Maroon">s</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">P</font> )
 <b>by </b><i>, <a class="ref" href="finseq_1.html#D4">FINSEQ_1:def 4</a>, <a class="ref" href="setfam_1.html#T4">SETFAM_1:4</a></i>;<br/><a NAME="E9:37_1_1_3_1"/><b>then </b>
 <a href="relat_1.html#K2">rng</a> <font color="Maroon">s</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">a0</font>
 <b>by </b><i><a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/><b>then reconsider </b><font color="Maroon">s0</font> = <font color="Maroon">s</font> as    <a href="finseq_1.html#M2">FinSequence</a> of <font color="Maroon">a0</font> <b>by </b><i><a class="ref" href="finseq_1.html#D4">FINSEQ_1:def 4</a></i>;<br/><a NAME="E11:37_1_1_3_1"/>
<font color="Maroon">o</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">s0</font> <a href="hidden.html#R2">in</a> <font color="Maroon">a0</font>
 <b>by </b><i>, , </i>;<br/><b>hence </b><a NAME="E12:37_1_1_3_1"/>
<font color="Maroon">o</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">s</font> <a href="hidden.html#R2">in</a> <font color="Maroon">a</font>
 ;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:37_1_1_3"/>
<font color="Maroon">o</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">s</font> <a href="hidden.html#R2">in</a> <font color="Maroon">P</font>
 <b>by </b><i><a class="txt" href="unialg_2.html#E2:37_1_1"><i><font color="Green">E26</font></i></a>, <a class="ref" href="setfam_1.html#D1">SETFAM_1:def 1</a></i>;<br/>


</div><b>end;</b></div>
<b>take </b><font color="Maroon">E</font> =  <a href="unialg_2.html#K4" target="_self">UniAlgSetClosed</a> <font color="Maroon">P</font>;<br/>

<a NAME="E12:37_1_1"/><i><font color="Green">E59</font></i>: 
<font color="Maroon">E</font> <a href="hidden.html#R1">=</a>  <a href="unialg_1.html#G1">UAStr</a>(# <font color="Maroon">P</font>,<span class="p1">(<span class="default"><a href="unialg_2.html#K3" target="_self">Opers</a> <font color="Maroon">U0</font>,<font color="Maroon">P</font></span>)</span> #)
 
<b>by </b><i><a class="txt" href="unialg_2.html#E5:37_1_1"><i><font color="Green">E30</font></i></a>, </i>;<br/>
<a NAME="E13:37_1_1"/>
<font color="Maroon">A</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">A</font> <a href="subset_1.html#K4">\/</a> <span class="p1">(<span class="default"><a href="unialg_2.html#K6" target="_self">Constants</a> <font color="Maroon">U0</font></span>)</span>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T7">XBOOLE_1:7</a></i>;<br/>
<b>hence </b><a NAME="E14:37_1_1"/>
<font color="Maroon">A</font> <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">E</font>
 <b>by </b><i>, , <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>

<b>let </b><font color="Maroon">U1</font> be    <a href="unialg_2.html#M3" target="_self">SubAlgebra</a> of <font color="Maroon">U0</font>;<br/>

<b>assume </b><a NAME="E15:37_1_1"/><i><font color="Green">E60</font></i>: 
<font color="Maroon">A</font> <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">U1</font>
 ;<br/>

<b>set </b><font color="Maroon">u1</font> = the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">U1</font>;<br/>
<a NAME="E16:37_1_1"/><i><font color="Green">E78</font></i>: 
 <a href="unialg_2.html#K6" target="_self">Constants</a> <font color="Maroon">U0</font> <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">U1</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="37_1_1_4"><b>proof </b></a><div class="add">

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

<b>assume </b><a NAME="E1:37_1_1_4"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="unialg_2.html#K6" target="_self">Constants</a> <font color="Maroon">U0</font>
 ;<br/>

<a NAME="E2:37_1_1_4"/><b>then </b>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <font color="Olive">a</font> where <font color="Olive">a</font> is   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">U0</font> :  ex <font color="Olive">o</font> being  <a href="unialg_2.html#NM5">operation</a> of <font color="Maroon">U0</font> st <br/>(  <a href="unialg_1.html#K3">arity</a> <font color="Olive">o</font> <a href="hidden.html#R1">=</a> 0 &amp; <font color="Olive">a</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <font color="Olive">o</font> ) </span>}</span> 
 
