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<b>let </b><font color="Maroon" title="c1">U1</font>, <font color="Maroon" title="c2">U2</font>, <font color="Maroon" title="c3">U3</font>, <font color="Maroon" title="c4">U4</font> be   <a href="unialg_1.html#NM2" title="UNIALG_1:NM.2">Universal_Algebra</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">U1</font> is    <a href="unialg_2.html#M3" title="UNIALG_2:mode.3">SubAlgebra</a> of <font color="Maroon" title="c2">U2</font> &amp; <font color="Maroon" title="c3">U3</font> is    <a href="unialg_2.html#M3" title="UNIALG_2:mode.3">SubAlgebra</a> of <font color="Maroon" title="c4">U4</font> &amp; <font color="Maroon" title="c2">U2</font>,<font color="Maroon" title="c4">U4</font> <a href="unialg_2.html#R1" title="UNIALG_2:pred.1">are_similar</a>  implies <span class="p1"><a href="pralg_1.html#K5" title="PRALG_1:func.5">[:</a><span class="default"><font color="Maroon" title="c1">U1</font>,<font color="Maroon" title="c3">U3</font></span><a href="pralg_1.html#K5" title="PRALG_1:func.5">:]</a></span> is    <a href="unialg_2.html#M3" title="UNIALG_2:mode.3">SubAlgebra</a> of <span class="p1"><a href="pralg_1.html#K5" title="PRALG_1:func.5">[:</a><span class="default"><font color="Maroon" title="c2">U2</font>,<font color="Maroon" title="c4">U4</font></span><a href="pralg_1.html#K5" title="PRALG_1:func.5">:]</a></span> )</span><br/>

<b>assume </b><a NAME="E1:13"/><i><font color="Green" title="E10">A1</font></i>: 
( <font color="Maroon" title="c1">U1</font> is    <a href="unialg_2.html#M3" title="UNIALG_2:mode.3">SubAlgebra</a> of <font color="Maroon" title="c2">U2</font> &amp; <font color="Maroon" title="c3">U3</font> is    <a href="unialg_2.html#M3" title="UNIALG_2:mode.3">SubAlgebra</a> of <font color="Maroon" title="c4">U4</font> &amp; <font color="Maroon" title="c2">U2</font>,<font color="Maroon" title="c4">U4</font> <a href="unialg_2.html#R1" title="UNIALG_2:pred.1">are_similar</a>  )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1"><a href="pralg_1.html#K5" title="PRALG_1:func.5">[:</a><span class="default"><font color="Maroon" title="c1">U1</font>,<font color="Maroon" title="c3">U3</font></span><a href="pralg_1.html#K5" title="PRALG_1:func.5">:]</a></span> is    <a href="unialg_2.html#M3" title="UNIALG_2:mode.3">SubAlgebra</a> of <span class="p1"><a href="pralg_1.html#K5" title="PRALG_1:func.5">[:</a><span class="default"><font color="Maroon" title="c2">U2</font>,<font color="Maroon" title="c4">U4</font></span><a href="pralg_1.html#K5" title="PRALG_1:func.5">:]</a></span></span><br/>

<a NAME="E2:13"/><b>then </b><i><font color="Green" title="E11">A2</font></i>: 
( <font color="Maroon" title="c1">U1</font>,<font color="Maroon" title="c2">U2</font> <a href="unialg_2.html#R1" title="UNIALG_2:pred.1">are_similar</a>  &amp; <font color="Maroon" title="c3">U3</font>,<font color="Maroon" title="c4">U4</font> <a href="unialg_2.html#R1" title="UNIALG_2:pred.1">are_similar</a>  )
 
<b>by </b><i><a class="ref" href="unialg_2.html#T16" title="UNIALG_2:th.16">UNIALG_2:16</a></i>;<br/>
<a NAME="E3:13"/><b>then </b><i><font color="Green" title="E12">A3</font></i>: 
<font color="Maroon" title="c1">U1</font>,<font color="Maroon" title="c4">U4</font> <a href="unialg_2.html#R1" title="UNIALG_2:pred.1">are_similar</a> 
 
<b>by </b><i><a class="txt" href="#E1:13"><i><font color="Green" title="E10">A1</font></i></a>, <a class="ref" href="unialg_2.html#T4" title="UNIALG_2:th.4">UNIALG_2:4</a></i>;<br/>
<a NAME="E4:13"/><b>then </b><i><font color="Green" title="E13">A4</font></i>: 
<font color="Maroon" title="c1">U1</font>,<font color="Maroon" title="c3">U3</font> <a href="unialg_2.html#R1" title="UNIALG_2:pred.1">are_similar</a> 
 
<b>by </b><i><a class="txt" href="#E2:13"><i><font color="Green" title="E11">A2</font></i></a>, <a class="ref" href="unialg_2.html#T4" title="UNIALG_2:th.4">UNIALG_2:4</a></i>;<br/>
<a NAME="E5:13"/><i><font color="Green" title="E14">A5</font></i>: 
( <span class="p1"><a href="pralg_1.html#K5" title="PRALG_1:func.5">[:</a><span class="default"><font color="Maroon" title="c1">U1</font>,<font color="Maroon" title="c3">U3</font></span><a href="pralg_1.html#K5" title="PRALG_1:func.5">:]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="unialg_1.html#G1" title="UNIALG_1:aggr.1">UAStr</a>(# <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">U1</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">U3</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>,<span class="p1">(<span class="default"><a href="pralg_1.html#K4" title="PRALG_1:func.4">Opers</a> <font color="Maroon" title="c1">U1</font>,<font color="Maroon" title="c3">U3</font></span>)</span> #) &amp; <span class="p1"><a href="pralg_1.html#K5" title="PRALG_1:func.5">[:</a><span class="default"><font color="Maroon" title="c2">U2</font>,<font color="Maroon" title="c4">U4</font></span><a href="pralg_1.html#K5" title="PRALG_1:func.5">:]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="unialg_1.html#G1" title="UNIALG_1:aggr.1">UAStr</a>(# <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">U2</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c4">U4</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>,<span class="p1">(<span class="default"><a href="pralg_1.html#K4" title="PRALG_1:func.4">Opers</a> <font color="Maroon" title="c2">U2</font>,<font color="Maroon" title="c4">U4</font></span>)</span> #) )
 
<b>by </b><i><a class="txt" href="#E2:13"><i><font color="Green" title="E11">A2</font></i></a>, <a class="txt" href="#E3:13"><i><font color="Green" title="E12">A3</font></i></a>, <a class="ref" href="pralg_1.html#D5" target="_self" title="PRALG_1:def.5">Def5</a>, <a class="ref" href="unialg_2.html#T4" title="UNIALG_2:th.4">UNIALG_2:4</a></i>;<br/>
<a NAME="E6:13"/><i><font color="Green" title="E15">A6</font></i>: 
( the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">U1</font> is   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c2">U2</font> &amp; the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">U3</font> is   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c4">U4</font> )
 
<b>by </b><i><a class="txt" href="#E1:13"><i><font color="Green" title="E10">A1</font></i></a>, <a class="ref" href="unialg_2.html#D8" title="UNIALG_2:def.8">UNIALG_2:def 8</a></i>;<br/>
<a NAME="E7:13"/><b>then </b><i><font color="Green" title="E16">A7</font></i>: 
<span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">U1</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">U3</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">U2</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c4">U4</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 
<b>by </b><i><a class="ref" href="zfmisc_1.html#T119" title="ZFMISC_1:th.119">ZFMISC_1:119</a></i>;<br/>
<b>thus </b><a NAME="E8:13"/>
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1"><a href="pralg_1.html#K5" title="PRALG_1:func.5">[:</a><span class="default"><font color="Maroon" title="c1">U1</font>,<font color="Maroon" title="c3">U3</font></span><a href="pralg_1.html#K5" title="PRALG_1:func.5">:]</a></span> is   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1"><a href="pralg_1.html#K5" title="PRALG_1:func.5">[:</a><span class="default"><font color="Maroon" title="c2">U2</font>,<font color="Maroon" title="c4">U4</font></span><a href="pralg_1.html#K5" title="PRALG_1:func.5">:]</a></span>
 <b>by </b><i><a class="txt" href="#E5:13"><i><font color="Green" title="E14">A5</font></i></a>, <a class="txt" href="#E6:13"><i><font color="Green" title="E15">A6</font></i></a>, <a class="ref" href="zfmisc_1.html#T119" title="ZFMISC_1:th.119">ZFMISC_1:119</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="unialg_2.html#D8" title="UNIALG_2:def.8">UNIALG_2:def 8</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive">b<sub>1</sub></font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <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 <span class="p1"><a href="pralg_1.html#K5" title="PRALG_1:func.5">[:</a><span class="default"><font color="Maroon" title="c2">U2</font>,<font color="Maroon" title="c4">U4</font></span><a href="pralg_1.html#K5" title="PRALG_1:func.5">:]</a></span>  holds <br/>(  not <font color="Olive">b<sub>1</sub></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 <span class="p1"><a href="pralg_1.html#K5" title="PRALG_1:func.5">[:</a><span class="default"><font color="Maroon" title="c1">U1</font>,<font color="Maroon" title="c3">U3</font></span><a href="pralg_1.html#K5" title="PRALG_1:func.5">:]</a></span> or ( the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <span class="p1"><a href="pralg_1.html#K5" title="PRALG_1:func.5">[:</a><span class="default"><font color="Maroon" title="c1">U1</font>,<font color="Maroon" title="c3">U3</font></span><a href="pralg_1.html#K5" title="PRALG_1:func.5">:]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="unialg_2.html#K3" title="UNIALG_2:func.3">Opers</a> <span class="p1"><a href="pralg_1.html#K5" title="PRALG_1:func.5">[:</a><span class="default"><font color="Maroon" title="c2">U2</font>,<font color="Maroon" title="c4">U4</font></span><a href="pralg_1.html#K5" title="PRALG_1:func.5">:]</a></span>,<font color="Olive">b<sub>1</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> is <a href="unialg_2.html#V1" title="UNIALG_2:attr.1">opers_closed</a> ) )</span><br/>

