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

<b>set </b><font color="Maroon" title="c3">C</font> =  <a href="zfmisc_1.html#K1" title="ZFMISC_1:func.1">bool</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">U0</font>;<br/>
<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ] <b>means </b>( <font color="Maroon" title="c2">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> $1 &amp;  <a href="unialg_2.html#K6" title="UNIALG_2:func.6">Constants</a> <font color="Maroon" title="c1">U0</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> $1 &amp; ( for <font color="Olive" title="b1">B</font> being non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">U0</font>  st <font color="Olive" title="b1">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> $1 holds <br/><font color="Olive" title="b1">B</font> is <a href="unialg_2.html#V1" title="UNIALG_2:attr.1">opers_closed</a> ) );<br/>
<b>consider </b><font color="Maroon" title="c4">X</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E2:37_1_1"/><i><font color="Green" title="E24">A2</font></i>: 
for <font color="Olive" title="b1">x</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  holds <br/> ( <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">X</font> iff ( <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="zfmisc_1.html#K1" title="ZFMISC_1:func.1">bool</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">U0</font> &amp; <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">x</font>] ) )
 <b>from </b><i><a class="ref" href="xboole_0.html#S1" title="XBOOLE_0:sch.1">XBOOLE_0:sch 1</a>();<br/></i>
<b>set </b><font color="Maroon" title="c5">P</font> =  <a href="setfam_1.html#K1" title="SETFAM_1:func.1">meet</a> <font color="Maroon" title="c4">X</font>;<br/>
<a NAME="E3:37_1_1"/><i><font color="Green" title="E25">A3</font></i>: 
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">U0</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="zfmisc_1.html#K1" title="ZFMISC_1:func.1">bool</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">U0</font>
 
<b>by </b><i><a class="ref" href="zfmisc_1.html#D1" title="ZFMISC_1:def.1">ZFMISC_1:def 1</a></i>;<br/>
<a NAME="E4:37_1_1"/>
for <font color="Olive" title="b1">B</font> being non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">U0</font>  st <font color="Olive" title="b1">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">U0</font> holds <br/><font color="Olive" title="b1">B</font> is <a href="unialg_2.html#V1" title="UNIALG_2:attr.1">opers_closed</a>
 
<b>by </b><i><a class="ref" href="unialg_2.html#T7" target="_self" title="UNIALG_2:th.7">Th7</a></i>;<br/>
<a NAME="E5:37_1_1"/><b>then </b><i><font color="Green" title="E26">A4</font></i>: 
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">U0</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">X</font>
 
<b>by </b><i><a class="txt" href="unialg_2.html#E2:37_1_1"><i><font color="Green" title="E24">A2</font></i></a>, <a class="txt" href="unialg_2.html#E3:37_1_1"><i><font color="Green" title="E25">A3</font></i></a></i>;<br/>
<a NAME="E6:37_1_1"/><i><font color="Green" title="E27">A5</font></i>: 
 <a href="setfam_1.html#K1" title="SETFAM_1:func.1">meet</a> <font color="Maroon" title="c4">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">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" title="c6">t</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:37_1_1_1"/>
<font color="Maroon" title="c6">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="setfam_1.html#K1" title="SETFAM_1:func.1">meet</a> <font color="Maroon" title="c4">X</font>
 ;<br/>

<b>hence </b><a NAME="E2:37_1_1_1"/>
<font color="Maroon" title="c6">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">U0</font>
 <b>by </b><i><a class="txt" href="unialg_2.html#E5:37_1_1"><i><font color="Green" title="E26">A4</font></i></a>, <a class="ref" href="setfam_1.html#D1" title="SETFAM_1:def.1">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" title="c6">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>assume </b><a NAME="E1:37_1_1_2"/>
<font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">X</font>
 ;<br/><a NAME="E2:37_1_1_2"/><b>then </b>
( <font color="Maroon" title="c2">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c6">x</font> &amp;  <a href="unialg_2.html#K6" title="UNIALG_2:func.6">Constants</a> <font color="Maroon" title="c1">U0</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c6">x</font> )
 <b>by </b><i><a class="txt" href="unialg_2.html#E2:37_1_1"><i><font color="Green" title="E24">A2</font></i></a></i>;<br/><b>hence </b><a NAME="E3:37_1_1_2"/>
<font color="Maroon" title="c2">A</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><a href="unialg_2.html#K6" title="UNIALG_2:func.6">Constants</a> <font color="Maroon" title="c1">U0</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c6">x</font>
 <b>by </b><i><a class="ref" href="xboole_1.html#T8" title="XBOOLE_1:th.8">XBOOLE_1:8</a></i>;<br/></div><b>end;</b></div>
<a NAME="E8:37_1_1"/><b>then </b><i><font color="Green" title="E28">A6</font></i>: 
<font color="Maroon" title="c2">A</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><a href="unialg_2.html#K6" title="UNIALG_2:func.6">Constants</a> <font color="Maroon" title="c1">U0</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="setfam_1.html#K1" title="SETFAM_1:func.1">meet</a> <font color="Maroon" title="c4">X</font>
 
<b>by </b><i><a class="txt" href="unialg_2.html#E5:37_1_1"><i><font color="Green" title="E26">A4</font></i></a>, <a class="ref" href="setfam_1.html#T6" title="SETFAM_1:th.6">SETFAM_1:6</a></i>;<br/>
<a NAME="E9:37_1_1"/><i><font color="Green" title="E29">A7</font></i>: 
<font color="Maroon" title="c2">A</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><a href="unialg_2.html#K6" title="UNIALG_2:func.6">Constants</a> <font color="Maroon" title="c1">U0</font></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
<b>by </b><i><a class="txt" href="unialg_2.html#E1:37"><i><font color="Green" title="E23">A1</font></i></a>, <a class="ref" href="xboole_1.html#T15" title="XBOOLE_1:th.15">XBOOLE_1:15</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c6">P</font> =  <a href="setfam_1.html#K1" title="SETFAM_1:func.1">meet</a> <font color="Maroon" title="c4">X</font> as  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">U0</font> <b>by </b><i><a class="txt" href="unialg_2.html#E6:37_1_1"><i><font color="Green" title="E27">A5</font></i></a>, <a class="txt" href="unialg_2.html#E8:37_1_1"><i><font color="Green" title="E28">A6</font></i></a>, <a class="ref" href="xboole_1.html#T3" title="XBOOLE_1:th.3">XBOOLE_1:3</a></i>;<br/>
<a NAME="E11:37_1_1"/><i><font color="Green" title="E30">A8</font></i>: 
<font color="Maroon" title="c6">P</font> is <a href="unialg_2.html#V1" title="UNIALG_2:attr.1">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" title="c7">o</font> be   <a href="unialg_2.html#NM5" title="UNIALG_2:NM.5">operation</a> of <font color="Maroon" title="c1">U0</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="unialg_2.html#D5" target="_self" title="UNIALG_2:def.5">UNIALG_2:def 5</a><br/><b>let </b><font color="Maroon" title="c8">s</font> be    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of <font color="Maroon" title="c6">P</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="unialg_2.html#D4" target="_self" title="UNIALG_2:def.4">UNIALG_2:def 4</a><br/>



