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<span class="kw">defpred </span><font color="Maroon">S<sub>1</sub></font>[   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ] <span class="kw">means </span>( <font color="Maroon" title="c2">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> $1 &amp;  <a href="unialg_2.html#K6" title="UNIALG_2:func.6">Constants</a> <font color="Maroon" title="c1">U0</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> $1 &amp; ( for <font color="Olive" title="b1">B</font> being non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">U0</font>  st <font color="Olive" title="b1">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> $1 holds <br/><font color="Olive" title="b1">B</font> is  <a href="unialg_2.html#V1" title="UNIALG_2:attr.1">opers_closed</a>  ) );<br/>
<span class="kw">set </span><font color="Maroon" title="c3">C</font> =  <a href="setfam_1.html#K9" title="SETFAM_1:func.9">bool</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">U0</font>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c4">X</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <span class="kw"> such that </span><br/><a NAME="E2:38_1_1"/><span class="lab"><font color="Green" title="E23">A2</font></span>: 
for <font color="Olive" title="b1">x</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  holds <br/> ( <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">X</font> iff ( <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="setfam_1.html#K9" title="SETFAM_1:func.9">bool</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">U0</font> &amp; <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">x</font>] ) )
 <span class="kw">from</span> <span class="lab"><a class="ref" href="xboole_0.html#S1" title="XBOOLE_0:sch.1">XBOOLE_0:sch 1</a>();<br/></span>
<span class="kw">set </span><font color="Maroon" title="c5">P</font> =  <a href="setfam_1.html#K1" title="SETFAM_1:func.1">meet</a> <font color="Maroon" title="c4">X</font>;<br/>
<a NAME="E3:38_1_1"/>
( the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">U0</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="setfam_1.html#K9" title="SETFAM_1:func.9">bool</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">U0</font> &amp; ( for <font color="Olive" title="b1">B</font> being non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">U0</font>  st <font color="Olive" title="b1">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">U0</font> holds <br/><font color="Olive" title="b1">B</font> is  <a href="unialg_2.html#V1" title="UNIALG_2:attr.1">opers_closed</a>  ) )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="unialg_2.html#T7" target="_self" title="UNIALG_2:th.7">Th7</a>, <a class="ref" href="zfmisc_1.html#D1" title="ZFMISC_1:def.1">ZFMISC_1:def 1</a></span>;<br/>
<a NAME="E4:38_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E24">A3</font></span>: 
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">U0</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">X</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:38_1_1"><span class="lab"><font color="Green" title="E23">A2</font></span></a></span>;<br/>
<a NAME="E5:38_1_1"/><span class="lab"><font color="Green" title="E25">A4</font></span>: 
 <a href="setfam_1.html#K1" title="SETFAM_1:func.1">meet</a> <font color="Maroon" title="c4">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">U0</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="38_1_1_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c6">t</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c6">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="setfam_1.html#K1" title="SETFAM_1:func.1">meet</a> <font color="Maroon" title="c4">X</font> or <font color="Maroon" title="c6">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">U0</font> )</span><br/>

<span class="kw">assume </span><a NAME="E1:38_1_1_1"/>
<font color="Maroon" title="c6">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="setfam_1.html#K1" title="SETFAM_1:func.1">meet</a> <font color="Maroon" title="c4">X</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c6">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">U0</font></span><br/>

<span class="kw">hence </span><a NAME="E2:38_1_1_1"/>
<font color="Maroon" title="c6">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">U0</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:38_1_1"><span class="lab"><font color="Green" title="E24">A3</font></span></a>, <a class="ref" href="setfam_1.html#D1" title="SETFAM_1:def.1">SETFAM_1:def 1</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="38_1_1_2"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c6">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">X</font> implies <font color="Maroon" title="c2">A</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><a href="unialg_2.html#K6" title="UNIALG_2:func.6">Constants</a> <font color="Maroon" title="c1">U0</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c6">x</font> )</span><br/><span class="kw">assume </span><a NAME="E1:38_1_1_2"/>