;<br/>
<b>then consider </b><font color="Maroon">a</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">U0</font><b> such that </b><br/><a NAME="E4:37_1_1_4"/><i><font color="Green">E79</font></i>: 
( <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font> &amp;  ex <font color="Olive">o</font> being  <a href="unialg_2.html#NM5">operation</a> of <font color="Maroon">U0</font> st <br/>(  <a href="unialg_1.html#K3">arity</a> <font color="Olive">o</font> <a href="hidden.html#R1">=</a> 0 &amp; <font color="Maroon">a</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <font color="Olive">o</font> ) )
 ;<br/>
<b>consider </b><font color="Maroon">o0</font> being   <a href="unialg_2.html#NM5">operation</a> of <font color="Maroon">U0</font><b> such that </b><br/><a NAME="E6:37_1_1_4"/><i><font color="Green">E80</font></i>: 
(  <a href="unialg_1.html#K3">arity</a> <font color="Maroon">o0</font> <a href="hidden.html#R1">=</a> 0 &amp; <font color="Maroon">a</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">o0</font> )
 <b>by </b><i/>;<br/>
<b>consider </b><font color="Maroon">n</font> being    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> <b> such that </b><br/><a NAME="E8:37_1_1_4"/><i><font color="Green">E81</font></i>: 
( <font color="Maroon">n</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> the <a href="unialg_1.html#U1">charact</a> of <font color="Maroon">U0</font> &amp; the <a href="unialg_1.html#U1">charact</a> of <font color="Maroon">U0</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">n</font> <a href="hidden.html#R1">=</a> <font color="Maroon">o0</font> )
 <b>by </b><i><a class="ref" href="finseq_2.html#T11">FINSEQ_2:11</a></i>;<br/>
<b>reconsider </b><font color="Maroon">B</font> = the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">U1</font> as  non <a href="xboole_0.html#V1">empty</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">U0</font> <b>by </b><i/>;<br/>
<a NAME="E10:37_1_1_4"/><i><font color="Green">E82</font></i>: 
( the <a href="unialg_1.html#U1">charact</a> of <font color="Maroon">U1</font> <a href="hidden.html#R1">=</a>  <a href="unialg_2.html#K3" target="_self">Opers</a> <font color="Maroon">U0</font>,<font color="Maroon">B</font> &amp; <font color="Maroon">B</font> is <a href="unialg_2.html#V1" target="_self">opers_closed</a> )
 
<b>by </b><i/>;<br/>
<a NAME="E11:37_1_1_4"/><i><font color="Green">E85</font></i>: 
<font color="Maroon">n</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> the <a href="unialg_1.html#U1">charact</a> of <font color="Maroon">U1</font>
 
<b>by </b><i><a class="ref" href="unialg_2.html#D1" target="_self">Def1</a>, </i>;<br/>
<b>then reconsider </b><font color="Maroon">o1</font> = the <a href="unialg_1.html#U1">charact</a> of <font color="Maroon">U1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">n</font> as   <a href="unialg_2.html#NM5">operation</a> of <font color="Maroon">U1</font> <b>by </b><i/>;<br/>
<a NAME="E13:37_1_1_4"/><i><font color="Green">E87</font></i>: 
<font color="Maroon">o1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">o0</font> <a href="unialg_2.html#K2" target="_self">/.</a> <font color="Maroon">B</font>
 
<b>by </b><i><a class="ref" href="unialg_2.html#D1" target="_self">Def1</a>, , , </i>;<br/>
<b>consider </b><font color="Maroon">y</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E15:37_1_1_4"/><i><font color="Green">E88</font></i>: 
( <font color="Maroon">y</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">o0</font> &amp; <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">o0</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">y</font> )
 <b>by </b><i>, <a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/>
<a NAME="E16:37_1_1_4"/><i><font color="Green">E89</font></i>: 
<font color="Maroon">B</font> <a href="unialg_2.html#R2" target="_self">is_closed_on</a> <font color="Maroon">o0</font>
 