<b>assume </b><a NAME="E1:37_1_1_3"/><i><font color="Green" title="E31">A9</font></i>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="unialg_1.html#K3" title="UNIALG_1:func.3">arity</a> <font color="Maroon" title="c7">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" title="c9">a</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>assume </b><a NAME="E1:37_1_1_3_1"/><i><font color="Green" title="E32">A10</font></i>: 
<font color="Maroon" title="c9">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">X</font>
 ;<br/><b>then reconsider </b><font color="Maroon" title="c10">a0</font> = <font color="Maroon" title="c9">a</font> as   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">U0</font> <b>by </b><i><a class="txt" href="unialg_2.html#E2:37_1_1"><i><font color="Green" title="E24">A2</font></i></a></i>;<br/><a NAME="E3:37_1_1_3_1"/>
( <font color="Maroon" title="c2">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c10">a0</font> &amp;  <a href="unialg_2.html#K6" title="UNIALG_2:func.6">Constants</a> <font color="Maroon" title="c1">U0</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c10">a0</font> )
 <b>by </b><i><a class="txt" href="unialg_2.html#E2:37_1_1"><i><font color="Green" title="E24">A2</font></i></a>, <a class="txt" href="unialg_2.html#E1:37_1_1_3_1"><i><font color="Green" title="E32">A10</font></i></a></i>;<br/><a NAME="E4:37_1_1_3_1"/><b>then </b>
<font color="Maroon" title="c2">A</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><a href="unialg_2.html#K6" title="UNIALG_2:func.6">Constants</a> <font color="Maroon" title="c1">U0</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c10">a0</font>
 <b>by </b><i><a class="ref" href="xboole_1.html#T8" title="XBOOLE_1:th.8">XBOOLE_1:8</a></i>;<br/><b>then reconsider </b><font color="Maroon" title="c11">a0</font> = <font color="Maroon" title="c10">a0</font> as  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">U0</font> <b>by </b><i><a class="txt" href="unialg_2.html#E9:37_1_1"><i><font color="Green" title="E29">A7</font></i></a>, <a class="ref" href="xboole_1.html#T3" title="XBOOLE_1:th.3">XBOOLE_1:3</a></i>;<br/><a NAME="E6:37_1_1_3_1"/>
<font color="Maroon" title="c11">a0</font> is <a href="unialg_2.html#V1" title="UNIALG_2:attr.1">opers_closed</a>
 <b>by </b><i><a class="txt" href="unialg_2.html#E2:37_1_1"><i><font color="Green" title="E24">A2</font></i></a>, <a class="txt" href="unialg_2.html#E1:37_1_1_3_1"><i><font color="Green" title="E32">A10</font></i></a></i>;<br/><a NAME="E7:37_1_1_3_1"/><b>then </b><i><font color="Green" title="E33">A11</font></i>: 
<font color="Maroon" title="c11">a0</font> <a href="unialg_2.html#R2" title="UNIALG_2:pred.2">is_closed_on</a> <font color="Maroon" title="c7">o</font>
 <b>by </b><i><a class="ref" href="unialg_2.html#D5" target="_self" title="UNIALG_2:def.5">Def5</a></i>;<br/><a NAME="E8:37_1_1_3_1"/>
( <font color="Maroon" title="c6">P</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c11">a0</font> &amp;  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c8">s</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c6">P</font> )
 <b>by </b><i><a class="txt" href="unialg_2.html#E1:37_1_1_3_1"><i><font color="Green" title="E32">A10</font></i></a>, <a class="ref" href="finseq_1.html#D4" title="FINSEQ_1:def.4">FINSEQ_1:def 4</a>, <a class="ref" href="setfam_1.html#T4" title="SETFAM_1:th.4">SETFAM_1:4</a></i>;<br/><a NAME="E9:37_1_1_3_1"/><b>then </b>
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c8">s</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c11">a0</font>
 <b>by </b><i><a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></i>;<br/><b>then reconsider </b><font color="Maroon" title="c12">s0</font> = <font color="Maroon" title="c8">s</font> as    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of <font color="Maroon" title="c11">a0</font> <b>by </b><i><a class="ref" href="finseq_1.html#D4" title="FINSEQ_1:def.4">FINSEQ_1:def 4</a></i>;<br/><a NAME="E11:37_1_1_3_1"/>
<font color="Maroon" title="c7">o</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c12">s0</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">a0</font>
 <b>by </b><i><a class="txt" href="unialg_2.html#E1:37_1_1_3"><i><font color="Green" title="E31">A9</font></i></a>, <a class="txt" href="unialg_2.html#E7:37_1_1_3_1"><i><font color="Green" title="E33">A11</font></i></a>, <a class="ref" href="unialg_2.html#D4" target="_self" title="UNIALG_2:def.4">Def4</a></i>;<br/><b>hence </b><a NAME="E12:37_1_1_3_1"/>
<font color="Maroon" title="c7">o</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">s</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">a</font>
 ;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:37_1_1_3"/>
<font color="Maroon" title="c7">o</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">s</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c6">P</font>
 <b>by </b><i><a class="txt" href="unialg_2.html#E5:37_1_1"><i><font color="Green" title="E26">A4</font></i></a>, <a class="ref" href="setfam_1.html#D1" title="SETFAM_1:def.1">SETFAM_1:def 1</a></i>;<br/>


</div><b>end;</b></div>
<b>take </b><font color="Maroon" title="c7">E</font> =  <a href="unialg_2.html#K4" title="UNIALG_2:func.4">UniAlgSetClosed</a> <font color="Maroon" title="c6">P</font>;<br/>

<a NAME="E12:37_1_1"/><i><font color="Green" title="E31">A12</font></i>: 
<font color="Maroon" title="c7">E</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="unialg_1.html#G1" title="UNIALG_1:aggr.1">UAStr</a>(# <font color="Maroon" title="c6">P</font>,<span class="p1">(<span class="default"><a href="unialg_2.html#K3" title="UNIALG_2:func.3">Opers</a> <font color="Maroon" title="c1">U0</font>,<font color="Maroon" title="c6">P</font></span>)</span> #)
 