<font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">X</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">A</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><a href="unialg_2.html#K6" title="UNIALG_2:func.6">Constants</a> <font color="Maroon" title="c1">U0</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c6">x</font></span><br/><a NAME="E2:38_1_1_2"/><span class="kw">then </span>
( <font color="Maroon" title="c2">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c6">x</font> &amp;  <a href="unialg_2.html#K6" title="UNIALG_2:func.6">Constants</a> <font color="Maroon" title="c1">U0</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c6">x</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:38_1_1"><span class="lab"><font color="Green" title="E23">A2</font></span></a></span>;<br/><span class="kw">hence </span><a NAME="E3:38_1_1_2"/>
<font color="Maroon" title="c2">A</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><a href="unialg_2.html#K6" title="UNIALG_2:func.6">Constants</a> <font color="Maroon" title="c1">U0</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c6">x</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_1.html#T8" title="XBOOLE_1:th.8">XBOOLE_1:8</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<a NAME="E7:38_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E26">A5</font></span>: 
<font color="Maroon" title="c2">A</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><a href="unialg_2.html#K6" title="UNIALG_2:func.6">Constants</a> <font color="Maroon" title="c1">U0</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="setfam_1.html#K1" title="SETFAM_1:func.1">meet</a> <font color="Maroon" title="c4">X</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:38_1_1"><span class="lab"><font color="Green" title="E24">A3</font></span></a>, <a class="ref" href="setfam_1.html#T6" title="SETFAM_1:th.6">SETFAM_1:6</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c6">P</font> =  <a href="setfam_1.html#K1" title="SETFAM_1:func.1">meet</a> <font color="Maroon" title="c4">X</font> as  non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">U0</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:38"><span class="lab"><font color="Green" title="E22">A1</font></span></a>, <a class="txt" href="#E5:38_1_1"><span class="lab"><font color="Green" title="E25">A4</font></span></a></span>;<br/>
<span class="kw">take </span><font color="Maroon" title="c7">E</font> =  <a href="unialg_2.html#K4" title="UNIALG_2:func.4">UniAlgSetClosed</a> <font color="Maroon" title="c6">P</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c7">E</font> &amp; ( for <font color="Olive" title="b1">U1</font> being   <a href="unialg_2.html#M3" title="UNIALG_2:mode.3">SubAlgebra</a> of <font color="Maroon" title="c1">U0</font>  st <font color="Maroon" title="c2">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b1">U1</font> holds <br/><font color="Maroon" title="c7">E</font> is    <a href="unialg_2.html#M3" title="UNIALG_2:mode.3">SubAlgebra</a> of <font color="Olive" title="b1">U1</font> ) )</span><br/>

<a NAME="E9:38_1_1"/><span class="lab"><font color="Green" title="E27">A6</font></span>: 
<font color="Maroon" title="c6">P</font> is  <a href="unialg_2.html#V1" title="UNIALG_2:attr.1">opers_closed</a> 
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="38_1_1_3"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c8">o</font> be   <a href="unialg_2.html#NM5" title="UNIALG_2:NM.5">operation</a> of <font color="Maroon" title="c1">U0</font>; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="unialg_2.html#D5" target="_self" title="UNIALG_2:def.5">UNIALG_2:def 5</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c6">P</font> <a href="unialg_2.html#R2" title="UNIALG_2:pred.2">is_closed_on</a> <font color="Maroon" title="c8">o</font></span><br/><span class="kw">let </span><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="c6">P</font>; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="unialg_2.html#D4" target="_self" title="UNIALG_2:def.4">UNIALG_2:def 4</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  <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> implies <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="c6">P</font> )</span><br/>



<span class="kw">assume </span><a NAME="E1:38_1_1_3"/><span class="lab"><font color="Green" title="E28">A7</font></span>: 
 <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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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="c6">P</font></span><br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="38_1_1_3_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c10">a</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c10">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">X</font> implies <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="c10">a</font> )</span><br/><a NAME="E1:38_1_1_3_1"/><span class="lab"><font color="Green" title="E29">A8</font></span>: 
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c9">s</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c6">P</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#D4" title="FINSEQ_1:def.4">FINSEQ_1:def 4</a></span>;<br/><span class="kw">assume </span><a NAME="E2:38_1_1_3_1"/><span class="lab"><font color="Green" title="E30">A9</font></span>: 