<b>let </b><font color="Maroon" title="c5">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 <span class="p1"><a href="pralg_1.html#K5" title="PRALG_1:func.5">[:</a><span class="default"><font color="Maroon" title="c2">U2</font>,<font color="Maroon" title="c4">U4</font></span><a href="pralg_1.html#K5" title="PRALG_1:func.5">:]</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  not <font color="Maroon" title="c5">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 <span class="p1"><a href="pralg_1.html#K5" title="PRALG_1:func.5">[:</a><span class="default"><font color="Maroon" title="c1">U1</font>,<font color="Maroon" title="c3">U3</font></span><a href="pralg_1.html#K5" title="PRALG_1:func.5">:]</a></span> or ( the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <span class="p1"><a href="pralg_1.html#K5" title="PRALG_1:func.5">[:</a><span class="default"><font color="Maroon" title="c1">U1</font>,<font color="Maroon" title="c3">U3</font></span><a href="pralg_1.html#K5" title="PRALG_1:func.5">:]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="unialg_2.html#K3" title="UNIALG_2:func.3">Opers</a> <span class="p1"><a href="pralg_1.html#K5" title="PRALG_1:func.5">[:</a><span class="default"><font color="Maroon" title="c2">U2</font>,<font color="Maroon" title="c4">U4</font></span><a href="pralg_1.html#K5" title="PRALG_1:func.5">:]</a></span>,<font color="Maroon" title="c5">B</font> &amp; <font color="Maroon" title="c5">B</font> is <a href="unialg_2.html#V1" title="UNIALG_2:attr.1">opers_closed</a> ) )</span><br/>

<b>assume </b><a NAME="E9:13"/><i><font color="Green" title="E17">A8</font></i>: 
<font color="Maroon" title="c5">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 <span class="p1"><a href="pralg_1.html#K5" title="PRALG_1:func.5">[:</a><span class="default"><font color="Maroon" title="c1">U1</font>,<font color="Maroon" title="c3">U3</font></span><a href="pralg_1.html#K5" title="PRALG_1:func.5">:]</a></span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <span class="p1"><a href="pralg_1.html#K5" title="PRALG_1:func.5">[:</a><span class="default"><font color="Maroon" title="c1">U1</font>,<font color="Maroon" title="c3">U3</font></span><a href="pralg_1.html#K5" title="PRALG_1:func.5">:]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="unialg_2.html#K3" title="UNIALG_2:func.3">Opers</a> <span class="p1"><a href="pralg_1.html#K5" title="PRALG_1:func.5">[:</a><span class="default"><font color="Maroon" title="c2">U2</font>,<font color="Maroon" title="c4">U4</font></span><a href="pralg_1.html#K5" title="PRALG_1:func.5">:]</a></span>,<font color="Maroon" title="c5">B</font> &amp; <font color="Maroon" title="c5">B</font> is <a href="unialg_2.html#V1" title="UNIALG_2:attr.1">opers_closed</a> )</span><br/>

<b>reconsider </b><font color="Maroon" title="c6">B1</font> = the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">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="c2">U2</font> <b>by </b><i><a class="txt" href="#E1:13"><i><font color="Green" title="E10">A1</font></i></a>, <a class="ref" href="unialg_2.html#D8" title="UNIALG_2:def.8">UNIALG_2:def 8</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c7">B3</font> = the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">U3</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="c4">U4</font> <b>by </b><i><a class="txt" href="#E1:13"><i><font color="Green" title="E10">A1</font></i></a>, <a class="ref" href="unialg_2.html#D8" title="UNIALG_2:def.8">UNIALG_2:def 8</a></i>;<br/>
<a NAME="E12:13"/><i><font color="Green" title="E18">A9</font></i>: 
( <font color="Maroon" title="c6">B1</font> is <a href="unialg_2.html#V1" title="UNIALG_2:attr.1">opers_closed</a> &amp; <font color="Maroon" title="c7">B3</font> is <a href="unialg_2.html#V1" title="UNIALG_2:attr.1">opers_closed</a> )
 
<b>by </b><i><a class="txt" href="#E1:13"><i><font color="Green" title="E10">A1</font></i></a>, <a class="ref" href="unialg_2.html#D8" title="UNIALG_2:def.8">UNIALG_2:def 8</a></i>;<br/>
<a NAME="E13:13"/><i><font color="Green" title="E19">A10</font></i>: 
for <font color="Olive" title="b1">o</font> being  <a href="unialg_2.html#NM5" title="UNIALG_2:NM.5">operation</a> of <span class="p1"><a href="pralg_1.html#K5" title="PRALG_1:func.5">[:</a><span class="default"><font color="Maroon" title="c2">U2</font>,<font color="Maroon" title="c4">U4</font></span><a href="pralg_1.html#K5" title="PRALG_1:func.5">:]</a></span> holds  <font color="Maroon" title="c5">B</font> <a href="unialg_2.html#R2" title="UNIALG_2:pred.2">is_closed_on</a> <font color="Olive" title="b1">o</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c8">o</font> be   <a href="unialg_2.html#NM5" title="UNIALG_2:NM.5">operation</a> of <span class="p1"><a href="pralg_1.html#K5" title="PRALG_1:func.5">[:</a><span class="default"><font color="Maroon" title="c2">U2</font>,<font color="Maroon" title="c4">U4</font></span><a href="pralg_1.html#K5" title="PRALG_1:func.5">:]</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c5">B</font> <a href="unialg_2.html#R2" title="UNIALG_2:pred.2">is_closed_on</a> <font color="Maroon" title="c8">o</font></span><br/><b>let </b><font color="Maroon" title="c9">s</font> be    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of <font color="Maroon" title="c5">B</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="unialg_2.html#D4" title="UNIALG_2:def.4">UNIALG_2:def 4</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  not  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c9">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="c8">o</font> or <font color="Maroon" title="c8">o</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">s</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">B</font> )</span><br/>



<b>assume </b><a NAME="E1:13_1"/><i><font color="Green" title="E20">A11</font></i>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c9">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="c8">o</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c8">o</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">s</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">B</font></span><br/>

<b>reconsider </b><font color="Maroon" title="c10">s0</font> = <font color="Maroon" title="c9">s</font> as    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">U1</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">U3</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a>  <b>by </b><i><a class="txt" href="#E5:13"><i><font color="Green" title="E14">A5</font></i></a>, <a class="txt" href="#E9:13"><i><font color="Green" title="E17">A8</font></i></a>, <a class="ref" href="finseq_1.html#D11" title="FINSEQ_1:def.11">FINSEQ_1:def 11</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c11">n</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a><b> such that </b><br/><a NAME="E4:13_1"/><i><font color="Green" title="E21">A12</font></i>: 
( <font color="Maroon" title="c11">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 <span class="p1"><a href="pralg_1.html#K5" title="PRALG_1:func.5">[:</a><span class="default"><font color="Maroon" title="c2">U2</font>,<font color="Maroon" title="c4">U4</font></span><a href="pralg_1.html#K5" title="PRALG_1:func.5">:]</a></span> &amp; the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <span class="p1"><a href="pralg_1.html#K5" title="PRALG_1:func.5">[:</a><span class="default"><font color="Maroon" title="c2">U2</font>,<font color="Maroon" title="c4">U4</font></span><a href="pralg_1.html#K5" title="PRALG_1:func.5">:]</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">o</font> )
 <b>by </b><i><a class="ref" href="finseq_2.html#T11" title="FINSEQ_2:th.11">FINSEQ_2:11</a></i>;<br/>
<a NAME="E5:13_1"/><i><font color="Green" title="E22">A13</font></i>: 
( <font color="Maroon" title="c11">n</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <span class="p2"><a href="pralg_1.html#K5" title="PRALG_1:func.5">[:</a><span class="default"><font color="Maroon" title="c2">U2</font>,<font color="Maroon" title="c4">U4</font></span><a href="pralg_1.html#K5" title="PRALG_1:func.5">:]</a></span></span>)</span> &amp; the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <span class="p1"><a href="pralg_1.html#K5" title="PRALG_1:func.5">[:</a><span class="default"><font color="Maroon" title="c2">U2</font>,<font color="Maroon" title="c4">U4</font></span><a href="pralg_1.html#K5" title="PRALG_1:func.5">:]</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">o</font> )
 
<b>by </b><i><a class="txt" href="#E4:13_1"><i><font color="Green" title="E21">A12</font></i></a>, <a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a></i>;<br/>
<a NAME="E6:13_1"/><i><font color="Green" title="E23">A14</font></i>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <span class="p1"><a href="pralg_1.html#K5" title="PRALG_1:func.5">[:</a><span class="default"><font color="Maroon" title="c2">U2</font>,<font color="Maroon" title="c4">U4</font></span><a href="pralg_1.html#K5" title="PRALG_1:func.5">:]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <font color="Maroon" title="c2">U2</font>
 
<b>by </b><i><a class="txt" href="#E1:13"><i><font color="Green" title="E10">A1</font></i></a>, <a class="txt" href="#E5:13"><i><font color="Green" title="E14">A5</font></i></a>, <a class="ref" href="pralg_1.html#D4" target="_self" title="PRALG_1:def.4">Def4</a></i>;<br/>
<a NAME="E7:13_1"/><b>then </b><i><font color="Green" title="E24">A15</font></i>: 
<font color="Maroon" title="c11">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="c2">U2</font>
 
<b>by </b><i><a class="txt" href="#E5:13_1"><i><font color="Green" title="E22">A13</font></i></a>, <a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c12">o2</font> = the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <font color="Maroon" title="c2">U2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">n</font> as   <a href="unialg_2.html#NM5" title="UNIALG_2:NM.5">operation</a> of <font color="Maroon" title="c2">U2</font> <b>by </b><i><a class="ref" href="funct_1.html#D5" title="FUNCT_1:def.5">FUNCT_1:def 5</a></i>;<br/>
<a NAME="E9:13_1"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <font color="Maroon" title="c4">U4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <font color="Maroon" title="c2">U2</font>
 