<b>by </b><i><a class="txt" href="unialg_2.html#E11:37_1_1"><i><font color="Green" title="E30">A8</font></i></a>, <a class="ref" href="unialg_2.html#D9" target="_self" title="UNIALG_2:def.9">Def9</a></i>;<br/>
<a NAME="E13:37_1_1"/>
<font color="Maroon" title="c2">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">A</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><a href="unialg_2.html#K6" title="UNIALG_2:func.6">Constants</a> <font color="Maroon" title="c1">U0</font></span>)</span>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T7" title="XBOOLE_1:th.7">XBOOLE_1:7</a></i>;<br/>
<b>hence </b><a NAME="E14:37_1_1"/>
<font color="Maroon" title="c2">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c7">E</font>
 <b>by </b><i><a class="txt" href="unialg_2.html#E8:37_1_1"><i><font color="Green" title="E28">A6</font></i></a>, <a class="txt" href="unialg_2.html#E12:37_1_1"><i><font color="Green" title="E31">A12</font></i></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></i>;<br/>

<b>let </b><font color="Maroon" title="c8">U1</font> be    <a href="unialg_2.html#M3" title="UNIALG_2:mode.3">SubAlgebra</a> of <font color="Maroon" title="c1">U0</font>;<br/>

<b>assume </b><a NAME="E15:37_1_1"/><i><font color="Green" title="E32">A13</font></i>: 
<font color="Maroon" title="c2">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c8">U1</font>
 ;<br/>

<b>set </b><font color="Maroon" title="c9">u1</font> = the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c8">U1</font>;<br/>
<a NAME="E16:37_1_1"/><i><font color="Green" title="E33">A14</font></i>: 
 <a href="unialg_2.html#K6" title="UNIALG_2:func.6">Constants</a> <font color="Maroon" title="c1">U0</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c8">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" title="c10">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:37_1_1_4"/>
<font color="Maroon" title="c10">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="unialg_2.html#K6" title="UNIALG_2:func.6">Constants</a> <font color="Maroon" title="c1">U0</font>
 ;<br/>

<a NAME="E2:37_1_1_4"/><b>then </b>
<font color="Maroon" title="c10">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <font color="Olive" title="b1">a</font> where <font color="Olive" title="b1">a</font> is   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">U0</font> :  ex <font color="Olive" title="b2">o</font> being  <a href="unialg_2.html#NM5" title="UNIALG_2:NM.5">operation</a> of <font color="Maroon" title="c1">U0</font> st <br/>(  <a href="unialg_1.html#K3" title="UNIALG_1:func.3">arity</a> <font color="Olive" title="b2">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0 &amp; <font color="Olive" title="b1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Olive" title="b2">o</font> ) </span>}</span> 
 
;<br/>
<b>then consider </b><font color="Maroon" title="c11">a</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">U0</font><b> such that </b><br/><a NAME="E4:37_1_1_4"/><i><font color="Green" title="E34">A15</font></i>: 
( <font color="Maroon" title="c11">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">x</font> &amp;  ex <font color="Olive" title="b1">o</font> being  <a href="unialg_2.html#NM5" title="UNIALG_2:NM.5">operation</a> of <font color="Maroon" title="c1">U0</font> st <br/>(  <a href="unialg_1.html#K3" title="UNIALG_1:func.3">arity</a> <font color="Olive" title="b1">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0 &amp; <font color="Maroon" title="c11">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Olive" title="b1">o</font> ) )
 ;<br/>
<b>consider </b><font color="Maroon" title="c12">o0</font> being   <a href="unialg_2.html#NM5" title="UNIALG_2:NM.5">operation</a> of <font color="Maroon" title="c1">U0</font><b> such that </b><br/><a NAME="E6:37_1_1_4"/><i><font color="Green" title="E35">A16</font></i>: 
(  <a href="unialg_1.html#K3" title="UNIALG_1:func.3">arity</a> <font color="Maroon" title="c12">o0</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0 &amp; <font color="Maroon" title="c11">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c12">o0</font> )
 <b>by </b><i><a class="txt" href="unialg_2.html#E4:37_1_1_4"><i><font color="Green" title="E34">A15</font></i></a></i>;<br/>
<b>consider </b><font color="Maroon" title="c13">n</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> <b> such that </b><br/><a NAME="E8:37_1_1_4"/><i><font color="Green" title="E36">A17</font></i>: 
( <font color="Maroon" title="c13">n</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <font color="Maroon" title="c1">U0</font> &amp; the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <font color="Maroon" title="c1">U0</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c13">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">o0</font> )
 <b>by </b><i><a class="ref" href="finseq_2.html#T11" title="FINSEQ_2:th.11">FINSEQ_2:11</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c14">B</font> = the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c8">U1</font> as  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">U0</font> <b>by </b><i><a class="ref" href="unialg_2.html#D8" target="_self" title="UNIALG_2:def.8">Def8</a></i>;<br/>
<a NAME="E10:37_1_1_4"/><i><font color="Green" title="E37">A18</font></i>: 
( the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <font color="Maroon" title="c8">U1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="unialg_2.html#K3" title="UNIALG_2:func.3">Opers</a> <font color="Maroon" title="c1">U0</font>,<font color="Maroon" title="c14">B</font> &amp; <font color="Maroon" title="c14">B</font> is <a href="unialg_2.html#V1" title="UNIALG_2:attr.1">opers_closed</a> )
 
<b>by </b><i><a class="ref" href="unialg_2.html#D8" target="_self" title="UNIALG_2:def.8">Def8</a></i>;<br/>
<a NAME="E11:37_1_1_4"/><i><font color="Green" title="E38">A19</font></i>: 
<font color="Maroon" title="c13">n</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <font color="Maroon" title="c8">U1</font>
 
<b>by </b><i><a class="txt" href="unialg_2.html#E8:37_1_1_4"><i><font color="Green" title="E36">A17</font></i></a>, <a class="ref" href="unialg_2.html#T10" target="_self" title="UNIALG_2:th.10">Th10</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c15">o1</font> = the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <font color="Maroon" title="c8">U1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c13">n</font> as   <a href="unialg_2.html#NM5" title="UNIALG_2:NM.5">operation</a> of <font color="Maroon" title="c8">U1</font> <b>by </b><i><a class="txt" href="unialg_2.html#E9"><i><font color="Green" title="E5">Lm1</font></i></a></i>;<br/>
<a NAME="E13:37_1_1_4"/><i><font color="Green" title="E39">A20</font></i>: 
<font color="Maroon" title="c15">o1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">o0</font> <a href="unialg_2.html#K2" title="UNIALG_2:func.2">/.</a> <font color="Maroon" title="c14">B</font>
 