<font color="Maroon" title="c10">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">X</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></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="c10">a</font></span><br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c11">a0</font> = <font color="Maroon" title="c10">a</font> as   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">U0</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:38_1_1"><span class="lab"><font color="Green" title="E23">A2</font></span></a></span>;<br/><a NAME="E4:38_1_1_3_1"/>
( <font color="Maroon" title="c2">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c11">a0</font> &amp;  <a href="unialg_2.html#K6" title="UNIALG_2:func.6">Constants</a> <font color="Maroon" title="c1">U0</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c11">a0</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:38_1_1"><span class="lab"><font color="Green" title="E23">A2</font></span></a>, <a class="txt" href="#E2:38_1_1_3_1"><span class="lab"><font color="Green" title="E30">A9</font></span></a></span>;<br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c12">a0</font> = <font color="Maroon" title="c11">a0</font> as  non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">U0</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:38"><span class="lab"><font color="Green" title="E22">A1</font></span></a></span>;<br/><a NAME="E6:38_1_1_3_1"/>
<font color="Maroon" title="c6">P</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c12">a0</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:38_1_1_3_1"><span class="lab"><font color="Green" title="E30">A9</font></span></a>, <a class="ref" href="setfam_1.html#T4" title="SETFAM_1:th.4">SETFAM_1:4</a></span>;<br/><a NAME="E7:38_1_1_3_1"/><span class="kw">then </span>
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c9">s</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c12">a0</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:38_1_1_3_1"><span class="lab"><font color="Green" title="E29">A8</font></span></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></span>;<br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c13">s0</font> = <font color="Maroon" title="c9">s</font> as    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of <font color="Maroon" title="c12">a0</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#D4" title="FINSEQ_1:def.4">FINSEQ_1:def 4</a></span>;<br/><a NAME="E9:38_1_1_3_1"/>
<font color="Maroon" title="c12">a0</font> is  <a href="unialg_2.html#V1" title="UNIALG_2:attr.1">opers_closed</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:38_1_1"><span class="lab"><font color="Green" title="E23">A2</font></span></a>, <a class="txt" href="#E2:38_1_1_3_1"><span class="lab"><font color="Green" title="E30">A9</font></span></a></span>;<br/><a NAME="E10:38_1_1_3_1"/><span class="kw">then </span>
<font color="Maroon" title="c12">a0</font> <a href="unialg_2.html#R2" title="UNIALG_2:pred.2">is_closed_on</a> <font color="Maroon" title="c8">o</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="unialg_2.html#D5" target="_self" title="UNIALG_2:def.5">Def5</a></span>;<br/><a NAME="E11:38_1_1_3_1"/><span class="kw">then </span>
<font color="Maroon" title="c8">o</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c13">s0</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">a0</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:38_1_1_3"><span class="lab"><font color="Green" title="E28">A7</font></span></a>, <a class="ref" href="unialg_2.html#D4" target="_self" title="UNIALG_2:def.4">Def4</a></span>;<br/><span class="kw">hence </span><a NAME="E12:38_1_1_3_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="c10">a</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E3:38_1_1_3"/>
<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="c6">P</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:38_1_1"><span class="lab"><font color="Green" title="E24">A3</font></span></a>, <a class="ref" href="setfam_1.html#D1" title="SETFAM_1:def.1">SETFAM_1:def 1</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<a NAME="E10:38_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E28">A10</font></span>: 
<font color="Maroon" title="c7">E</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="unialg_1.html#G1" title="UNIALG_1:aggr.1">UAStr</a>(# <font color="Maroon" title="c6">P</font>,<span class="p1">(<span class="default"><a href="unialg_2.html#K3" title="UNIALG_2:func.3">Opers</a> <font color="Maroon" title="c1">U0</font>,<font color="Maroon" title="c6">P</font></span>)</span> #)
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="unialg_2.html#D9" target="_self" title="UNIALG_2:def.9">Def9</a></span>;<br/>
<a NAME="E11:38_1_1"/>
<font color="Maroon" title="c2">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">A</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><a href="unialg_2.html#K6" title="UNIALG_2:func.6">Constants</a> <font color="Maroon" title="c1">U0</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_1.html#T7" title="XBOOLE_1:th.7">XBOOLE_1:7</a></span>;<br/>