<b>by </b><i><a class="txt" href="#E1:13"><i><font color="Green" title="E10">A1</font></i></a>, <a class="ref" href="unialg_2.html#T3" title="UNIALG_2:th.3">UNIALG_2:3</a></i>;<br/>
<a NAME="E10:13_1"/><b>then </b>
<font color="Maroon" title="c11">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="c4">U4</font>
 
<b>by </b><i><a class="txt" href="#E5:13_1"><i><font color="Green" title="E22">A13</font></i></a>, <a class="txt" href="#E6:13_1"><i><font color="Green" title="E23">A14</font></i></a>, <a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c13">o4</font> = the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <font color="Maroon" title="c4">U4</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">n</font> as   <a href="unialg_2.html#NM5" title="UNIALG_2:NM.5">operation</a> of <font color="Maroon" title="c4">U4</font> <b>by </b><i><a class="ref" href="funct_1.html#D5" title="FUNCT_1:def.5">FUNCT_1:def 5</a></i>;<br/>
<a NAME="E12:13_1"/>
( <font color="Maroon" title="c12">o2</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="c2">U2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">n</font> &amp; <font color="Maroon" title="c13">o4</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="c4">U4</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">n</font> )
 
;<br/>
<a NAME="E13:13_1"/><b>then </b><i><font color="Green" title="E25">A16</font></i>: 
(  <a href="unialg_1.html#K3" title="UNIALG_1:func.3">arity</a> <font color="Maroon" title="c8">o</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">o2</font> &amp;  <a href="unialg_1.html#K3" title="UNIALG_1:func.3">arity</a> <font color="Maroon" title="c8">o</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="c13">o4</font> &amp; <font color="Maroon" title="c8">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="pralg_1.html#K3" title="PRALG_1:func.3">[[:</a><span class="default"><font color="Maroon" title="c12">o2</font>,<font color="Maroon" title="c13">o4</font></span><a href="pralg_1.html#K3" title="PRALG_1:func.3">:]]</a></span> )
 
<b>by </b><i><a class="txt" href="#E1:13"><i><font color="Green" title="E10">A1</font></i></a>, <a class="txt" href="#E4:13_1"><i><font color="Green" title="E21">A12</font></i></a>, <a class="txt" href="#E7:13_1"><i><font color="Green" title="E24">A15</font></i></a>, <a class="ref" href="pralg_1.html#T6" target="_self" title="PRALG_1:th.6">Th6</a></i>;<br/>
<a NAME="E14:13_1"/><b>then </b><i><font color="Green" title="E26">A17</font></i>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1"><a href="pralg_1.html#K3" title="PRALG_1:func.3">[[:</a><span class="default"><font color="Maroon" title="c12">o2</font>,<font color="Maroon" title="c13">o4</font></span><a href="pralg_1.html#K3" title="PRALG_1:func.3">:]]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="unialg_1.html#K3" title="UNIALG_1:func.3">arity</a> <font color="Maroon" title="c12">o2</font></span>)</span> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">U2</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c4">U4</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 
<b>by </b><i><a class="ref" href="pralg_1.html#D3" target="_self" title="PRALG_1:def.3">Def3</a></i>;<br/>
<a NAME="E15:13_1"/>
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c10">s0</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">U1</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">U3</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 
<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="E16:13_1"/><b>then </b>
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c10">s0</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">U2</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c4">U4</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 
<b>by </b><i><a class="txt" href="#E7:13"><i><font color="Green" title="E16">A7</font></i></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></i>;<br/>
<a NAME="E17:13_1"/><b>then </b>
<font color="Maroon" title="c10">s0</font> is    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">U2</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c4">U4</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 
<b>by </b><i><a class="ref" href="finseq_1.html#D4" title="FINSEQ_1:def.4">FINSEQ_1:def 4</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c14">ss</font> = <font color="Maroon" title="c10">s0</font> as    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">U2</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c4">U4</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> <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/>
<a NAME="E19:13_1"/><i><font color="Green" title="E27">A18</font></i>: 
<font color="Maroon" title="c14">ss</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <font color="Olive" title="b1">w</font> where <font color="Olive" title="b1">w</font> is    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">U2</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c4">U4</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> <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">w</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">o2</font> </span>}</span> 
 
<b>by </b><i><a class="txt" href="#E1:13_1"><i><font color="Green" title="E20">A11</font></i></a>, <a class="txt" href="#E13:13_1"><i><font color="Green" title="E25">A16</font></i></a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c15">s1</font> =  <a href="pralg_1.html#K1" title="PRALG_1:func.1">pr1</a> <font color="Maroon" title="c10">s0</font> as    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <font color="Maroon" title="c6">B1</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/>
<b>reconsider </b><font color="Maroon" title="c16">s3</font> =  <a href="pralg_1.html#K2" title="PRALG_1:func.2">pr2</a> <font color="Maroon" title="c10">s0</font> as    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <font color="Maroon" title="c7">B3</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/>
<a NAME="E22:13_1"/><i><font color="Green" title="E28">A19</font></i>: 
( <font color="Maroon" title="c6">B1</font> <a href="unialg_2.html#R2" title="UNIALG_2:pred.2">is_closed_on</a> <font color="Maroon" title="c12">o2</font> &amp; <font color="Maroon" title="c7">B3</font> <a href="unialg_2.html#R2" title="UNIALG_2:pred.2">is_closed_on</a> <font color="Maroon" title="c13">o4</font> )
 
<b>by </b><i><a class="txt" href="#E12:13"><i><font color="Green" title="E18">A9</font></i></a>, <a class="ref" href="unialg_2.html#D5" title="UNIALG_2:def.5">UNIALG_2:def 5</a></i>;<br/>
<a NAME="E23:13_1"/>
(  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c15">s1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c10">s0</font> &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c16">s3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c10">s0</font> )
 
<b>by </b><i><a class="ref" href="pralg_1.html#D1" target="_self" title="PRALG_1:def.1">Def1</a>, <a class="ref" href="pralg_1.html#D2" target="_self" title="PRALG_1:def.2">Def2</a></i>;<br/>
<a NAME="E24:13_1"/><b>then </b><i><font color="Green" title="E29">A20</font></i>: 
( <font color="Maroon" title="c12">o2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c15">s1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c6">B1</font> &amp; <font color="Maroon" title="c13">o4</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c16">s3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c7">B3</font> )
 
<b>by </b><i><a class="txt" href="#E1:13_1"><i><font color="Green" title="E20">A11</font></i></a>, <a class="txt" href="#E13:13_1"><i><font color="Green" title="E25">A16</font></i></a>, <a class="txt" href="#E22:13_1"><i><font color="Green" title="E28">A19</font></i></a>, <a class="ref" href="unialg_2.html#D4" title="UNIALG_2:def.4">UNIALG_2:def 4</a></i>;<br/>
<a NAME="E25:13_1"/>
<font color="Maroon" title="c8">o</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c12">o2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3">(<span class="default"><a href="pralg_1.html#K1" title="PRALG_1:func.1">pr1</a> <font color="Maroon" title="c14">ss</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c13">o4</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3">(<span class="default"><a href="pralg_1.html#K2" title="PRALG_1:func.2">pr2</a> <font color="Maroon" title="c14">ss</font></span>)</span></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 
<b>by </b><i><a class="txt" href="#E13:13_1"><i><font color="Green" title="E25">A16</font></i></a>, <a class="txt" href="#E14:13_1"><i><font color="Green" title="E26">A17</font></i></a>, <a class="txt" href="#E19:13_1"><i><font color="Green" title="E27">A18</font></i></a>, <a class="ref" href="pralg_1.html#D3" target="_self" title="PRALG_1:def.3">Def3</a></i>;<br/>
<b>hence </b><a NAME="E26:13_1"/>
<font color="Maroon" title="c8">o</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">s</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">B</font>
 <b>by </b><i><a class="txt" href="#E5:13"><i><font color="Green" title="E14">A5</font></i></a>, <a class="txt" href="#E9:13"><i><font color="Green" title="E17">A8</font></i></a>, <a class="txt" href="#E24:13_1"><i><font color="Green" title="E29">A20</font></i></a>, <a class="ref" href="zfmisc_1.html#T106" title="ZFMISC_1:th.106">ZFMISC_1:106</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<a NAME="E14:13"/><i><font color="Green" title="E20">A21</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 <span class="p1"><a href="pralg_1.html#K5" title="PRALG_1:func.5">[:</a><span class="default"><font color="Maroon" title="c2">U2</font>,<font color="Maroon" title="c4">U4</font></span><a href="pralg_1.html#K5" title="PRALG_1:func.5">:]</a></span> <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> <span class="p2"><a href="pralg_1.html#K5" title="PRALG_1:func.5">[:</a><span class="default"><font color="Maroon" title="c2">U2</font>,<font color="Maroon" title="c4">U4</font></span><a href="pralg_1.html#K5" title="PRALG_1:func.5">:]</a></span>,<font color="Maroon" title="c5">B</font></span>)</span>
 
<b>by </b><i><a class="ref" href="unialg_2.html#D7" title="UNIALG_2:def.7">UNIALG_2:def 7</a></i>;<br/>
<a NAME="E15:13"/><b>then </b>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <span class="p1"><a href="pralg_1.html#K5" title="PRALG_1:func.5">[:</a><span class="default"><font color="Maroon" title="c2">U2</font>,<font color="Maroon" title="c4">U4</font></span><a href="pralg_1.html#K5" title="PRALG_1:func.5">:]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="unialg_2.html#K3" title="UNIALG_2:func.3">Opers</a> <span class="p2"><a href="pralg_1.html#K5" title="PRALG_1:func.5">[:</a><span class="default"><font color="Maroon" title="c2">U2</font>,<font color="Maroon" title="c4">U4</font></span><a href="pralg_1.html#K5" title="PRALG_1:func.5">:]</a></span>,<font color="Maroon" title="c5">B</font></span>)</span>
 