<b>by </b><i>, </i>;<br/>
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">o0</font> = 
0 <a href="finseq_2.html#K4">-tuples_on</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">U0</font>
<b>by </b><i>, </i>
<br/>.= 
<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K6">&lt;*&gt;</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">U0</font></span>)</span></span><a href="tarski.html#K1">}</a></span>
<b>by </b><i><a class="ref" href="finseq_2.html#T112">FINSEQ_2:112</a></i>
;<br/>
<a NAME="E18:37_1_1_4"/><b>then </b>
<font color="Maroon">y</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K6">&lt;*&gt;</a> <font color="Maroon">B</font></span>)</span></span><a href="tarski.html#K1">}</a></span>
 
<b>by </b><i><a class="ref" href="unialg_2.html#D2" target="_self">Def2</a></i>;<br/>
<a NAME="E19:37_1_1_4"/><b>then </b>
<font color="Maroon">y</font> <a href="hidden.html#R2">in</a> 0 <a href="finseq_2.html#K4">-tuples_on</a> <font color="Maroon">B</font>
 
<b>by </b><i><a class="ref" href="finseq_2.html#T112">FINSEQ_2:112</a></i>;<br/>
<a NAME="E20:37_1_1_4"/><b>then </b>
<font color="Maroon">y</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">o0</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="unialg_1.html#K3">arity</a> <font color="Maroon">o0</font></span>)</span> <a href="finseq_2.html#K4">-tuples_on</a> <font color="Maroon">B</font></span>)</span>
 
<b>by </b><i>, <a class="ref" href="unialg_2.html#D2" target="_self">Def2</a>, <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/>
<a NAME="E21:37_1_1_4"/><b>then </b><i><font color="Green">E90</font></i>: 
<font color="Maroon">y</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">o0</font> <a href="partfun1.html#K2">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="unialg_1.html#K3">arity</a> <font color="Maroon">o0</font></span>)</span> <a href="finseq_2.html#K4">-tuples_on</a> <font color="Maroon">B</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_1.html#T68">FUNCT_1:68</a></i>;<br/>
<a NAME="E22:37_1_1_4"/><b>then </b><i><font color="Green">E91</font></i>: 
<font color="Maroon">y</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">o0</font> <a href="unialg_2.html#K2" target="_self">/.</a> <font color="Maroon">B</font></span>)</span>
 
<b>by </b><i>, </i>;<br/>
<i><font color="Green">E92</font></i>: <font color="Maroon">o1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">y</font> = 
<span class="p1">(<span class="default"><font color="Maroon">o0</font> <a href="partfun1.html#K2">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="unialg_1.html#K3">arity</a> <font color="Maroon">o0</font></span>)</span> <a href="finseq_2.html#K4">-tuples_on</a> <font color="Maroon">B</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">y</font>
<b>by </b><i>, , </i>
<br/>.= 
<font color="Maroon">a</font>
<b>by </b><i><a class="ref" href="unialg_2.html#D2" target="_self">Def2</a>, , <a class="ref" href="funct_1.html#T68">FUNCT_1:68</a></i>
;<br/>
<a NAME="E24:37_1_1_4"/>
( <font color="Maroon">o1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">y</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">o1</font> &amp;  <a href="relat_1.html#K2">rng</a> <font color="Maroon">o1</font> <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">U1</font> )
 
<b>by </b><i>, , <a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a>, <a class="ref" href="relset_1.html#T12">RELSET_1:12</a></i>;<br/>
<b>hence </b><a NAME="E25:37_1_1_4"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">U1</font>
 <b>by </b><i>, </i>;<br/>


</div><b>end;</b></div>
<a NAME="E17:37_1_1"/>
( the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">U1</font> is   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">U0</font> &amp; ( for <font color="Olive">B</font> being non <a href="xboole_0.html#V1">empty</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">U0</font>  st <font color="Olive">B</font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">U1</font> holds <br/>( the <a href="unialg_1.html#U1">charact</a> of <font color="Maroon">U1</font> <a href="hidden.html#R1">=</a>  <a href="unialg_2.html#K3" target="_self">Opers</a> <font color="Maroon">U0</font>,<font color="Olive">B</font> &amp; <font color="Olive">B</font> is <a href="unialg_2.html#V1" target="_self">opers_closed</a> ) ) )
 