<span class="kw">hence </span><a NAME="E12:38_1_1"/>
<font color="Maroon" title="c2">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c7">E</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:38_1_1"><span class="lab"><font color="Green" title="E26">A5</font></span></a>, <a class="txt" href="#E10:38_1_1"><span class="lab"><font color="Green" title="E28">A10</font></span></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">U1</font> being   <a href="unialg_2.html#M3" title="UNIALG_2:mode.3">SubAlgebra</a> of <font color="Maroon" title="c1">U0</font>  st <font color="Maroon" title="c2">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b1">U1</font> holds <br/><font color="Maroon" title="c7">E</font> is    <a href="unialg_2.html#M3" title="UNIALG_2:mode.3">SubAlgebra</a> of <font color="Olive" title="b1">U1</font></span><br/>

<span class="kw">let </span><font color="Maroon" title="c8">U1</font> be    <a href="unialg_2.html#M3" title="UNIALG_2:mode.3">SubAlgebra</a> of <font color="Maroon" title="c1">U0</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c8">U1</font> implies <font color="Maroon" title="c7">E</font> is    <a href="unialg_2.html#M3" title="UNIALG_2:mode.3">SubAlgebra</a> of <font color="Maroon" title="c8">U1</font> )</span><br/>

<span class="kw">assume </span><a NAME="E13:38_1_1"/><span class="lab"><font color="Green" title="E29">A11</font></span>: 
<font color="Maroon" title="c2">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c8">U1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c7">E</font> is    <a href="unialg_2.html#M3" title="UNIALG_2:mode.3">SubAlgebra</a> of <font color="Maroon" title="c8">U1</font></span><br/>

<span class="kw">set </span><font color="Maroon" title="c9">u1</font> = the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c8">U1</font>;<br/>
<a NAME="E14:38_1_1"/><span class="lab"><font color="Green" title="E30">A12</font></span>: 
 <a href="unialg_2.html#K6" title="UNIALG_2:func.6">Constants</a> <font color="Maroon" title="c1">U0</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c8">U1</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="38_1_1_4"><span class="kw">proof </span></a><div class="add">

<span class="kw">reconsider </span><font color="Maroon" title="c10">B</font> = the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c8">U1</font> as  non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">U0</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="unialg_2.html#D8" target="_self" title="UNIALG_2:def.8">Def8</a></span>;<br/>
<span class="kw">let </span><font color="Maroon" title="c11">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c11">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="unialg_2.html#K6" title="UNIALG_2:func.6">Constants</a> <font color="Maroon" title="c1">U0</font> or <font color="Maroon" title="c11">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c8">U1</font> )</span><br/>

<span class="kw">assume </span><a NAME="E2:38_1_1_4"/>
<font color="Maroon" title="c11">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="unialg_2.html#K6" title="UNIALG_2:func.6">Constants</a> <font color="Maroon" title="c1">U0</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c11">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c8">U1</font></span><br/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c12">a</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">U0</font><span class="kw"> such that </span><br/><a NAME="E4:38_1_1_4"/><span class="lab"><font color="Green" title="E31">A13</font></span>: 
<font color="Maroon" title="c12">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">x</font>
 <span class="kw">and </span><br/><a NAME="E5:38_1_1_4"/><span class="lab"><font color="Green" title="E32">A14</font></span>: 
 ex <font color="Olive" title="b1">o</font> being  <a href="unialg_2.html#NM5" title="UNIALG_2:NM.5">operation</a> of <font color="Maroon" title="c1">U0</font> st <br/>(  <a href="unialg_1.html#K3" title="UNIALG_1:func.3">arity</a> <font color="Olive" title="b1">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp; <font color="Maroon" title="c12">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Olive" title="b1">o</font> )
 ;<br/>
<span class="kw">consider </span><font color="Maroon" title="c13">o0</font> being   <a href="unialg_2.html#NM5" title="UNIALG_2:NM.5">operation</a> of <font color="Maroon" title="c1">U0</font><span class="kw"> such that </span><br/><a NAME="E7:38_1_1_4"/><span class="lab"><font color="Green" title="E33">A15</font></span>: 
 <a href="unialg_1.html#K3" title="UNIALG_1:func.3">arity</a> <font color="Maroon" title="c13">o0</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <span class="kw">and </span><br/><a NAME="E8:38_1_1_4"/><span class="lab"><font color="Green" title="E34">A16</font></span>: 