<b>by </b><i><a class="ref" href="finseq_3.html#T31" title="FINSEQ_3:th.31">FINSEQ_3:31</a></i>;<br/>
<a NAME="E16:13"/><b>then </b><i><font color="Green" title="E21">A22</font></i>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <font color="Maroon" title="c2">U2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="unialg_2.html#K3" title="UNIALG_2:func.3">Opers</a> <span class="p2"><a href="pralg_1.html#K5" title="PRALG_1:func.5">[:</a><span class="default"><font color="Maroon" title="c2">U2</font>,<font color="Maroon" title="c4">U4</font></span><a href="pralg_1.html#K5" title="PRALG_1:func.5">:]</a></span>,<font color="Maroon" title="c5">B</font></span>)</span>
 
<b>by </b><i><a class="txt" href="#E1:13"><i><font color="Green" title="E10">A1</font></i></a>, <a class="txt" href="#E5:13"><i><font color="Green" title="E14">A5</font></i></a>, <a class="ref" href="pralg_1.html#D4" target="_self" title="PRALG_1:def.4">Def4</a></i>;<br/>
<a NAME="E17:13"/><i><font color="Green" title="E22">A23</font></i>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <span class="p1"><a href="pralg_1.html#K5" title="PRALG_1:func.5">[:</a><span class="default"><font color="Maroon" title="c1">U1</font>,<font color="Maroon" title="c3">U3</font></span><a href="pralg_1.html#K5" title="PRALG_1:func.5">:]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <font color="Maroon" title="c1">U1</font>
 
<b>by </b><i><a class="txt" href="#E4:13"><i><font color="Green" title="E13">A4</font></i></a>, <a class="txt" href="#E5:13"><i><font color="Green" title="E14">A5</font></i></a>, <a class="ref" href="pralg_1.html#D4" target="_self" title="PRALG_1:def.4">Def4</a></i>;<br/>
<a NAME="E18:13"/>
 <a href="unialg_1.html#K4" title="UNIALG_1:func.4">signature</a> <font color="Maroon" title="c1">U1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="unialg_1.html#K4" title="UNIALG_1:func.4">signature</a> <font color="Maroon" title="c2">U2</font>
 
<b>by </b><i><a class="txt" href="#E2:13"><i><font color="Green" title="E11">A2</font></i></a>, <a class="ref" href="unialg_2.html#D2" title="UNIALG_2:def.2">UNIALG_2:def 2</a></i>;<br/>
<a NAME="E19:13"/><b>then </b>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <font color="Maroon" title="c1">U1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="unialg_1.html#K4" title="UNIALG_1:func.4">signature</a> <font color="Maroon" title="c2">U2</font></span>)</span>
 
<b>by </b><i><a class="ref" href="unialg_1.html#D11" title="UNIALG_1:def.11">UNIALG_1:def 11</a></i>;<br/>
<a NAME="E20:13"/><b>then </b><i><font color="Green" title="E23">A24</font></i>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <span class="p1"><a href="pralg_1.html#K5" title="PRALG_1:func.5">[:</a><span class="default"><font color="Maroon" title="c1">U1</font>,<font color="Maroon" title="c3">U3</font></span><a href="pralg_1.html#K5" title="PRALG_1:func.5">:]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="unialg_2.html#K3" title="UNIALG_2:func.3">Opers</a> <span class="p2"><a href="pralg_1.html#K5" title="PRALG_1:func.5">[:</a><span class="default"><font color="Maroon" title="c2">U2</font>,<font color="Maroon" title="c4">U4</font></span><a href="pralg_1.html#K5" title="PRALG_1:func.5">:]</a></span>,<font color="Maroon" title="c5">B</font></span>)</span>
 
<b>by </b><i><a class="txt" href="#E16:13"><i><font color="Green" title="E21">A22</font></i></a>, <a class="txt" href="#E17:13"><i><font color="Green" title="E22">A23</font></i></a>, <a class="ref" href="unialg_1.html#D11" title="UNIALG_1:def.11">UNIALG_1:def 11</a></i>;<br/>
<a NAME="E21:13"/><i><font color="Green" title="E24">A25</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">U1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <font color="Maroon" title="c1">U1</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="c2">U2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <font color="Maroon" title="c2">U2</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="c3">U3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <font color="Maroon" title="c3">U3</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="c4">U4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <font color="Maroon" title="c4">U4</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 <span class="p1"><a href="pralg_1.html#K5" title="PRALG_1:func.5">[:</a><span class="default"><font color="Maroon" title="c1">U1</font>,<font color="Maroon" title="c3">U3</font></span><a href="pralg_1.html#K5" title="PRALG_1:func.5">:]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <span class="p2"><a href="pralg_1.html#K5" title="PRALG_1:func.5">[:</a><span class="default"><font color="Maroon" title="c1">U1</font>,<font color="Maroon" title="c3">U3</font></span><a href="pralg_1.html#K5" title="PRALG_1:func.5">:]</a></span></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 <span class="p1"><a href="pralg_1.html#K5" title="PRALG_1:func.5">[:</a><span class="default"><font color="Maroon" title="c2">U2</font>,<font color="Maroon" title="c4">U4</font></span><a href="pralg_1.html#K5" title="PRALG_1:func.5">:]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <span class="p2"><a href="pralg_1.html#K5" title="PRALG_1:func.5">[:</a><span class="default"><font color="Maroon" title="c2">U2</font>,<font color="Maroon" title="c4">U4</font></span><a href="pralg_1.html#K5" title="PRALG_1:func.5">:]</a></span></span>)</span> &amp;  <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> <span class="p2"><a href="pralg_1.html#K5" title="PRALG_1:func.5">[:</a><span class="default"><font color="Maroon" title="c2">U2</font>,<font color="Maroon" title="c4">U4</font></span><a href="pralg_1.html#K5" title="PRALG_1:func.5">:]</a></span>,<font color="Maroon" title="c5">B</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p2">(<span class="default"><a href="unialg_2.html#K3" title="UNIALG_2:func.3">Opers</a> <span class="p3"><a href="pralg_1.html#K5" title="PRALG_1:func.5">[:</a><span class="default"><font color="Maroon" title="c2">U2</font>,<font color="Maroon" title="c4">U4</font></span><a href="pralg_1.html#K5" title="PRALG_1:func.5">:]</a></span>,<font color="Maroon" title="c5">B</font></span>)</span></span>)</span> &amp;  <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="c2">U2</font>,<font color="Maroon" title="c6">B1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p2">(<span class="default"><a href="unialg_2.html#K3" title="UNIALG_2:func.3">Opers</a> <font color="Maroon" title="c2">U2</font>,<font color="Maroon" title="c6">B1</font></span>)</span></span>)</span> &amp;  <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="c4">U4</font>,<font color="Maroon" title="c7">B3</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p2">(<span class="default"><a href="unialg_2.html#K3" title="UNIALG_2:func.3">Opers</a> <font color="Maroon" title="c4">U4</font>,<font color="Maroon" title="c7">B3</font></span>)</span></span>)</span> )
 
<b>by </b><i><a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a></i>;<br/>
<a NAME="E22:13"/>
 <a href="unialg_1.html#K4" title="UNIALG_1:func.4">signature</a> <font color="Maroon" title="c4">U4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="unialg_1.html#K4" title="UNIALG_1:func.4">signature</a> <font color="Maroon" title="c2">U2</font>
 
<b>by </b><i><a class="txt" href="#E1:13"><i><font color="Green" title="E10">A1</font></i></a>, <a class="ref" href="unialg_2.html#D2" title="UNIALG_2:def.2">UNIALG_2:def 2</a></i>;<br/>
<a NAME="E23:13"/><b>then </b>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <font color="Maroon" title="c4">U4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="unialg_1.html#K4" title="UNIALG_1:func.4">signature</a> <font color="Maroon" title="c2">U2</font></span>)</span>
 
<b>by </b><i><a class="ref" href="unialg_1.html#D11" title="UNIALG_1:def.11">UNIALG_1:def 11</a></i>;<br/>
<a NAME="E24:13"/><b>then </b><i><font color="Green" title="E25">A26</font></i>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <font color="Maroon" title="c4">U4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <font color="Maroon" title="c2">U2</font>
 
<b>by </b><i><a class="ref" href="unialg_1.html#D11" title="UNIALG_1:def.11">UNIALG_1:def 11</a></i>;<br/>
<a NAME="E25:13"/>
 <a href="unialg_1.html#K4" title="UNIALG_1:func.4">signature</a> <font color="Maroon" title="c1">U1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="unialg_1.html#K4" title="UNIALG_1:func.4">signature</a> <font color="Maroon" title="c3">U3</font>
 
<b>by </b><i><a class="txt" href="#E4:13"><i><font color="Green" title="E13">A4</font></i></a>, <a class="ref" href="unialg_2.html#D2" title="UNIALG_2:def.2">UNIALG_2:def 2</a></i>;<br/>
<a NAME="E26:13"/><b>then </b>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <font color="Maroon" title="c1">U1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="unialg_1.html#K4" title="UNIALG_1:func.4">signature</a> <font color="Maroon" title="c3">U3</font></span>)</span>
 
<b>by </b><i><a class="ref" href="unialg_1.html#D11" title="UNIALG_1:def.11">UNIALG_1:def 11</a></i>;<br/>
<a NAME="E27:13"/><b>then </b><i><font color="Green" title="E26">A27</font></i>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <font color="Maroon" title="c1">U1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <font color="Maroon" title="c3">U3</font>
 
<b>by </b><i><a class="ref" href="unialg_1.html#D11" title="UNIALG_1:def.11">UNIALG_1:def 11</a></i>;<br/>
<a NAME="E28:13"/><i><font color="Green" title="E27">A28</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="c2">U2</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="c2">U2</font>,<font color="Maroon" title="c6">B1</font></span>)</span>
 
<b>by </b><i><a class="ref" href="unialg_2.html#D7" title="UNIALG_2:def.7">UNIALG_2:def 7</a></i>;<br/>
<a NAME="E29:13"/><i><font color="Green" title="E28">A29</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="c4">U4</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="c4">U4</font>,<font color="Maroon" title="c7">B3</font></span>)</span>
 