<b>by </b><i><a class="txt" href="unialg_2.html#E8:37_1_1_4"><i><font color="Green" title="E36">A17</font></i></a>, <a class="txt" href="unialg_2.html#E10:37_1_1_4"><i><font color="Green" title="E37">A18</font></i></a>, <a class="txt" href="unialg_2.html#E11:37_1_1_4"><i><font color="Green" title="E38">A19</font></i></a>, <a class="ref" href="unialg_2.html#D7" target="_self" title="UNIALG_2:def.7">Def7</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c16">y</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E15:37_1_1_4"/><i><font color="Green" title="E40">A21</font></i>: 
( <font color="Maroon" title="c16">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c12">o0</font> &amp; <font color="Maroon" title="c11">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">o0</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c16">y</font> )
 <b>by </b><i><a class="txt" href="unialg_2.html#E6:37_1_1_4"><i><font color="Green" title="E35">A16</font></i></a>, <a class="ref" href="funct_1.html#D5" title="FUNCT_1:def.5">FUNCT_1:def 5</a></i>;<br/>
<a NAME="E16:37_1_1_4"/><i><font color="Green" title="E41">A22</font></i>: 
<font color="Maroon" title="c14">B</font> <a href="unialg_2.html#R2" title="UNIALG_2:pred.2">is_closed_on</a> <font color="Maroon" title="c12">o0</font>
 
<b>by </b><i><a class="txt" href="unialg_2.html#E10:37_1_1_4"><i><font color="Green" title="E37">A18</font></i></a>, <a class="ref" href="unialg_2.html#D5" target="_self" title="UNIALG_2:def.5">Def5</a></i>;<br/>
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c12">o0</font> = 
0 <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">U0</font>
<b>by </b><i><a class="txt" href="unialg_2.html#E6:37_1_1_4"><i><font color="Green" title="E35">A16</font></i></a>, <a class="ref" href="unialg_2.html#T2" target="_self" title="UNIALG_2:th.2">Th2</a></i>
<br/>.= 
<span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K6" title="FINSEQ_1:func.6">&lt;*&gt;</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">U0</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
<b>by </b><i><a class="ref" href="finseq_2.html#T112" title="FINSEQ_2:th.112">FINSEQ_2:112</a></i>
;<br/>
<a NAME="E18:37_1_1_4"/><b>then </b>
<font color="Maroon" title="c16">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K6" title="FINSEQ_1:func.6">&lt;*&gt;</a> <font color="Maroon" title="c14">B</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<b>by </b><i><a class="txt" href="unialg_2.html#E15:37_1_1_4"><i><font color="Green" title="E40">A21</font></i></a></i>;<br/>
<a NAME="E19:37_1_1_4"/><b>then </b>
<font color="Maroon" title="c16">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> 0 <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <font color="Maroon" title="c14">B</font>
 
<b>by </b><i><a class="ref" href="finseq_2.html#T112" title="FINSEQ_2:th.112">FINSEQ_2:112</a></i>;<br/>
<a NAME="E20:37_1_1_4"/><b>then </b>
<font color="Maroon" title="c16">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c12">o0</font></span>)</span> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="unialg_1.html#K3" title="UNIALG_1:func.3">arity</a> <font color="Maroon" title="c12">o0</font></span>)</span> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <font color="Maroon" title="c14">B</font></span>)</span>
 
<b>by </b><i><a class="txt" href="unialg_2.html#E6:37_1_1_4"><i><font color="Green" title="E35">A16</font></i></a>, <a class="txt" href="unialg_2.html#E15:37_1_1_4"><i><font color="Green" title="E40">A21</font></i></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></i>;<br/>
<a NAME="E21:37_1_1_4"/><b>then </b><i><font color="Green" title="E42">A23</font></i>: 
<font color="Maroon" title="c16">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">o0</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="unialg_1.html#K3" title="UNIALG_1:func.3">arity</a> <font color="Maroon" title="c12">o0</font></span>)</span> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <font color="Maroon" title="c14">B</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_1.html#T68" title="FUNCT_1:th.68">FUNCT_1:68</a></i>;<br/>
<a NAME="E22:37_1_1_4"/><b>then </b><i><font color="Green" title="E43">A24</font></i>: 
<font color="Maroon" title="c16">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">o0</font> <a href="unialg_2.html#K2" title="UNIALG_2:func.2">/.</a> <font color="Maroon" title="c14">B</font></span>)</span>
 
<b>by </b><i><a class="txt" href="unialg_2.html#E16:37_1_1_4"><i><font color="Green" title="E41">A22</font></i></a>, <a class="ref" href="unialg_2.html#D6" target="_self" title="UNIALG_2:def.6">Def6</a></i>;<br/>
<i><font color="Green" title="E44">A25</font></i>: <font color="Maroon" title="c15">o1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c16">y</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c12">o0</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="unialg_1.html#K3" title="UNIALG_1:func.3">arity</a> <font color="Maroon" title="c12">o0</font></span>)</span> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <font color="Maroon" title="c14">B</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c16">y</font>
<b>by </b><i><a class="txt" href="unialg_2.html#E13:37_1_1_4"><i><font color="Green" title="E39">A20</font></i></a>, <a class="txt" href="unialg_2.html#E16:37_1_1_4"><i><font color="Green" title="E41">A22</font></i></a>, <a class="ref" href="unialg_2.html#D6" target="_self" title="UNIALG_2:def.6">Def6</a></i>
<br/>.= 
<font color="Maroon" title="c11">a</font>
<b>by </b><i><a class="txt" href="unialg_2.html#E15:37_1_1_4"><i><font color="Green" title="E40">A21</font></i></a>, <a class="txt" href="unialg_2.html#E21:37_1_1_4"><i><font color="Green" title="E42">A23</font></i></a>, <a class="ref" href="funct_1.html#T68" title="FUNCT_1:th.68">FUNCT_1:68</a></i>
;<br/>
<a NAME="E24:37_1_1_4"/>
( <font color="Maroon" title="c15">o1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c16">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c15">o1</font> &amp;  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c15">o1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c8">U1</font> )
 