<font color="Maroon" title="c12">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c13">o0</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:38_1_1_4"><span class="lab"><font color="Green" title="E32">A14</font></span></a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c14">y</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <span class="kw"> such that </span><br/><a NAME="E10:38_1_1_4"/><span class="lab"><font color="Green" title="E35">A17</font></span>: 
<font color="Maroon" title="c14">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c13">o0</font>
 <span class="kw">and </span><br/><a NAME="E11:38_1_1_4"/><span class="lab"><font color="Green" title="E36">A18</font></span>: 
<font color="Maroon" title="c12">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">o0</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c14">y</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:38_1_1_4"><span class="lab"><font color="Green" title="E34">A16</font></span></a>, <a class="ref" href="funct_1.html#D5" title="FUNCT_1:def.5">FUNCT_1:def 5</a></span>;<br/>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c13">o0</font> = 
<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">U0</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:38_1_1_4"><span class="lab"><font color="Green" title="E33">A15</font></span></a>, <a class="ref" href="unialg_2.html#T2" target="_self" title="UNIALG_2:th.2">Th2</a></span>
<br/>.= 
<span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K6" title="FINSEQ_1:func.6">&lt;*&gt;</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">U0</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_2.html#T112" title="FINSEQ_2:th.112">FINSEQ_2:112</a></span>
;<br/>
<a NAME="E13:38_1_1_4"/><span class="kw">then </span>
<font color="Maroon" title="c14">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K6" title="FINSEQ_1:func.6">&lt;*&gt;</a> <font color="Maroon" title="c10">B</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:38_1_1_4"><span class="lab"><font color="Green" title="E35">A17</font></span></a></span>;<br/>
<a NAME="E14:38_1_1_4"/><span class="kw">then </span>
<font color="Maroon" title="c14">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <font color="Maroon" title="c10">B</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_2.html#T112" title="FINSEQ_2:th.112">FINSEQ_2:112</a></span>;<br/>
<a NAME="E15:38_1_1_4"/><span class="kw">then </span>
<font color="Maroon" title="c14">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c13">o0</font></span>)</span> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="unialg_1.html#K3" title="UNIALG_1:func.3">arity</a> <font color="Maroon" title="c13">o0</font></span>)</span> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <font color="Maroon" title="c10">B</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:38_1_1_4"><span class="lab"><font color="Green" title="E33">A15</font></span></a>, <a class="txt" href="#E10:38_1_1_4"><span class="lab"><font color="Green" title="E35">A17</font></span></a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></span>;<br/>
<a NAME="E16:38_1_1_4"/><span class="kw">then </span><span class="lab"><font color="Green" title="E37">A19</font></span>: 
<font color="Maroon" title="c14">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c13">o0</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="unialg_1.html#K3" title="UNIALG_1:func.3">arity</a> <font color="Maroon" title="c13">o0</font></span>)</span> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <font color="Maroon" title="c10">B</font></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#T90" title="RELAT_1:th.90">RELAT_1:90</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c15">n</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a><span class="kw"> such that </span><br/><a NAME="E18:38_1_1_4"/><span class="lab"><font color="Green" title="E38">A20</font></span>: 
<font color="Maroon" title="c15">n</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <font color="Maroon" title="c1">U0</font>
 <span class="kw">and </span><br/><a NAME="E19:38_1_1_4"/><span class="lab"><font color="Green" title="E39">A21</font></span>: 
the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <font color="Maroon" title="c1">U0</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c15">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">o0</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_2.html#T11" title="FINSEQ_2:th.11">FINSEQ_2:11</a></span>;<br/>
<a NAME="E20:38_1_1_4"/><span class="lab"><font color="Green" title="E40">A22</font></span>: 
<font color="Maroon" title="c15">n</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <font color="Maroon" title="c8">U1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E18:38_1_1_4"><span class="lab"><font color="Green" title="E38">A20</font></span></a>, <a class="ref" href="unialg_2.html#T10" target="_self" title="UNIALG_2:th.10">Th10</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c16">o1</font> = the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <font color="Maroon" title="c8">U1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c15">n</font> as   <a href="unialg_2.html#NM5" title="UNIALG_2:NM.5">operation</a> of <font color="Maroon" title="c8">U1</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_1.html#D5" title="FUNCT_1:def.5">FUNCT_1:def 5</a></span>;<br/>