<b>by </b><i><a class="ref" href="unialg_2.html#D7" title="UNIALG_2:def.7">UNIALG_2:def 7</a></i>;<br/>
<a NAME="E30:13"/>
for <font color="Olive" title="b1">n</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st <font color="Olive" title="b1">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 <span class="p1"><a href="pralg_1.html#K5" title="PRALG_1:func.5">[:</a><span class="default"><font color="Maroon" title="c1">U1</font>,<font color="Maroon" title="c3">U3</font></span><a href="pralg_1.html#K5" title="PRALG_1:func.5">:]</a></span> holds <br/>the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <span class="p1"><a href="pralg_1.html#K5" title="PRALG_1:func.5">[:</a><span class="default"><font color="Maroon" title="c1">U1</font>,<font color="Maroon" title="c3">U3</font></span><a href="pralg_1.html#K5" title="PRALG_1:func.5">:]</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="unialg_2.html#K3" title="UNIALG_2:func.3">Opers</a> <span class="p2"><a href="pralg_1.html#K5" title="PRALG_1:func.5">[:</a><span class="default"><font color="Maroon" title="c2">U2</font>,<font color="Maroon" title="c4">U4</font></span><a href="pralg_1.html#K5" title="PRALG_1:func.5">:]</a></span>,<font color="Maroon" title="c5">B</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">n</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c8">n</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c8">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 <span class="p1"><a href="pralg_1.html#K5" title="PRALG_1:func.5">[:</a><span class="default"><font color="Maroon" title="c1">U1</font>,<font color="Maroon" title="c3">U3</font></span><a href="pralg_1.html#K5" title="PRALG_1:func.5">:]</a></span> implies the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <span class="p1"><a href="pralg_1.html#K5" title="PRALG_1:func.5">[:</a><span class="default"><font color="Maroon" title="c1">U1</font>,<font color="Maroon" title="c3">U3</font></span><a href="pralg_1.html#K5" title="PRALG_1:func.5">:]</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="unialg_2.html#K3" title="UNIALG_2:func.3">Opers</a> <span class="p2"><a href="pralg_1.html#K5" title="PRALG_1:func.5">[:</a><span class="default"><font color="Maroon" title="c2">U2</font>,<font color="Maroon" title="c4">U4</font></span><a href="pralg_1.html#K5" title="PRALG_1:func.5">:]</a></span>,<font color="Maroon" title="c5">B</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">n</font> )</span><br/>

<b>assume </b><a NAME="E1:13_2"/><i><font color="Green" title="E29">A30</font></i>: 
<font color="Maroon" title="c8">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 <span class="p1"><a href="pralg_1.html#K5" title="PRALG_1:func.5">[:</a><span class="default"><font color="Maroon" title="c1">U1</font>,<font color="Maroon" title="c3">U3</font></span><a href="pralg_1.html#K5" title="PRALG_1:func.5">:]</a></span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <span class="p1"><a href="pralg_1.html#K5" title="PRALG_1:func.5">[:</a><span class="default"><font color="Maroon" title="c1">U1</font>,<font color="Maroon" title="c3">U3</font></span><a href="pralg_1.html#K5" title="PRALG_1:func.5">:]</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="unialg_2.html#K3" title="UNIALG_2:func.3">Opers</a> <span class="p2"><a href="pralg_1.html#K5" title="PRALG_1:func.5">[:</a><span class="default"><font color="Maroon" title="c2">U2</font>,<font color="Maroon" title="c4">U4</font></span><a href="pralg_1.html#K5" title="PRALG_1:func.5">:]</a></span>,<font color="Maroon" title="c5">B</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">n</font></span><br/>

<b>then reconsider </b><font color="Maroon" title="c9">o2</font> = the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <font color="Maroon" title="c2">U2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">n</font> as   <a href="unialg_2.html#NM5" title="UNIALG_2:NM.5">operation</a> of <font color="Maroon" title="c2">U2</font> <b>by </b><i><a class="txt" href="#E16:13"><i><font color="Green" title="E21">A22</font></i></a>, <a class="txt" href="#E20:13"><i><font color="Green" title="E23">A24</font></i></a>, <a class="txt" href="#E21:13"><i><font color="Green" title="E24">A25</font></i></a>, <a class="ref" href="funct_1.html#D5" title="FUNCT_1:def.5">FUNCT_1:def 5</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c10">o4</font> = the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <font color="Maroon" title="c4">U4</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">n</font> as   <a href="unialg_2.html#NM5" title="UNIALG_2:NM.5">operation</a> of <font color="Maroon" title="c4">U4</font> <b>by </b><i><a class="txt" href="#E16:13"><i><font color="Green" title="E21">A22</font></i></a>, <a class="txt" href="#E20:13"><i><font color="Green" title="E23">A24</font></i></a>, <a class="txt" href="#E21:13"><i><font color="Green" title="E24">A25</font></i></a>, <a class="txt" href="#E24:13"><i><font color="Green" title="E25">A26</font></i></a>, <a class="txt" href="#E1:13_2"><i><font color="Green" title="E29">A30</font></i></a>, <a class="ref" href="funct_1.html#D5" title="FUNCT_1:def.5">FUNCT_1:def 5</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c11">o24</font> = the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <span class="p1"><a href="pralg_1.html#K5" title="PRALG_1:func.5">[:</a><span class="default"><font color="Maroon" title="c2">U2</font>,<font color="Maroon" title="c4">U4</font></span><a href="pralg_1.html#K5" title="PRALG_1:func.5">:]</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">n</font> as   <a href="unialg_2.html#NM5" title="UNIALG_2:NM.5">operation</a> of <span class="p1"><a href="pralg_1.html#K5" title="PRALG_1:func.5">[:</a><span class="default"><font color="Maroon" title="c2">U2</font>,<font color="Maroon" title="c4">U4</font></span><a href="pralg_1.html#K5" title="PRALG_1:func.5">:]</a></span> <b>by </b><i><a class="txt" href="#E14:13"><i><font color="Green" title="E20">A21</font></i></a>, <a class="txt" href="#E20:13"><i><font color="Green" title="E23">A24</font></i></a>, <a class="txt" href="#E21:13"><i><font color="Green" title="E24">A25</font></i></a>, <a class="txt" href="#E1:13_2"><i><font color="Green" title="E29">A30</font></i></a>, <a class="ref" href="funct_1.html#D5" title="FUNCT_1:def.5">FUNCT_1:def 5</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c12">o1</font> = the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <font color="Maroon" title="c1">U1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">n</font> as   <a href="unialg_2.html#NM5" title="UNIALG_2:NM.5">operation</a> of <font color="Maroon" title="c1">U1</font> <b>by </b><i><a class="txt" href="#E17:13"><i><font color="Green" title="E22">A23</font></i></a>, <a class="txt" href="#E21:13"><i><font color="Green" title="E24">A25</font></i></a>, <a class="txt" href="#E1:13_2"><i><font color="Green" title="E29">A30</font></i></a>, <a class="ref" href="funct_1.html#D5" title="FUNCT_1:def.5">FUNCT_1:def 5</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c13">o3</font> = the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <font color="Maroon" title="c3">U3</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">n</font> as   <a href="unialg_2.html#NM5" title="UNIALG_2:NM.5">operation</a> of <font color="Maroon" title="c3">U3</font> <b>by </b><i><a class="txt" href="#E17:13"><i><font color="Green" title="E22">A23</font></i></a>, <a class="txt" href="#E21:13"><i><font color="Green" title="E24">A25</font></i></a>, <a class="txt" href="#E27:13"><i><font color="Green" title="E26">A27</font></i></a>, <a class="txt" href="#E1:13_2"><i><font color="Green" title="E29">A30</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="E7:13_2"/>
( <font color="Maroon" title="c9">o2</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="c2">U2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">n</font> &amp; <font color="Maroon" title="c10">o4</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="c4">U4</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">n</font> )
 
;<br/>
<a NAME="E8:13_2"/><b>then </b><i><font color="Green" title="E30">A31</font></i>: 
( <font color="Maroon" title="c11">o24</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="pralg_1.html#K3" title="PRALG_1:func.3">[[:</a><span class="default"><font color="Maroon" title="c9">o2</font>,<font color="Maroon" title="c10">o4</font></span><a href="pralg_1.html#K3" title="PRALG_1:func.3">:]]</a></span> &amp;  <a href="unialg_1.html#K3" title="UNIALG_1:func.3">arity</a> <font color="Maroon" title="c11">o24</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="c10">o4</font> &amp;  <a href="unialg_1.html#K3" title="UNIALG_1:func.3">arity</a> <font color="Maroon" title="c11">o24</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="c9">o2</font> )
 
<b>by </b><i><a class="txt" href="#E1:13"><i><font color="Green" title="E10">A1</font></i></a>, <a class="txt" href="#E16:13"><i><font color="Green" title="E21">A22</font></i></a>, <a class="txt" href="#E20:13"><i><font color="Green" title="E23">A24</font></i></a>, <a class="txt" href="#E21:13"><i><font color="Green" title="E24">A25</font></i></a>, <a class="txt" href="#E1:13_2"><i><font color="Green" title="E29">A30</font></i></a>, <a class="ref" href="pralg_1.html#T6" target="_self" title="PRALG_1:th.6">Th6</a></i>;<br/>
<a NAME="E9:13_2"/><i><font color="Green" title="E31">A32</font></i>: 
<span class="p1">(<span class="default"><a href="unialg_2.html#K3" title="UNIALG_2:func.3">Opers</a> <font color="Maroon" title="c2">U2</font>,<font color="Maroon" title="c6">B1</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">o2</font> <a href="unialg_2.html#K2" title="UNIALG_2:func.2">/.</a> <font color="Maroon" title="c6">B1</font>
 