<b>by </b><i><a class="txt" href="unialg_2.html#E13:37_1_1_4"><i><font color="Green" title="E39">A20</font></i></a>, <a class="txt" href="unialg_2.html#E22:37_1_1_4"><i><font color="Green" title="E43">A24</font></i></a>, <a class="ref" href="funct_1.html#D5" title="FUNCT_1:def.5">FUNCT_1:def 5</a>, <a class="ref" href="relset_1.html#T12" title="RELSET_1:th.12">RELSET_1:12</a></i>;<br/>
<b>hence </b><a NAME="E25:37_1_1_4"/>
<font color="Maroon" title="c10">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c8">U1</font>
 <b>by </b><i><a class="txt" href="unialg_2.html#E4:37_1_1_4"><i><font color="Green" title="E34">A15</font></i></a>, <a class="txt" href="unialg_2.html#E23:37_1_1_4"><i><font color="Green" title="E44">A25</font></i></a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E17:37_1_1"/>
( the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c8">U1</font> is   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">U0</font> &amp; ( for <font color="Olive" title="b1">B</font> being non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">U0</font>  st <font color="Olive" title="b1">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c8">U1</font> holds <br/>( the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <font color="Maroon" title="c8">U1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="unialg_2.html#K3" title="UNIALG_2:func.3">Opers</a> <font color="Maroon" title="c1">U0</font>,<font color="Olive" title="b1">B</font> &amp; <font color="Olive" title="b1">B</font> is <a href="unialg_2.html#V1" title="UNIALG_2:attr.1">opers_closed</a> ) ) )
 
<b>by </b><i><a class="ref" href="unialg_2.html#D8" target="_self" title="UNIALG_2:def.8">Def8</a></i>;<br/>
<a NAME="E18:37_1_1"/><b>then </b>
( the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c8">U1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="zfmisc_1.html#K1" title="ZFMISC_1:func.1">bool</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">U0</font> &amp; ( for <font color="Olive" title="b1">B</font> being non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">U0</font>  st <font color="Olive" title="b1">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c8">U1</font> holds <br/><font color="Olive" title="b1">B</font> is <a href="unialg_2.html#V1" title="UNIALG_2:attr.1">opers_closed</a> ) )
 
;<br/>
<a NAME="E19:37_1_1"/><b>then </b><i><font color="Green" title="E34">A26</font></i>: 
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c8">U1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">X</font>
 
<b>by </b><i><a class="txt" href="unialg_2.html#E2:37_1_1"><i><font color="Green" title="E24">A2</font></i></a>, <a class="txt" href="unialg_2.html#E15:37_1_1"><i><font color="Green" title="E32">A13</font></i></a>, <a class="txt" href="unialg_2.html#E16:37_1_1"><i><font color="Green" title="E33">A14</font></i></a></i>;<br/>
<a NAME="E20:37_1_1"/><b>then </b><i><font color="Green" title="E35">A27</font></i>: 
<font color="Maroon" title="c6">P</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c8">U1</font>
 
<b>by </b><i><a class="ref" href="setfam_1.html#T4" title="SETFAM_1:th.4">SETFAM_1:4</a></i>;<br/>
<b>thus </b><a NAME="E21:37_1_1"/>
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c7">E</font> is   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c8">U1</font>
 <b>by </b><i><a class="txt" href="unialg_2.html#E12:37_1_1"><i><font color="Green" title="E31">A12</font></i></a>, <a class="txt" href="unialg_2.html#E19:37_1_1"><i><font color="Green" title="E34">A26</font></i></a>, <a class="ref" href="setfam_1.html#T4" title="SETFAM_1:th.4">SETFAM_1:4</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="unialg_2.html#D8" target="_self" title="UNIALG_2:def.8">UNIALG_2:def 8</a><br/>

<b>let </b><font color="Maroon" title="c10">B</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c8">U1</font>;<br/>

<b>assume </b><a NAME="E22:37_1_1"/><i><font color="Green" title="E36">A28</font></i>: 
<font color="Maroon" title="c10">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c7">E</font>
 ;<br/>

<b>reconsider </b><font color="Maroon" title="c11">u11</font> = the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c8">U1</font> as  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">U0</font> <b>by </b><i><a class="ref" href="unialg_2.html#D8" target="_self" title="UNIALG_2:def.8">Def8</a></i>;<br/>
<a NAME="E24:37_1_1"/><i><font color="Green" title="E37">A29</font></i>: 
( the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <font color="Maroon" title="c8">U1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="unialg_2.html#K3" title="UNIALG_2:func.3">Opers</a> <font color="Maroon" title="c1">U0</font>,<font color="Maroon" title="c11">u11</font> &amp; <font color="Maroon" title="c11">u11</font> is <a href="unialg_2.html#V1" title="UNIALG_2:attr.1">opers_closed</a> )
 
<b>by </b><i><a class="ref" href="unialg_2.html#D8" target="_self" title="UNIALG_2:def.8">Def8</a></i>;<br/>
<a NAME="E25:37_1_1"/><i><font color="Green" title="E38">A30</font></i>: 
(  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <font color="Maroon" title="c1">U0</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="unialg_2.html#K3" title="UNIALG_2:func.3">Opers</a> <font color="Maroon" title="c1">U0</font>,<font color="Maroon" title="c6">P</font></span>)</span> &amp;  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <font color="Maroon" title="c1">U0</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="unialg_2.html#K3" title="UNIALG_2:func.3">Opers</a> <font color="Maroon" title="c1">U0</font>,<font color="Maroon" title="c11">u11</font></span>)</span> )
 