<a NAME="E22:38_1_1_4"/>
the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <font color="Maroon" title="c8">U1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="unialg_2.html#K3" title="UNIALG_2:func.3">Opers</a> <font color="Maroon" title="c1">U0</font>,<font color="Maroon" title="c10">B</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="unialg_2.html#D8" target="_self" title="UNIALG_2:def.8">Def8</a></span>;<br/>
<a NAME="E23:38_1_1_4"/><span class="kw">then </span><span class="lab"><font color="Green" title="E41">A23</font></span>: 
<font color="Maroon" title="c16">o1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">o0</font> <a href="unialg_2.html#K2" title="UNIALG_2:func.2">/.</a> <font color="Maroon" title="c10">B</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:38_1_1_4"><span class="lab"><font color="Green" title="E39">A21</font></span></a>, <a class="txt" href="#E20:38_1_1_4"><span class="lab"><font color="Green" title="E40">A22</font></span></a>, <a class="ref" href="unialg_2.html#D7" target="_self" title="UNIALG_2:def.7">Def7</a></span>;<br/>
<a NAME="E24:38_1_1_4"/>
<font color="Maroon" title="c10">B</font> is  <a href="unialg_2.html#V1" title="UNIALG_2:attr.1">opers_closed</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="unialg_2.html#D8" target="_self" title="UNIALG_2:def.8">Def8</a></span>;<br/>
<a NAME="E25:38_1_1_4"/><span class="kw">then </span><span class="lab"><font color="Green" title="E42">A24</font></span>: 
<font color="Maroon" title="c10">B</font> <a href="unialg_2.html#R2" title="UNIALG_2:pred.2">is_closed_on</a> <font color="Maroon" title="c13">o0</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="unialg_2.html#D5" target="_self" title="UNIALG_2:def.5">Def5</a></span>;<br/>
<a NAME="E26:38_1_1_4"/><span class="kw">then </span>
<font color="Maroon" title="c14">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c13">o0</font> <a href="unialg_2.html#K2" title="UNIALG_2:func.2">/.</a> <font color="Maroon" title="c10">B</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E16:38_1_1_4"><span class="lab"><font color="Green" title="E37">A19</font></span></a>, <a class="ref" href="unialg_2.html#D6" target="_self" title="UNIALG_2:def.6">Def6</a></span>;<br/>
<a NAME="E27:38_1_1_4"/><span class="kw">then </span><span class="lab"><font color="Green" title="E43">A25</font></span>: 
<font color="Maroon" title="c16">o1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c14">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c16">o1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E23:38_1_1_4"><span class="lab"><font color="Green" title="E41">A23</font></span></a>, <a class="ref" href="funct_1.html#D5" title="FUNCT_1:def.5">FUNCT_1:def 5</a></span>;<br/>
<a NAME="E28:38_1_1_4"/><span class="lab"><font color="Green" title="E44">A26</font></span>: 
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c16">o1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c8">U1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#D19" title="RELAT_1:def.19">RELAT_1:def 19</a></span>;<br/>
<font color="Maroon" title="c16">o1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c14">y</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c13">o0</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="unialg_1.html#K3" title="UNIALG_1:func.3">arity</a> <font color="Maroon" title="c13">o0</font></span>)</span> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <font color="Maroon" title="c10">B</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c14">y</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E23:38_1_1_4"><span class="lab"><font color="Green" title="E41">A23</font></span></a>, <a class="txt" href="#E25:38_1_1_4"><span class="lab"><font color="Green" title="E42">A24</font></span></a>, <a class="ref" href="unialg_2.html#D6" target="_self" title="UNIALG_2:def.6">Def6</a></span>
<br/>.= 
<font color="Maroon" title="c12">a</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:38_1_1_4"><span class="lab"><font color="Green" title="E36">A18</font></span></a>, <a class="txt" href="#E16:38_1_1_4"><span class="lab"><font color="Green" title="E37">A19</font></span></a>, <a class="ref" href="funct_1.html#T70" title="FUNCT_1:th.70">FUNCT_1:70</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E30:38_1_1_4"/>
<font color="Maroon" title="c11">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c8">U1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:38_1_1_4"><span class="lab"><font color="Green" title="E31">A13</font></span></a>, <a class="txt" href="#E27:38_1_1_4"><span class="lab"><font color="Green" title="E43">A25</font></span></a>, <a class="txt" href="#E28:38_1_1_4"><span class="lab"><font color="Green" title="E44">A26</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<a NAME="E15:38_1_1"/>