<b>by </b><i><a class="txt" href="#E16:13"><i><font color="Green" title="E21">A22</font></i></a>, <a class="txt" href="#E20:13"><i><font color="Green" title="E23">A24</font></i></a>, <a class="txt" href="#E21:13"><i><font color="Green" title="E24">A25</font></i></a>, <a class="txt" href="#E28:13"><i><font color="Green" title="E27">A28</font></i></a>, <a class="txt" href="#E1:13_2"><i><font color="Green" title="E29">A30</font></i></a>, <a class="ref" href="unialg_2.html#D7" title="UNIALG_2:def.7">UNIALG_2:def 7</a></i>;<br/>
<a NAME="E10:13_2"/><i><font color="Green" title="E32">A33</font></i>: 
<span class="p1">(<span class="default"><a href="unialg_2.html#K3" title="UNIALG_2:func.3">Opers</a> <font color="Maroon" title="c4">U4</font>,<font color="Maroon" title="c7">B3</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">o4</font> <a href="unialg_2.html#K2" title="UNIALG_2:func.2">/.</a> <font color="Maroon" title="c7">B3</font>
 
<b>by </b><i><a class="txt" href="#E16:13"><i><font color="Green" title="E21">A22</font></i></a>, <a class="txt" href="#E20:13"><i><font color="Green" title="E23">A24</font></i></a>, <a class="txt" href="#E21:13"><i><font color="Green" title="E24">A25</font></i></a>, <a class="txt" href="#E24:13"><i><font color="Green" title="E25">A26</font></i></a>, <a class="txt" href="#E29:13"><i><font color="Green" title="E28">A29</font></i></a>, <a class="txt" href="#E1:13_2"><i><font color="Green" title="E29">A30</font></i></a>, <a class="ref" href="unialg_2.html#D7" title="UNIALG_2:def.7">UNIALG_2:def 7</a></i>;<br/>
<a NAME="E11:13_2"/><i><font color="Green" title="E33">A34</font></i>: 
<font color="Maroon" title="c12">o1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">o2</font> <a href="unialg_2.html#K2" title="UNIALG_2:func.2">/.</a> <font color="Maroon" title="c6">B1</font>
 
<b>by </b><i><a class="txt" href="#E1:13"><i><font color="Green" title="E10">A1</font></i></a>, <a class="txt" href="#E9:13_2"><i><font color="Green" title="E31">A32</font></i></a>, <a class="ref" href="unialg_2.html#D8" title="UNIALG_2:def.8">UNIALG_2:def 8</a></i>;<br/>
<a NAME="E12:13_2"/><i><font color="Green" title="E34">A35</font></i>: 
<font color="Maroon" title="c13">o3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">o4</font> <a href="unialg_2.html#K2" title="UNIALG_2:func.2">/.</a> <font color="Maroon" title="c7">B3</font>
 
<b>by </b><i><a class="txt" href="#E1:13"><i><font color="Green" title="E10">A1</font></i></a>, <a class="txt" href="#E10:13_2"><i><font color="Green" title="E32">A33</font></i></a>, <a class="ref" href="unialg_2.html#D8" title="UNIALG_2:def.8">UNIALG_2:def 8</a></i>;<br/>
<a NAME="E13:13_2"/><i><font color="Green" title="E35">A36</font></i>: 
( <font color="Maroon" title="c5">B</font> <a href="unialg_2.html#R2" title="UNIALG_2:pred.2">is_closed_on</a> <font color="Maroon" title="c11">o24</font> &amp; <font color="Maroon" title="c6">B1</font> <a href="unialg_2.html#R2" title="UNIALG_2:pred.2">is_closed_on</a> <font color="Maroon" title="c9">o2</font> &amp; <font color="Maroon" title="c7">B3</font> <a href="unialg_2.html#R2" title="UNIALG_2:pred.2">is_closed_on</a> <font color="Maroon" title="c10">o4</font> )
 
<b>by </b><i><a class="txt" href="#E12:13"><i><font color="Green" title="E18">A9</font></i></a>, <a class="txt" href="#E13:13"><i><font color="Green" title="E19">A10</font></i></a>, <a class="ref" href="unialg_2.html#D5" title="UNIALG_2:def.5">UNIALG_2:def 5</a></i>;<br/>
<a NAME="E14:13_2"/><b>then </b><i><font color="Green" title="E36">A37</font></i>: 
(  <a href="unialg_1.html#K3" title="UNIALG_1:func.3">arity</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">o2</font> <a href="unialg_2.html#K2" title="UNIALG_2:func.2">/.</a> <font color="Maroon" title="c6">B1</font></span>)</span> <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="c9">o2</font> &amp;  <a href="unialg_1.html#K3" title="UNIALG_1:func.3">arity</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">o4</font> <a href="unialg_2.html#K2" title="UNIALG_2:func.2">/.</a> <font color="Maroon" title="c7">B3</font></span>)</span> <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="c10">o4</font> )
 
<b>by </b><i><a class="ref" href="unialg_2.html#T8" title="UNIALG_2:th.8">UNIALG_2:8</a></i>;<br/>
<a NAME="E15:13_2"/><b>then </b><i><font color="Green" title="E37">A38</font></i>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1"><a href="pralg_1.html#K3" title="PRALG_1:func.3">[[:</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c9">o2</font> <a href="unialg_2.html#K2" title="UNIALG_2:func.2">/.</a> <font color="Maroon" title="c6">B1</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c10">o4</font> <a href="unialg_2.html#K2" title="UNIALG_2:func.2">/.</a> <font color="Maroon" title="c7">B3</font></span>)</span></span><a href="pralg_1.html#K3" title="PRALG_1:func.3">:]]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="unialg_1.html#K3" title="UNIALG_1:func.3">arity</a> <font color="Maroon" title="c9">o2</font></span>)</span> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <font color="Maroon" title="c5">B</font>
 