<b>by </b><i/>;<br/>
<a NAME="E18:37_1_1"/><b>then </b>
( the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">U1</font> <a href="hidden.html#R2">in</a>  <a href="zfmisc_1.html#K1">bool</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">U0</font> &amp; ( for <font color="Olive">B</font> being non <a href="xboole_0.html#V1">empty</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">U0</font>  st <font color="Olive">B</font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">U1</font> holds <br/><font color="Olive">B</font> is <a href="unialg_2.html#V1" target="_self">opers_closed</a> ) )
 
;<br/>
<a NAME="E19:37_1_1"/><b>then </b><i><font color="Green">E93</font></i>: 
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">U1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font>
 
<b>by </b><i>, , </i>;<br/>
<a NAME="E20:37_1_1"/><b>then </b><i><font color="Green">E94</font></i>: 
<font color="Maroon">P</font> <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">U1</font>
 
<b>by </b><i><a class="ref" href="setfam_1.html#T4">SETFAM_1:4</a></i>;<br/>
<b>thus </b><a NAME="E21:37_1_1"/>
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">E</font> is   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">U1</font>
 <b>by </b><i>, , <a class="ref" href="setfam_1.html#T4">SETFAM_1:4</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="unialg_2.html#D8" target="_self">UNIALG_2:def 8</a><br/>

<b>let </b><font color="Maroon">B</font> be  non <a href="xboole_0.html#V1">empty</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">U1</font>;<br/>

<b>assume </b><a NAME="E22:37_1_1"/><i><font color="Green">E95</font></i>: 
<font color="Maroon">B</font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">E</font>
 ;<br/>

<b>reconsider </b><font color="Maroon">u11</font> = the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">U1</font> as  non <a href="xboole_0.html#V1">empty</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">U0</font> <b>by </b><i/>;<br/>
<a NAME="E24:37_1_1"/><i><font color="Green">E96</font></i>: 
( the <a href="unialg_1.html#U1">charact</a> of <font color="Maroon">U1</font> <a href="hidden.html#R1">=</a>  <a href="unialg_2.html#K3" target="_self">Opers</a> <font color="Maroon">U0</font>,<font color="Maroon">u11</font> &amp; <font color="Maroon">u11</font> is <a href="unialg_2.html#V1" target="_self">opers_closed</a> )
 
<b>by </b><i/>;<br/>
<a NAME="E25:37_1_1"/><i><font color="Green">E121</font></i>: 
(  <a href="finseq_1.html#K4">dom</a> the <a href="unialg_1.html#U1">charact</a> of <font color="Maroon">U0</font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="unialg_2.html#K3" target="_self">Opers</a> <font color="Maroon">U0</font>,<font color="Maroon">P</font></span>)</span> &amp;  <a href="finseq_1.html#K4">dom</a> the <a href="unialg_1.html#U1">charact</a> of <font color="Maroon">U0</font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="unialg_2.html#K3" target="_self">Opers</a> <font color="Maroon">U0</font>,<font color="Maroon">u11</font></span>)</span> )
 