<b>by </b><i><a class="ref" href="unialg_2.html#D7" target="_self" title="UNIALG_2:def.7">Def7</a></i>;<br/>
<div><i><font color="Green" title="E39">A31</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" title="c12">o1</font> be   <a href="unialg_2.html#NM5" title="UNIALG_2:NM.5">operation</a> of <font color="Maroon" title="c8">U1</font>;<br/><b>consider </b><font color="Maroon" title="c13">n</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> <b> such that </b><br/><a NAME="E2:37_1_1_5"/><i><font color="Green" title="E40">A32</font></i>: 
( <font color="Maroon" title="c13">n</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <font color="Maroon" title="c8">U1</font> &amp; <font color="Maroon" title="c12">o1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <font color="Maroon" title="c8">U1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c13">n</font> )
 <b>by </b><i><a class="ref" href="finseq_2.html#T11" title="FINSEQ_2:th.11">FINSEQ_2:11</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c14">o0</font> = the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <font color="Maroon" title="c1">U0</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c13">n</font> as   <a href="unialg_2.html#NM5" title="UNIALG_2:NM.5">operation</a> of <font color="Maroon" title="c1">U0</font> <b>by </b><i><a class="txt" href="unialg_2.html#E24:37_1_1"><i><font color="Green" title="E37">A29</font></i></a>, <a class="txt" href="unialg_2.html#E25:37_1_1"><i><font color="Green" title="E38">A30</font></i></a>, <a class="txt" href="unialg_2.html#E2:37_1_1_5"><i><font color="Green" title="E40">A32</font></i></a>, <a class="txt" href="unialg_2.html#E9"><i><font color="Green" title="E5">Lm1</font></i></a></i>;<br/><a NAME="E4:37_1_1_5"/><i><font color="Green" title="E41">A33</font></i>: 
 <a href="unialg_1.html#K3" title="UNIALG_1:func.3">arity</a> <font color="Maroon" title="c14">o0</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="unialg_1.html#K3" title="UNIALG_1:func.3">arity</a> <font color="Maroon" title="c12">o1</font>
 <b>by </b><i><a class="txt" href="unialg_2.html#E2:37_1_1_5"><i><font color="Green" title="E40">A32</font></i></a>, <a class="ref" href="unialg_2.html#T9" target="_self" title="UNIALG_2:th.9">Th9</a></i>;<br/><a NAME="E5:37_1_1_5"/><i><font color="Green" title="E42">A34</font></i>: 
<font color="Maroon" title="c11">u11</font> <a href="unialg_2.html#R2" title="UNIALG_2:pred.2">is_closed_on</a> <font color="Maroon" title="c14">o0</font>
 <b>by </b><i><a class="txt" href="unialg_2.html#E24:37_1_1"><i><font color="Green" title="E37">A29</font></i></a>, <a class="ref" href="unialg_2.html#D5" target="_self" title="UNIALG_2:def.5">Def5</a></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" title="c15">s</font> be    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of <font color="Maroon" title="c10">B</font>;<br/><b>assume </b><a NAME="E1:37_1_1_5_1"/><i><font color="Green" title="E43">A35</font></i>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c15">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="unialg_1.html#K3" title="UNIALG_1:func.3">arity</a> <font color="Maroon" title="c12">o1</font>
 ;<br/><b>reconsider </b><font color="Maroon" title="c16">sE</font> = <font color="Maroon" title="c15">s</font> as    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <font color="Maroon" title="c6">P</font> <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a>  <b>by </b><i><a class="txt" href="unialg_2.html#E12:37_1_1"><i><font color="Green" title="E31">A12</font></i></a>, <a class="txt" href="unialg_2.html#E22:37_1_1"><i><font color="Green" title="E36">A28</font></i></a>, <a class="ref" href="finseq_1.html#D11" title="FINSEQ_1:def.11">FINSEQ_1:def 11</a></i>;<br/><a NAME="E3:37_1_1_5_1"/>
<font color="Maroon" title="c15">s</font> is    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of <font color="Maroon" title="c11">u11</font>
 <b>by </b><i><a class="ref" href="finseq_2.html#T27" title="FINSEQ_2:th.27">FINSEQ_2:27</a></i>;<br/><b>then reconsider </b><font color="Maroon" title="c17">s1</font> = <font color="Maroon" title="c15">s</font> as    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <font color="Maroon" title="c11">u11</font> <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a>  <b>by </b><i><a class="ref" href="finseq_1.html#D11" title="FINSEQ_1:def.11">FINSEQ_1:def 11</a></i>;<br/><i><font color="Green" title="E44">A36</font></i>:  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c14">o0</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="unialg_1.html#K3" title="UNIALG_1:func.3">arity</a> <font color="Maroon" title="c14">o0</font></span>)</span> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <font color="Maroon" title="c11">u11</font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c14">o0</font></span>)</span> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="unialg_1.html#K3" title="UNIALG_1:func.3">arity</a> <font color="Maroon" title="c14">o0</font></span>)</span> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <font color="Maroon" title="c11">u11</font></span>)</span>
<b>by </b><i><a class="ref" href="funct_1.html#T68" title="FUNCT_1:th.68">FUNCT_1:68</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="unialg_1.html#K3" title="UNIALG_1:func.3">arity</a> <font color="Maroon" title="c14">o0</font></span>)</span> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">U0</font></span>)</span> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="unialg_1.html#K3" title="UNIALG_1:func.3">arity</a> <font color="Maroon" title="c14">o0</font></span>)</span> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <font color="Maroon" title="c11">u11</font></span>)</span>