<b>by </b><i><a class="txt" href="#E5:13"><i><font color="Green" title="E14">A5</font></i></a>, <a class="txt" href="#E9:13"><i><font color="Green" title="E17">A8</font></i></a>, <a class="txt" href="#E8:13_2"><i><font color="Green" title="E30">A31</font></i></a>, <a class="ref" href="pralg_1.html#D3" target="_self" title="PRALG_1:def.3">Def3</a></i>;<br/>
<i><font color="Green" title="E38">A39</font></i>:  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><span class="p2"><a href="pralg_1.html#K3" title="PRALG_1:func.3">[[:</a><span class="default"><font color="Maroon" title="c9">o2</font>,<font color="Maroon" title="c10">o4</font></span><a href="pralg_1.html#K3" title="PRALG_1:func.3">:]]</a></span> <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="c11">o24</font></span>)</span> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <font color="Maroon" title="c5">B</font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2"><a href="pralg_1.html#K3" title="PRALG_1:func.3">[[:</a><span class="default"><font color="Maroon" title="c9">o2</font>,<font color="Maroon" title="c10">o4</font></span><a href="pralg_1.html#K3" title="PRALG_1:func.3">:]]</a></span></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="c9">o2</font></span>)</span> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <font color="Maroon" title="c5">B</font></span>)</span>
<b>by </b><i><a class="txt" href="#E8:13_2"><i><font color="Green" title="E30">A31</font></i></a>, <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="c9">o2</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 <span class="p2"><a href="pralg_1.html#K5" title="PRALG_1:func.5">[:</a><span class="default"><font color="Maroon" title="c2">U2</font>,<font color="Maroon" title="c4">U4</font></span><a href="pralg_1.html#K5" title="PRALG_1:func.5">:]</a></span></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="c9">o2</font></span>)</span> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <font color="Maroon" title="c5">B</font></span>)</span>
<b>by </b><i><a class="txt" href="#E5:13"><i><font color="Green" title="E14">A5</font></i></a>, <a class="txt" href="#E8:13_2"><i><font color="Green" title="E30">A31</font></i></a>, <a class="ref" href="pralg_1.html#D3" target="_self" title="PRALG_1:def.3">Def3</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="c9">o2</font></span>)</span> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <font color="Maroon" title="c5">B</font>
<b>by </b><i><a class="ref" href="unialg_2.html#T1" title="UNIALG_2:th.1">UNIALG_2:1</a></i>
;<br/>
<div><i><font color="Green" title="E39">A40</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="13_2_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c14">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c14">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="unialg_1.html#K3" title="UNIALG_1:func.3">arity</a> <font color="Maroon" title="c9">o2</font></span>)</span> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <font color="Maroon" title="c5">B</font> implies <span class="p1"><a href="pralg_1.html#K3" title="PRALG_1:func.3">[[:</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c9">o2</font> <a href="unialg_2.html#K2" title="UNIALG_2:func.2">/.</a> <font color="Maroon" title="c6">B1</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c10">o4</font> <a href="unialg_2.html#K2" title="UNIALG_2:func.2">/.</a> <font color="Maroon" title="c7">B3</font></span>)</span></span><a href="pralg_1.html#K3" title="PRALG_1:func.3">:]]</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c14">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2"><a href="pralg_1.html#K3" title="PRALG_1:func.3">[[:</a><span class="default"><font color="Maroon" title="c9">o2</font>,<font color="Maroon" title="c10">o4</font></span><a href="pralg_1.html#K3" title="PRALG_1:func.3">:]]</a></span> <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="c11">o24</font></span>)</span> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <font color="Maroon" title="c5">B</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c14">x</font> )</span><br/><b>assume </b><a NAME="E1:13_2_2"/><i><font color="Green" title="E40">A41</font></i>: 
<font color="Maroon" title="c14">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="unialg_1.html#K3" title="UNIALG_1:func.3">arity</a> <font color="Maroon" title="c9">o2</font></span>)</span> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <font color="Maroon" title="c5">B</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1"><a href="pralg_1.html#K3" title="PRALG_1:func.3">[[:</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c9">o2</font> <a href="unialg_2.html#K2" title="UNIALG_2:func.2">/.</a> <font color="Maroon" title="c6">B1</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c10">o4</font> <a href="unialg_2.html#K2" title="UNIALG_2:func.2">/.</a> <font color="Maroon" title="c7">B3</font></span>)</span></span><a href="pralg_1.html#K3" title="PRALG_1:func.3">:]]</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c14">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2"><a href="pralg_1.html#K3" title="PRALG_1:func.3">[[:</a><span class="default"><font color="Maroon" title="c9">o2</font>,<font color="Maroon" title="c10">o4</font></span><a href="pralg_1.html#K3" title="PRALG_1:func.3">:]]</a></span> <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="c11">o24</font></span>)</span> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <font color="Maroon" title="c5">B</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c14">x</font></span><br/><b>then consider </b><font color="Maroon" title="c15">s</font> being    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <font color="Maroon" title="c5">B</font> <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a> <b> such that </b><br/><a NAME="E3:13_2_2"/><i><font color="Green" title="E41">A42</font></i>: 
( <font color="Maroon" title="c15">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">x</font> &amp;  <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="c9">o2</font> )
 ;<br/><a NAME="E4:13_2_2"/>
( <font color="Maroon" title="c5">B</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">U2</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c4">U4</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> &amp;  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c15">s</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c5">B</font> )
 <b>by </b><i><a class="txt" href="#E5:13"><i><font color="Green" title="E14">A5</font></i></a>, <a class="ref" href="finseq_1.html#D4" title="FINSEQ_1:def.4">FINSEQ_1:def 4</a></i>;<br/><a NAME="E5:13_2_2"/><b>then </b>
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c15">s</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">U2</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c4">U4</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 <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="c16">s0</font> = <font color="Maroon" title="c15">s</font> as    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">U2</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c4">U4</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> <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="E7:13_2_2"/><i><font color="Green" title="E42">A43</font></i>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><span class="p2"><a href="pralg_1.html#K3" title="PRALG_1:func.3">[[:</a><span class="default"><font color="Maroon" title="c9">o2</font>,<font color="Maroon" title="c10">o4</font></span><a href="pralg_1.html#K3" title="PRALG_1:func.3">:]]</a></span> <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="c11">o24</font></span>)</span> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <font color="Maroon" title="c5">B</font></span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1"><a href="pralg_1.html#K3" title="PRALG_1:func.3">[[:</a><span class="default"><font color="Maroon" title="c9">o2</font>,<font color="Maroon" title="c10">o4</font></span><a href="pralg_1.html#K3" title="PRALG_1:func.3">:]]</a></span>
 <b>by </b><i><a class="ref" href="relat_1.html#T89" title="RELAT_1:th.89">RELAT_1:89</a></i>;<br/><i><font color="Green" title="E43">A44</font></i>: <span class="p1">(<span class="default"><span class="p2"><a href="pralg_1.html#K3" title="PRALG_1:func.3">[[:</a><span class="default"><font color="Maroon" title="c9">o2</font>,<font color="Maroon" title="c10">o4</font></span><a href="pralg_1.html#K3" title="PRALG_1:func.3">:]]</a></span> <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="c11">o24</font></span>)</span> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <font color="Maroon" title="c5">B</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c14">x</font> = 
<span class="p1"><a href="pralg_1.html#K3" title="PRALG_1:func.3">[[:</a><span class="default"><font color="Maroon" title="c9">o2</font>,<font color="Maroon" title="c10">o4</font></span><a href="pralg_1.html#K3" title="PRALG_1:func.3">:]]</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c16">s0</font>
<b>by </b><i><a class="txt" href="#E16:13_2"><i><font color="Green" title="E38">A39</font></i></a>, <a class="txt" href="#E1:13_2_2"><i><font color="Green" title="E40">A41</font></i></a>, <a class="txt" href="#E3:13_2_2"><i><font color="Green" title="E41">A42</font></i></a>, <a class="ref" href="funct_1.html#T68" title="FUNCT_1:th.68">FUNCT_1:68</a></i>
<br/>.= 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c9">o2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3">(<span class="default"><a href="pralg_1.html#K1" title="PRALG_1:func.1">pr1</a> <font color="Maroon" title="c16">s0</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c10">o4</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3">(<span class="default"><a href="pralg_1.html#K2" title="PRALG_1:func.2">pr2</a> <font color="Maroon" title="c16">s0</font></span>)</span></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
<b>by </b><i><a class="txt" href="#E8:13_2"><i><font color="Green" title="E30">A31</font></i></a>, <a class="txt" href="#E16:13_2"><i><font color="Green" title="E38">A39</font></i></a>, <a class="txt" href="#E1:13_2_2"><i><font color="Green" title="E40">A41</font></i></a>, <a class="txt" href="#E3:13_2_2"><i><font color="Green" title="E41">A42</font></i></a>, <a class="txt" href="#E7:13_2_2"><i><font color="Green" title="E42">A43</font></i></a>, <a class="ref" href="pralg_1.html#D3" target="_self" title="PRALG_1:def.3">Def3</a></i>
;<br/><b>reconsider </b><font color="Maroon" title="c17">s1</font> = <font color="Maroon" title="c15">s</font> as    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Maroon" title="c6">B1</font>,<font color="Maroon" title="c7">B3</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> <b>by </b><i><a class="txt" href="#E5:13"><i><font color="Green" title="E14">A5</font></i></a>, <a class="txt" href="#E9:13"><i><font color="Green" title="E17">A8</font></i></a></i>;<br/><b>reconsider </b><font color="Maroon" title="c18">s11</font> =  <a href="pralg_1.html#K1" title="PRALG_1:func.1">pr1</a> <font color="Maroon" title="c17">s1</font> as    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <font color="Maroon" title="c6">B1</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/><b>reconsider </b><font color="Maroon" title="c19">s12</font> =  <a href="pralg_1.html#K2" title="PRALG_1:func.2">pr2</a> <font color="Maroon" title="c17">s1</font> as    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <font color="Maroon" title="c7">B3</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/><a NAME="E12:13_2_2"/>
(  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="pralg_1.html#K1" title="PRALG_1:func.1">pr1</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c17">s1</font> &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="pralg_1.html#K1" title="PRALG_1:func.1">pr1</a> <font color="Maroon" title="c16">s0</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c16">s0</font> )
 <b>by </b><i><a class="ref" href="pralg_1.html#D1" target="_self" title="PRALG_1:def.1">Def1</a></i>;<br/><a NAME="E13:13_2_2"/><b>then </b><i><font color="Green" title="E44">A45</font></i>: 
<font color="Maroon" title="c18">s11</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="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <font color="Maroon" title="c6">B1</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">a</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="c9">o2</font> </span>}</span> 
 <b>by </b><i><a class="txt" href="#E3:13_2_2"><i><font color="Green" title="E41">A42</font></i></a></i>;<br/><i><font color="Green" title="E45">A46</font></i>:  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">o2</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="c9">o2</font></span>)</span> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <font color="Maroon" title="c6">B1</font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c9">o2</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="c9">o2</font></span>)</span> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <font color="Maroon" title="c6">B1</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="c9">o2</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="c2">U2</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="c9">o2</font></span>)</span> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <font color="Maroon" title="c6">B1</font></span>)</span>
<b>by </b><i><a class="ref" href="unialg_2.html#T2" title="UNIALG_2:th.2">UNIALG_2:2</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="c9">o2</font></span>)</span> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <font color="Maroon" title="c6">B1</font>