<b>by </b><i/>;<br/>
<div><i><font color="Green">E122</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="37_1_1_5"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">o1</font> be   <a href="unialg_2.html#NM5">operation</a> of <font color="Maroon">U1</font>;<br/><b>consider </b><font color="Maroon">n</font> being    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> <b> such that </b><br/><a NAME="E2:37_1_1_5"/><i><font color="Green">E123</font></i>: 
( <font color="Maroon">n</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> the <a href="unialg_1.html#U1">charact</a> of <font color="Maroon">U1</font> &amp; <font color="Maroon">o1</font> <a href="hidden.html#R1">=</a> the <a href="unialg_1.html#U1">charact</a> of <font color="Maroon">U1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">n</font> )
 <b>by </b><i><a class="ref" href="finseq_2.html#T11">FINSEQ_2:11</a></i>;<br/><b>reconsider </b><font color="Maroon">o0</font> = the <a href="unialg_1.html#U1">charact</a> of <font color="Maroon">U0</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">n</font> as   <a href="unialg_2.html#NM5">operation</a> of <font color="Maroon">U0</font> <b>by </b><i>, , <a class="ref" href="unialg_2.html#D2" target="_self">Def2</a>, </i>;<br/><a NAME="E4:37_1_1_5"/><i><font color="Green">E124</font></i>: 
 <a href="unialg_1.html#K3">arity</a> <font color="Maroon">o0</font> <a href="hidden.html#R1">=</a>  <a href="unialg_1.html#K3">arity</a> <font color="Maroon">o1</font>
 <b>by </b><i><a class="ref" href="unialg_2.html#D2" target="_self">Def2</a>, </i>;<br/><a NAME="E5:37_1_1_5"/><i><font color="Green">E125</font></i>: 
<font color="Maroon">u11</font> <a href="unialg_2.html#R2" target="_self">is_closed_on</a> <font color="Maroon">o0</font>
 <b>by </b><i>, </i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="37_1_1_5_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">s</font> be    <a href="finseq_1.html#M2">FinSequence</a> of <font color="Maroon">B</font>;<br/><b>assume </b><a NAME="E1:37_1_1_5_1"/><i><font color="Green">E126</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">s</font> <a href="hidden.html#R1">=</a>  <a href="unialg_1.html#K3">arity</a> <font color="Maroon">o1</font>
 ;<br/><b>reconsider </b><font color="Maroon">sE</font> = <font color="Maroon">s</font> as    <a href="finseq_2.html#M2">Element</a> of <font color="Maroon">P</font> <a href="finseq_2.html#K3">*</a>  <b>by </b><i>, <a class="ref" href="unialg_2.html#D1" target="_self">Def1</a>, <a class="ref" href="finseq_1.html#D11">FINSEQ_1:def 11</a></i>;<br/><a NAME="E3:37_1_1_5_1"/>
<font color="Maroon">s</font> is    <a href="finseq_1.html#M2">FinSequence</a> of <font color="Maroon">u11</font>
 <b>by </b><i><a class="ref" href="finseq_2.html#T27">FINSEQ_2:27</a></i>;<br/><b>then reconsider </b><font color="Maroon">s1</font> = <font color="Maroon">s</font> as    <a href="finseq_2.html#M2">Element</a> of <font color="Maroon">u11</font> <a href="finseq_2.html#K3">*</a>  <b>by </b><i><a class="ref" href="finseq_1.html#D11">FINSEQ_1:def 11</a></i>;<br/><i><font color="Green">E128</font></i>:  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">o0</font> <a href="partfun1.html#K2">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="unialg_1.html#K3">arity</a> <font color="Maroon">o0</font></span>)</span> <a href="finseq_2.html#K4">-tuples_on</a> <font color="Maroon">u11</font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">o0</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="unialg_1.html#K3">arity</a> <font color="Maroon">o0</font></span>)</span> <a href="finseq_2.html#K4">-tuples_on</a> <font color="Maroon">u11</font></span>)</span>