<b>by </b><i><a class="ref" href="unialg_2.html#T2" target="_self" title="UNIALG_2:th.2">Th2</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="unialg_1.html#K3" title="UNIALG_1:func.3">arity</a> <font color="Maroon" title="c14">o0</font></span>)</span> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <font color="Maroon" title="c11">u11</font>
<b>by </b><i><a class="ref" href="unialg_2.html#T1" target="_self" title="UNIALG_2:th.1">Th1</a></i>
;<br/><a NAME="E6:37_1_1_5_1"/>
<font color="Maroon" title="c17">s1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <font color="Olive" title="b1">q</font> where <font color="Olive" title="b1">q</font> is    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <font color="Maroon" title="c11">u11</font> <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a>  :  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b1">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="unialg_1.html#K3" title="UNIALG_1:func.3">arity</a> <font color="Maroon" title="c14">o0</font> </span>}</span> 
 <b>by </b><i><a class="txt" href="unialg_2.html#E4:37_1_1_5"><i><font color="Green" title="E41">A33</font></i></a>, <a class="txt" href="unialg_2.html#E1:37_1_1_5_1"><i><font color="Green" title="E43">A35</font></i></a></i>;<br/><a NAME="E7:37_1_1_5_1"/><b>then </b><i><font color="Green" title="E45">A37</font></i>: 
<font color="Maroon" title="c17">s1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c14">o0</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="unialg_1.html#K3" title="UNIALG_1:func.3">arity</a> <font color="Maroon" title="c14">o0</font></span>)</span> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <font color="Maroon" title="c11">u11</font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="unialg_2.html#E5:37_1_1_5_1"><i><font color="Green" title="E44">A36</font></i></a>, <a class="ref" href="finseq_2.html#D4" title="FINSEQ_2:def.4">FINSEQ_2:def 4</a></i>;<br/><a NAME="E8:37_1_1_5_1"/><i><font color="Green" title="E46">A38</font></i>: 
<font color="Maroon" title="c6">P</font> <a href="unialg_2.html#R2" title="UNIALG_2:pred.2">is_closed_on</a> <font color="Maroon" title="c14">o0</font>
 <b>by </b><i><a class="txt" href="unialg_2.html#E11:37_1_1"><i><font color="Green" title="E30">A8</font></i></a>, <a class="ref" href="unialg_2.html#D5" target="_self" title="UNIALG_2:def.5">Def5</a></i>;<br/><font color="Maroon" title="c12">o1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c15">s</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c14">o0</font> <a href="unialg_2.html#K2" title="UNIALG_2:func.2">/.</a> <font color="Maroon" title="c11">u11</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c17">s1</font>
<b>by </b><i><a class="txt" href="unialg_2.html#E24:37_1_1"><i><font color="Green" title="E37">A29</font></i></a>, <a class="txt" href="unialg_2.html#E2:37_1_1_5"><i><font color="Green" title="E40">A32</font></i></a>, <a class="ref" href="unialg_2.html#D7" target="_self" title="UNIALG_2:def.7">Def7</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c14">o0</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="unialg_1.html#K3" title="UNIALG_1:func.3">arity</a> <font color="Maroon" title="c14">o0</font></span>)</span> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <font color="Maroon" title="c11">u11</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c17">s1</font>
<b>by </b><i><a class="txt" href="unialg_2.html#E5:37_1_1_5"><i><font color="Green" title="E42">A34</font></i></a>, <a class="ref" href="unialg_2.html#D6" target="_self" title="UNIALG_2:def.6">Def6</a></i>
<br/>.= 
<font color="Maroon" title="c14">o0</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c16">sE</font>
<b>by </b><i><a class="txt" href="unialg_2.html#E7:37_1_1_5_1"><i><font color="Green" title="E45">A37</font></i></a>, <a class="ref" href="funct_1.html#T68" title="FUNCT_1:th.68">FUNCT_1:68</a></i>
;<br/><b>hence </b><a NAME="E10:37_1_1_5_1"/>
<font color="Maroon" title="c12">o1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c15">s</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">B</font>
 <b>by </b><i><a class="txt" href="unialg_2.html#E12:37_1_1"><i><font color="Green" title="E31">A12</font></i></a>, <a class="txt" href="unialg_2.html#E22:37_1_1"><i><font color="Green" title="E36">A28</font></i></a>, <a class="txt" href="unialg_2.html#E4:37_1_1_5"><i><font color="Green" title="E41">A33</font></i></a>, <a class="txt" href="unialg_2.html#E1:37_1_1_5_1"><i><font color="Green" title="E43">A35</font></i></a>, <a class="txt" href="unialg_2.html#E8:37_1_1_5_1"><i><font color="Green" title="E46">A38</font></i></a>, <a class="ref" href="unialg_2.html#D4" target="_self" title="UNIALG_2:def.4">Def4</a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E7:37_1_1_5"/>
<font color="Maroon" title="c10">B</font> <a href="unialg_2.html#R2" title="UNIALG_2:pred.2">is_closed_on</a> <font color="Maroon" title="c12">o1</font>
 <b>by </b><i><a class="ref" href="unialg_2.html#D4" target="_self" title="UNIALG_2:def.4">Def4</a></i>;<br/></div><b>end;</b></div>
<a NAME="E27:37_1_1"/><i><font color="Green" title="E40">A39</font></i>: 
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="unialg_2.html#K3" title="UNIALG_2:func.3">Opers</a> <font color="Maroon" title="c8">U1</font>,<font color="Maroon" title="c10">B</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <font color="Maroon" title="c8">U1</font>
 