<b>by </b><i><a class="ref" href="unialg_2.html#T1" title="UNIALG_2:th.1">UNIALG_2:1</a></i>
;<br/><a NAME="E15:13_2_2"/>
(  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="pralg_1.html#K2" title="PRALG_1:func.2">pr2</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c17">s1</font> &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="pralg_1.html#K2" title="PRALG_1:func.2">pr2</a> <font color="Maroon" title="c16">s0</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c16">s0</font> )
 <b>by </b><i><a class="ref" href="pralg_1.html#D2" target="_self" title="PRALG_1:def.2">Def2</a></i>;<br/><a NAME="E16:13_2_2"/><b>then </b><i><font color="Green" title="E46">A47</font></i>: 
<font color="Maroon" title="c19">s12</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <font color="Olive" title="b1">b</font> where <font color="Olive" title="b1">b</font> is    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <font color="Maroon" title="c7">B3</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">b</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="c10">o4</font> </span>}</span> 
 <b>by </b><i><a class="txt" href="#E8:13_2"><i><font color="Green" title="E30">A31</font></i></a>, <a class="txt" href="#E3:13_2_2"><i><font color="Green" title="E41">A42</font></i></a></i>;<br/><i><font color="Green" title="E47">A48</font></i>:  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">o4</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="c10">o4</font></span>)</span> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <font color="Maroon" title="c7">B3</font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c10">o4</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="c10">o4</font></span>)</span> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <font color="Maroon" title="c7">B3</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="c10">o4</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="c4">U4</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="c10">o4</font></span>)</span> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <font color="Maroon" title="c7">B3</font></span>)</span>
<b>by </b><i><a class="ref" href="unialg_2.html#T2" title="UNIALG_2:th.2">UNIALG_2:2</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="c10">o4</font></span>)</span> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <font color="Maroon" title="c7">B3</font>
<b>by </b><i><a class="ref" href="unialg_2.html#T1" title="UNIALG_2:th.1">UNIALG_2:1</a></i>
;<br/><span class="p1"><a href="pralg_1.html#K3" title="PRALG_1:func.3">[[:</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c9">o2</font> <a href="unialg_2.html#K2" title="UNIALG_2:func.2">/.</a> <font color="Maroon" title="c6">B1</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c10">o4</font> <a href="unialg_2.html#K2" title="UNIALG_2:func.2">/.</a> <font color="Maroon" title="c7">B3</font></span>)</span></span><a href="pralg_1.html#K3" title="PRALG_1:func.3">:]]</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c14">x</font> = 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c9">o2</font> <a href="unialg_2.html#K2" title="UNIALG_2:func.2">/.</a> <font color="Maroon" title="c6">B1</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3">(<span class="default"><a href="pralg_1.html#K1" title="PRALG_1:func.1">pr1</a> <font color="Maroon" title="c17">s1</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c10">o4</font> <a href="unialg_2.html#K2" title="UNIALG_2:func.2">/.</a> <font color="Maroon" title="c7">B3</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3">(<span class="default"><a href="pralg_1.html#K2" title="PRALG_1:func.2">pr2</a> <font color="Maroon" title="c17">s1</font></span>)</span></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
<b>by </b><i><a class="txt" href="#E8:13_2"><i><font color="Green" title="E30">A31</font></i></a>, <a class="txt" href="#E14:13_2"><i><font color="Green" title="E36">A37</font></i></a>, <a class="txt" href="#E15:13_2"><i><font color="Green" title="E37">A38</font></i></a>, <a class="txt" href="#E1:13_2_2"><i><font color="Green" title="E40">A41</font></i></a>, <a class="txt" href="#E3:13_2_2"><i><font color="Green" title="E41">A42</font></i></a>, <a class="ref" href="pralg_1.html#D3" target="_self" title="PRALG_1:def.3">Def3</a></i>
<br/>.= 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c9">o2</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="unialg_1.html#K3" title="UNIALG_1:func.3">arity</a> <font color="Maroon" title="c9">o2</font></span>)</span> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <font color="Maroon" title="c6">B1</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c18">s11</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c10">o4</font> <a href="unialg_2.html#K2" title="UNIALG_2:func.2">/.</a> <font color="Maroon" title="c7">B3</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3">(<span class="default"><a href="pralg_1.html#K2" title="PRALG_1:func.2">pr2</a> <font color="Maroon" title="c17">s1</font></span>)</span></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
<b>by </b><i><a class="txt" href="#E13:13_2"><i><font color="Green" title="E35">A36</font></i></a>, <a class="ref" href="unialg_2.html#D6" title="UNIALG_2:def.6">UNIALG_2:def 6</a></i>
<br/>.= 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c9">o2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3">(<span class="default"><a href="pralg_1.html#K1" title="PRALG_1:func.1">pr1</a> <font color="Maroon" title="c17">s1</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c10">o4</font> <a href="unialg_2.html#K2" title="UNIALG_2:func.2">/.</a> <font color="Maroon" title="c7">B3</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3">(<span class="default"><a href="pralg_1.html#K2" title="PRALG_1:func.2">pr2</a> <font color="Maroon" title="c17">s1</font></span>)</span></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
<b>by </b><i><a class="txt" href="#E13:13_2_2"><i><font color="Green" title="E44">A45</font></i></a>, <a class="txt" href="#E14:13_2_2"><i><font color="Green" title="E45">A46</font></i></a>, <a class="ref" href="funct_1.html#T68" title="FUNCT_1:th.68">FUNCT_1:68</a></i>
<br/>.= 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c9">o2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3">(<span class="default"><a href="pralg_1.html#K1" title="PRALG_1:func.1">pr1</a> <font color="Maroon" title="c17">s1</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c10">o4</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="unialg_1.html#K3" title="UNIALG_1:func.3">arity</a> <font color="Maroon" title="c10">o4</font></span>)</span> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <font color="Maroon" title="c7">B3</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3">(<span class="default"><a href="pralg_1.html#K2" title="PRALG_1:func.2">pr2</a> <font color="Maroon" title="c17">s1</font></span>)</span></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
<b>by </b><i><a class="txt" href="#E13:13_2"><i><font color="Green" title="E35">A36</font></i></a>, <a class="ref" href="unialg_2.html#D6" title="UNIALG_2:def.6">UNIALG_2:def 6</a></i>
<br/>.= 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c9">o2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3">(<span class="default"><a href="pralg_1.html#K1" title="PRALG_1:func.1">pr1</a> <font color="Maroon" title="c17">s1</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c10">o4</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3">(<span class="default"><a href="pralg_1.html#K2" title="PRALG_1:func.2">pr2</a> <font color="Maroon" title="c17">s1</font></span>)</span></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
<b>by </b><i><a class="txt" href="#E16:13_2_2"><i><font color="Green" title="E46">A47</font></i></a>, <a class="txt" href="#E17:13_2_2"><i><font color="Green" title="E47">A48</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="E19:13_2_2"/>
<span class="p1"><a href="pralg_1.html#K3" title="PRALG_1:func.3">[[:</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c9">o2</font> <a href="unialg_2.html#K2" title="UNIALG_2:func.2">/.</a> <font color="Maroon" title="c6">B1</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c10">o4</font> <a href="unialg_2.html#K2" title="UNIALG_2:func.2">/.</a> <font color="Maroon" title="c7">B3</font></span>)</span></span><a href="pralg_1.html#K3" title="PRALG_1:func.3">:]]</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c14">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2"><a href="pralg_1.html#K3" title="PRALG_1:func.3">[[:</a><span class="default"><font color="Maroon" title="c9">o2</font>,<font color="Maroon" title="c10">o4</font></span><a href="pralg_1.html#K3" title="PRALG_1:func.3">:]]</a></span> <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="c11">o24</font></span>)</span> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <font color="Maroon" title="c5">B</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c14">x</font>
 <b>by </b><i><a class="txt" href="#E8:13_2_2"><i><font color="Green" title="E43">A44</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<b>thus </b><span class="p1">(<span class="default"><a href="unialg_2.html#K3" title="UNIALG_2:func.3">Opers</a> <span class="p2"><a href="pralg_1.html#K5" title="PRALG_1:func.5">[:</a><span class="default"><font color="Maroon" title="c2">U2</font>,<font color="Maroon" title="c4">U4</font></span><a href="pralg_1.html#K5" title="PRALG_1:func.5">:]</a></span>,<font color="Maroon" title="c5">B</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">n</font> = 
<font color="Maroon" title="c11">o24</font> <a href="unialg_2.html#K2" title="UNIALG_2:func.2">/.</a> <font color="Maroon" title="c5">B</font>
<b>by </b><i><a class="txt" href="#E20:13"><i><font color="Green" title="E23">A24</font></i></a>, <a class="txt" href="#E21:13"><i><font color="Green" title="E24">A25</font></i></a>, <a class="txt" href="#E1:13_2"><i><font color="Green" title="E29">A30</font></i></a>, <a class="ref" href="unialg_2.html#D7" title="UNIALG_2:def.7">UNIALG_2:def 7</a></i>
<br/>.= 
<span class="p1"><a href="pralg_1.html#K3" title="PRALG_1:func.3">[[:</a><span class="default"><font color="Maroon" title="c9">o2</font>,<font color="Maroon" title="c10">o4</font></span><a href="pralg_1.html#K3" title="PRALG_1:func.3">:]]</a></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="c11">o24</font></span>)</span> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <font color="Maroon" title="c5">B</font></span>)</span>
<b>by </b><i><a class="txt" href="#E8:13_2"><i><font color="Green" title="E30">A31</font></i></a>, <a class="txt" href="#E13:13_2"><i><font color="Green" title="E35">A36</font></i></a>, <a class="ref" href="unialg_2.html#D6" title="UNIALG_2:def.6">UNIALG_2:def 6</a></i>
<br/>.= 
<span class="p1"><a href="pralg_1.html#K3" title="PRALG_1:func.3">[[:</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c9">o2</font> <a href="unialg_2.html#K2" title="UNIALG_2:func.2">/.</a> <font color="Maroon" title="c6">B1</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c10">o4</font> <a href="unialg_2.html#K2" title="UNIALG_2:func.2">/.</a> <font color="Maroon" title="c7">B3</font></span>)</span></span><a href="pralg_1.html#K3" title="PRALG_1:func.3">:]]</a></span>
<b>by </b><i><a class="txt" href="#E15:13_2"><i><font color="Green" title="E37">A38</font></i></a>, <a class="txt" href="#E16:13_2"><i><font color="Green" title="E38">A39</font></i></a>, <a class="txt" href="#E17:13_2"><i><font color="Green" title="E39">A40</font></i></a>, <a class="ref" href="funct_1.html#T9" title="FUNCT_1:th.9">FUNCT_1:9</a></i>
<br/>.= 
the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <span class="p1"><a href="pralg_1.html#K5" title="PRALG_1:func.5">[:</a><span class="default"><font color="Maroon" title="c1">U1</font>,<font color="Maroon" title="c3">U3</font></span><a href="pralg_1.html#K5" title="PRALG_1:func.5">:]</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">n</font>
<b>by </b><i><a class="txt" href="#E4:13"><i><font color="Green" title="E13">A4</font></i></a>, <a class="txt" href="#E5:13"><i><font color="Green" title="E14">A5</font></i></a>, <a class="txt" href="#E1:13_2"><i><font color="Green" title="E29">A30</font></i></a>, <a class="txt" href="#E11:13_2"><i><font color="Green" title="E33">A34</font></i></a>, <a class="txt" href="#E12:13_2"><i><font color="Green" title="E34">A35</font></i></a>, <a class="ref" href="pralg_1.html#D4" target="_self" title="PRALG_1:def.4">Def4</a></i>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E31:13"/>
( the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <span class="p1"><a href="pralg_1.html#K5" title="PRALG_1:func.5">[:</a><span class="default"><font color="Maroon" title="c1">U1</font>,<font color="Maroon" title="c3">U3</font></span><a href="pralg_1.html#K5" title="PRALG_1:func.5">:]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="unialg_2.html#K3" title="UNIALG_2:func.3">Opers</a> <span class="p1"><a href="pralg_1.html#K5" title="PRALG_1:func.5">[:</a><span class="default"><font color="Maroon" title="c2">U2</font>,<font color="Maroon" title="c4">U4</font></span><a href="pralg_1.html#K5" title="PRALG_1:func.5">:]</a></span>,<font color="Maroon" title="c5">B</font> &amp; <font color="Maroon" title="c5">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="#E13:13"><i><font color="Green" title="E19">A10</font></i></a>, <a class="txt" href="#E20:13"><i><font color="Green" title="E23">A24</font></i></a>, <a class="ref" href="finseq_2.html#T10" title="FINSEQ_2:th.10">FINSEQ_2:10</a>, <a class="ref" href="unialg_2.html#D5" title="UNIALG_2:def.5">UNIALG_2:def 5</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