<b>by </b><i><a class="ref" href="funct_1.html#T68">FUNCT_1:68</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="unialg_1.html#K3">arity</a> <font color="Maroon">o0</font></span>)</span> <a href="finseq_2.html#K4">-tuples_on</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">U0</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="unialg_1.html#K3">arity</a> <font color="Maroon">o0</font></span>)</span> <a href="finseq_2.html#K4">-tuples_on</a> <font color="Maroon">u11</font></span>)</span>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><a href="unialg_1.html#K3">arity</a> <font color="Maroon">o0</font></span>)</span> <a href="finseq_2.html#K4">-tuples_on</a> <font color="Maroon">u11</font>
<b>by </b><i/>
;<br/><a NAME="E6:37_1_1_5_1"/>
<font color="Maroon">s1</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <font color="Olive">q</font> where <font color="Olive">q</font> is    <a href="finseq_2.html#M2">Element</a> of <font color="Maroon">u11</font> <a href="finseq_2.html#K3">*</a>  :  <a href="finseq_1.html#K3">len</a> <font color="Olive">q</font> <a href="hidden.html#R1">=</a>  <a href="unialg_1.html#K3">arity</a> <font color="Maroon">o0</font> </span>}</span> 
 <b>by </b><i>, </i>;<br/><a NAME="E7:37_1_1_5_1"/><b>then </b><i><font color="Green">E130</font></i>: 
<font color="Maroon">s1</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">o0</font> <a href="partfun1.html#K2">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="unialg_1.html#K3">arity</a> <font color="Maroon">o0</font></span>)</span> <a href="finseq_2.html#K4">-tuples_on</a> <font color="Maroon">u11</font></span>)</span></span>)</span>
 <b>by </b><i>, <a class="ref" href="finseq_2.html#D4">FINSEQ_2:def 4</a></i>;<br/><a NAME="E8:37_1_1_5_1"/><i><font color="Green">E131</font></i>: 
<font color="Maroon">P</font> <a href="unialg_2.html#R2" target="_self">is_closed_on</a> <font color="Maroon">o0</font>
 <b>by </b><i><a class="txt" href="unialg_2.html#E5:37_1_1"><i><font color="Green">E30</font></i></a>, </i>;<br/><font color="Maroon">o1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">s</font> = 
<span class="p1">(<span class="default"><font color="Maroon">o0</font> <a href="unialg_2.html#K2" target="_self">/.</a> <font color="Maroon">u11</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">s1</font>
<b>by </b><i>, <a class="ref" href="unialg_2.html#D2" target="_self">Def2</a>, </i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">o0</font> <a href="partfun1.html#K2">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="unialg_1.html#K3">arity</a> <font color="Maroon">o0</font></span>)</span> <a href="finseq_2.html#K4">-tuples_on</a> <font color="Maroon">u11</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">s1</font>
<b>by </b><i>, </i>
<br/>.= 
<font color="Maroon">o0</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">sE</font>
<b>by </b><i>, <a class="ref" href="funct_1.html#T68">FUNCT_1:68</a></i>
;<br/><b>hence </b><a NAME="E10:37_1_1_5_1"/>
<font color="Maroon">o1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">s</font> <a href="hidden.html#R2">in</a> <font color="Maroon">B</font>
 <b>by </b><i>, <a class="ref" href="unialg_2.html#D1" target="_self">Def1</a>, , , <a class="ref" href="unialg_2.html#T6" target="_self">Th6</a>, </i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E7:37_1_1_5"/>
<font color="Maroon">B</font> <a href="unialg_2.html#R2" target="_self">is_closed_on</a> <font color="Maroon">o1</font>
 <b>by </b><i/>;<br/></div><b>end;</b></div>
<a NAME="E27:37_1_1"/><i><font color="Green">E132</font></i>: 
 <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="unialg_2.html#K3" target="_self">Opers</a> <font color="Maroon">U1</font>,<font color="Maroon">B</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K4">dom</a> the <a href="unialg_1.html#U1">charact</a> of <font color="Maroon">U1</font>
 