<b>by </b><i><a class="ref" href="unialg_2.html#D7" target="_self" title="UNIALG_2:def.7">Def7</a></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" title="c12">n</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/><b>assume </b><a NAME="E1:37_1_1_6"/><i><font color="Green" title="E41">A40</font></i>: 
<font color="Maroon" title="c12">n</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <font color="Maroon" title="c1">U0</font>
 ;<br/><b>then reconsider </b><font color="Maroon" title="c13">o0</font> = the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <font color="Maroon" title="c1">U0</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c12">n</font> as   <a href="unialg_2.html#NM5" title="UNIALG_2:NM.5">operation</a> of <font color="Maroon" title="c1">U0</font> <b>by </b><i><a class="txt" href="unialg_2.html#E9"><i><font color="Green" title="E5">Lm1</font></i></a></i>;<br/><b>reconsider </b><font color="Maroon" title="c14">o1</font> = the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <font color="Maroon" title="c8">U1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c12">n</font> as   <a href="unialg_2.html#NM5" title="UNIALG_2:NM.5">operation</a> of <font color="Maroon" title="c8">U1</font> <b>by </b><i><a class="txt" href="unialg_2.html#E24:37_1_1"><i><font color="Green" title="E37">A29</font></i></a>, <a class="txt" href="unialg_2.html#E25:37_1_1"><i><font color="Green" title="E38">A30</font></i></a>, <a class="txt" href="unialg_2.html#E1:37_1_1_6"><i><font color="Green" title="E41">A40</font></i></a>, <a class="txt" href="unialg_2.html#E9"><i><font color="Green" title="E5">Lm1</font></i></a></i>;<br/><a NAME="E4:37_1_1_6"/><i><font color="Green" title="E42">A41</font></i>: 
<font color="Maroon" title="c11">u11</font> <a href="unialg_2.html#R2" title="UNIALG_2:pred.2">is_closed_on</a> <font color="Maroon" title="c13">o0</font>
 <b>by </b><i><a class="txt" href="unialg_2.html#E24:37_1_1"><i><font color="Green" title="E37">A29</font></i></a>, <a class="ref" href="unialg_2.html#D5" target="_self" title="UNIALG_2:def.5">Def5</a></i>;<br/><a NAME="E5:37_1_1_6"/><i><font color="Green" title="E43">A42</font></i>: 
<font color="Maroon" title="c10">B</font> <a href="unialg_2.html#R2" title="UNIALG_2:pred.2">is_closed_on</a> <font color="Maroon" title="c14">o1</font>
 <b>by </b><i><a class="txt" href="unialg_2.html#E26:37_1_1"><i><font color="Green" title="E39">A31</font></i></a></i>;<br/><a NAME="E6:37_1_1_6"/><i><font color="Green" title="E44">A43</font></i>: 
<font color="Maroon" title="c6">P</font> <a href="unialg_2.html#R2" title="UNIALG_2:pred.2">is_closed_on</a> <font color="Maroon" title="c13">o0</font>
 <b>by </b><i><a class="txt" href="unialg_2.html#E11:37_1_1"><i><font color="Green" title="E30">A8</font></i></a>, <a class="ref" href="unialg_2.html#D5" target="_self" title="UNIALG_2:def.5">Def5</a></i>;<br/><b>thus </b>the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <font color="Maroon" title="c7">E</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c12">n</font> = 
<font color="Maroon" title="c13">o0</font> <a href="unialg_2.html#K2" title="UNIALG_2:func.2">/.</a> <font color="Maroon" title="c6">P</font>
<b>by </b><i><a class="txt" href="unialg_2.html#E12:37_1_1"><i><font color="Green" title="E31">A12</font></i></a>, <a class="txt" href="unialg_2.html#E25:37_1_1"><i><font color="Green" title="E38">A30</font></i></a>, <a class="txt" href="unialg_2.html#E1:37_1_1_6"><i><font color="Green" title="E41">A40</font></i></a>, <a class="ref" href="unialg_2.html#D7" target="_self" title="UNIALG_2:def.7">Def7</a></i>
<br/>.= 
<font color="Maroon" title="c13">o0</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="unialg_1.html#K3" title="UNIALG_1:func.3">arity</a> <font color="Maroon" title="c13">o0</font></span>)</span> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <font color="Maroon" title="c6">P</font></span>)</span>
<b>by </b><i><a class="txt" href="unialg_2.html#E6:37_1_1_6"><i><font color="Green" title="E44">A43</font></i></a>, <a class="ref" href="unialg_2.html#D6" target="_self" title="UNIALG_2:def.6">Def6</a></i>
<br/>.= 
<font color="Maroon" title="c13">o0</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</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" title="UNIALG_1:func.3">arity</a> <font color="Maroon" title="c13">o0</font></span>)</span> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <font color="Maroon" title="c11">u11</font></span>)</span> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="unialg_1.html#K3" title="UNIALG_1:func.3">arity</a> <font color="Maroon" title="c13">o0</font></span>)</span> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <font color="Maroon" title="c6">P</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="unialg_2.html#E20:37_1_1"><i><font color="Green" title="E35">A27</font></i></a>, <a class="ref" href="unialg_2.html#T1" target="_self" title="UNIALG_2:th.1">Th1</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c13">o0</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="unialg_1.html#K3" title="UNIALG_1:func.3">arity</a> <font color="Maroon" title="c13">o0</font></span>)</span> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <font color="Maroon" title="c11">u11</font></span>)</span></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="unialg_1.html#K3" title="UNIALG_1:func.3">arity</a> <font color="Maroon" title="c13">o0</font></span>)</span> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <font color="Maroon" title="c6">P</font></span>)</span>
<b>by </b><i><a class="ref" href="relat_1.html#T100" title="RELAT_1:th.100">RELAT_1:100</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c13">o0</font> <a href="unialg_2.html#K2" title="UNIALG_2:func.2">/.</a> <font color="Maroon" title="c11">u11</font></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="unialg_1.html#K3" title="UNIALG_1:func.3">arity</a> <font color="Maroon" title="c13">o0</font></span>)</span> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <font color="Maroon" title="c6">P</font></span>)</span>
<b>by </b><i><a class="txt" href="unialg_2.html#E4:37_1_1_6"><i><font color="Green" title="E42">A41</font></i></a>, <a class="ref" href="unialg_2.html#D6" target="_self" title="UNIALG_2:def.6">Def6</a></i>
<br/>.= 
<font color="Maroon" title="c14">o1</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="unialg_1.html#K3" title="UNIALG_1:func.3">arity</a> <font color="Maroon" title="c13">o0</font></span>)</span> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <font color="Maroon" title="c6">P</font></span>)</span>
<b>by </b><i><a class="txt" href="unialg_2.html#E24:37_1_1"><i><font color="Green" title="E37">A29</font></i></a>, <a class="txt" href="unialg_2.html#E25:37_1_1"><i><font color="Green" title="E38">A30</font></i></a>, <a class="txt" href="unialg_2.html#E1:37_1_1_6"><i><font color="Green" title="E41">A40</font></i></a>, <a class="ref" href="unialg_2.html#D7" target="_self" title="UNIALG_2:def.7">Def7</a></i>
<br/>.= 
<font color="Maroon" title="c14">o1</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="unialg_1.html#K3" title="UNIALG_1:func.3">arity</a> <font color="Maroon" title="c14">o1</font></span>)</span> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <font color="Maroon" title="c10">B</font></span>)</span>
<b>by </b><i><a class="txt" href="unialg_2.html#E12:37_1_1"><i><font color="Green" title="E31">A12</font></i></a>, <a class="txt" href="unialg_2.html#E22:37_1_1"><i><font color="Green" title="E36">A28</font></i></a>, <a class="txt" href="unialg_2.html#E24:37_1_1"><i><font color="Green" title="E37">A29</font></i></a>, <a class="txt" href="unialg_2.html#E25:37_1_1"><i><font color="Green" title="E38">A30</font></i></a>, <a class="txt" href="unialg_2.html#E1:37_1_1_6"><i><font color="Green" title="E41">A40</font></i></a>, <a class="ref" href="unialg_2.html#T9" target="_self" title="UNIALG_2:th.9">Th9</a></i>
<br/>.= 
<font color="Maroon" title="c14">o1</font> <a href="unialg_2.html#K2" title="UNIALG_2:func.2">/.</a> <font color="Maroon" title="c10">B</font>
<b>by </b><i><a class="txt" href="unialg_2.html#E5:37_1_1_6"><i><font color="Green" title="E43">A42</font></i></a>, <a class="ref" href="unialg_2.html#D6" target="_self" title="UNIALG_2:def.6">Def6</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="unialg_2.html#K3" title="UNIALG_2:func.3">Opers</a> <font color="Maroon" title="c8">U1</font>,<font color="Maroon" title="c10">B</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c12">n</font>
<b>by </b><i><a class="txt" href="unialg_2.html#E24:37_1_1"><i><font color="Green" title="E37">A29</font></i></a>, <a class="txt" href="unialg_2.html#E25:37_1_1"><i><font color="Green" title="E38">A30</font></i></a>, <a class="txt" href="unialg_2.html#E27:37_1_1"><i><font color="Green" title="E40">A39</font></i></a>, <a class="txt" href="unialg_2.html#E1:37_1_1_6"><i><font color="Green" title="E41">A40</font></i></a>, <a class="ref" href="unialg_2.html#D7" target="_self" title="UNIALG_2:def.7">Def7</a></i>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E29:37_1_1"/>
( the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <font color="Maroon" title="c7">E</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="unialg_2.html#K3" title="UNIALG_2:func.3">Opers</a> <font color="Maroon" title="c8">U1</font>,<font color="Maroon" title="c10">B</font> &amp; <font color="Maroon" title="c10">B</font> is <a href="unialg_2.html#V1" title="UNIALG_2:attr.1">opers_closed</a> )
 <b>by </b><i><a class="txt" href="unialg_2.html#E12:37_1_1"><i><font color="Green" title="E31">A12</font></i></a>, <a class="txt" href="unialg_2.html#E24:37_1_1"><i><font color="Green" title="E37">A29</font></i></a>, <a class="txt" href="unialg_2.html#E25:37_1_1"><i><font color="Green" title="E38">A30</font></i></a>, <a class="txt" href="unialg_2.html#E26:37_1_1"><i><font color="Green" title="E39">A31</font></i></a>, <a class="txt" href="unialg_2.html#E27:37_1_1"><i><font color="Green" title="E40">A39</font></i></a>, <a class="ref" href="unialg_2.html#D5" target="_self" title="UNIALG_2:def.5">Def5</a>, <a class="ref" href="finseq_1.html#T17" title="FINSEQ_1:th.17">FINSEQ_1:17</a></i>;<br/>


</div>