<b>by </b><i/>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="37_1_1_6"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">n</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>assume </b><a NAME="E1:37_1_1_6"/><i><font color="Green">E133</font></i>: 
<font color="Maroon">n</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> the <a href="unialg_1.html#U1">charact</a> of <font color="Maroon">U0</font>
 ;<br/><b>then reconsider </b><font color="Maroon">o0</font> = the <a href="unialg_1.html#U1">charact</a> of <font color="Maroon">U0</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">n</font> as   <a href="unialg_2.html#NM5">operation</a> of <font color="Maroon">U0</font> <b>by </b><i/>;<br/><b>reconsider </b><font color="Maroon">o1</font> = the <a href="unialg_1.html#U1">charact</a> of <font color="Maroon">U1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">n</font> as   <a href="unialg_2.html#NM5">operation</a> of <font color="Maroon">U1</font> <b>by </b><i>, , , </i>;<br/><a NAME="E4:37_1_1_6"/><i><font color="Green">E134</font></i>: 
<font color="Maroon">u11</font> <a href="unialg_2.html#R2" target="_self">is_closed_on</a> <font color="Maroon">o0</font>
 <b>by </b><i>, </i>;<br/><a NAME="E5:37_1_1_6"/><i><font color="Green">E135</font></i>: 
<font color="Maroon">B</font> <a href="unialg_2.html#R2" target="_self">is_closed_on</a> <font color="Maroon">o1</font>
 <b>by </b><i/>;<br/><a NAME="E6:37_1_1_6"/><i><font color="Green">E136</font></i>: 
<font color="Maroon">P</font> <a href="unialg_2.html#R2" target="_self">is_closed_on</a> <font color="Maroon">o0</font>
 <b>by </b><i><a class="txt" href="unialg_2.html#E5:37_1_1"><i><font color="Green">E30</font></i></a>, </i>;<br/><b>thus </b>the <a href="unialg_1.html#U1">charact</a> of <font color="Maroon">E</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">n</font> = 
<font color="Maroon">o0</font> <a href="unialg_2.html#K2" target="_self">/.</a> <font color="Maroon">P</font>
<b>by </b><i>, , , </i>
<br/>.= 
<font color="Maroon">o0</font> <a href="partfun1.html#K2">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="unialg_1.html#K3">arity</a> <font color="Maroon">o0</font></span>)</span> <a href="finseq_2.html#K4">-tuples_on</a> <font color="Maroon">P</font></span>)</span>
<b>by </b><i>, </i>
<br/>.= 
<font color="Maroon">o0</font> <a href="partfun1.html#K2">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="unialg_1.html#K3">arity</a> <font color="Maroon">o0</font></span>)</span> <a href="finseq_2.html#K4">-tuples_on</a> <font color="Maroon">u11</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="unialg_1.html#K3">arity</a> <font color="Maroon">o0</font></span>)</span> <a href="finseq_2.html#K4">-tuples_on</a> <font color="Maroon">P</font></span>)</span></span>)</span>
<b>by </b><i>, </i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">o0</font> <a href="partfun1.html#K2">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="unialg_1.html#K3">arity</a> <font color="Maroon">o0</font></span>)</span> <a href="finseq_2.html#K4">-tuples_on</a> <font color="Maroon">u11</font></span>)</span></span>)</span> <a href="partfun1.html#K2">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="unialg_1.html#K3">arity</a> <font color="Maroon">o0</font></span>)</span> <a href="finseq_2.html#K4">-tuples_on</a> <font color="Maroon">P</font></span>)</span>
<b>by </b><i><a class="ref" href="relat_1.html#T100">RELAT_1:100</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">o0</font> <a href="unialg_2.html#K2" target="_self">/.</a> <font color="Maroon">u11</font></span>)</span> <a href="partfun1.html#K2">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="unialg_1.html#K3">arity</a> <font color="Maroon">o0</font></span>)</span> <a href="finseq_2.html#K4">-tuples_on</a> <font color="Maroon">P</font></span>)</span>
<b>by </b><i>, </i>
<br/>.= 
<font color="Maroon">o1</font> <a href="partfun1.html#K2">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="unialg_1.html#K3">arity</a> <font color="Maroon">o0</font></span>)</span> <a href="finseq_2.html#K4">-tuples_on</a> <font color="Maroon">P</font></span>)</span>
<b>by </b><i>, , , </i>
<br/>.= 
<font color="Maroon">o1</font> <a href="partfun1.html#K2">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="unialg_1.html#K3">arity</a> <font color="Maroon">o1</font></span>)</span> <a href="finseq_2.html#K4">-tuples_on</a> <font color="Maroon">B</font></span>)</span>
<b>by </b><i>, <a class="ref" href="unialg_2.html#D1" target="_self">Def1</a>, , , , </i>
<br/>.= 
<font color="Maroon">o1</font> <a href="unialg_2.html#K2" target="_self">/.</a> <font color="Maroon">B</font>
<b>by </b><i>, </i>
<br/>.= 
<span class="p1">(<span class="default"><a href="unialg_2.html#K3" target="_self">Opers</a> <font color="Maroon">U1</font>,<font color="Maroon">B</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">n</font>
<b>by </b><i>, , <a class="ref" href="unialg_2.html#D2" target="_self">Def2</a>, , </i>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E29:37_1_1"/>
( the <a href="unialg_1.html#U1">charact</a> of <font color="Maroon">E</font> <a href="hidden.html#R1">=</a>  <a href="unialg_2.html#K3" target="_self">Opers</a> <font color="Maroon">U1</font>,<font color="Maroon">B</font> &amp; <font color="Maroon">B</font> is <a href="unialg_2.html#V1" target="_self">opers_closed</a> )
 <b>by </b><i>, , , , <a class="ref" href="unialg_2.html#D2" target="_self">Def2</a>, , <a class="ref" href="finseq_1.html#T17">FINSEQ_1:17</a></i>;<br/>


</div>