( the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c8">U1</font> is   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">U0</font> &amp; ( for <font color="Olive" title="b1">B</font> being non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">U0</font>  st <font color="Olive" title="b1">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c8">U1</font> holds <br/><font color="Olive" title="b1">B</font> is  <a href="unialg_2.html#V1" title="UNIALG_2:attr.1">opers_closed</a>  ) )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="unialg_2.html#D8" target="_self" title="UNIALG_2:def.8">Def8</a></span>;<br/>
<a NAME="E16:38_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E31">A27</font></span>: 
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c8">U1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">X</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:38_1_1"><span class="lab"><font color="Green" title="E23">A2</font></span></a>, <a class="txt" href="#E13:38_1_1"><span class="lab"><font color="Green" title="E29">A11</font></span></a>, <a class="txt" href="#E14:38_1_1"><span class="lab"><font color="Green" title="E30">A12</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E17:38_1_1"/>
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c7">E</font> is   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c8">U1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:38_1_1"><span class="lab"><font color="Green" title="E28">A10</font></span></a>, <a class="ref" href="setfam_1.html#T4" title="SETFAM_1:th.4">SETFAM_1:4</a></span>; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="unialg_2.html#D8" target="_self" title="UNIALG_2:def.8">UNIALG_2:def 8</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">B</font> being non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c8">U1</font>  st <font color="Olive" title="b1">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c7">E</font> holds <br/>( the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <font color="Maroon" title="c7">E</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="unialg_2.html#K3" title="UNIALG_2:func.3">Opers</a> <font color="Maroon" title="c8">U1</font>,<font color="Olive" title="b1">B</font> &amp; <font color="Olive" title="b1">B</font> is  <a href="unialg_2.html#V1" title="UNIALG_2:attr.1">opers_closed</a>  )</span><br/>

<span class="kw">let </span><font color="Maroon" title="c10">B</font> be  non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c8">U1</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c10">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c7">E</font> implies ( the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <font color="Maroon" title="c7">E</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="unialg_2.html#K3" title="UNIALG_2:func.3">Opers</a> <font color="Maroon" title="c8">U1</font>,<font color="Maroon" title="c10">B</font> &amp; <font color="Maroon" title="c10">B</font> is  <a href="unialg_2.html#V1" title="UNIALG_2:attr.1">opers_closed</a>  ) )</span><br/>

<span class="kw">assume </span><a NAME="E18:38_1_1"/><span class="lab"><font color="Green" title="E32">A28</font></span>: 
<font color="Maroon" title="c10">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c7">E</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <font color="Maroon" title="c7">E</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="unialg_2.html#K3" title="UNIALG_2:func.3">Opers</a> <font color="Maroon" title="c8">U1</font>,<font color="Maroon" title="c10">B</font> &amp; <font color="Maroon" title="c10">B</font> is  <a href="unialg_2.html#V1" title="UNIALG_2:attr.1">opers_closed</a>  )</span><br/>

<span class="kw">reconsider </span><font color="Maroon" title="c11">u11</font> = the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c8">U1</font> as  non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">U0</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="unialg_2.html#D8" target="_self" title="UNIALG_2:def.8">Def8</a></span>;<br/>
<a NAME="E20:38_1_1"/><span class="lab"><font color="Green" title="E33">A29</font></span>: 
the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <font color="Maroon" title="c8">U1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="unialg_2.html#K3" title="UNIALG_2:func.3">Opers</a> <font color="Maroon" title="c1">U0</font>,<font color="Maroon" title="c11">u11</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="unialg_2.html#D8" target="_self" title="UNIALG_2:def.8">Def8</a></span>;<br/>
<a NAME="E21:38_1_1"/><span class="lab"><font color="Green" title="E34">A30</font></span>: 
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <font color="Maroon" title="c1">U0</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="unialg_2.html#K3" title="UNIALG_2:func.3">Opers</a> <font color="Maroon" title="c1">U0</font>,<font color="Maroon" title="c11">u11</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="unialg_2.html#D7" target="_self" title="UNIALG_2:def.7">Def7</a></span>;<br/>
<a NAME="E22:38_1_1"/><span class="lab"><font color="Green" title="E35">A31</font></span>: 
<font color="Maroon" title="c11">u11</font> is  <a href="unialg_2.html#V1" title="UNIALG_2:attr.1">opers_closed</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="unialg_2.html#D8" target="_self" title="UNIALG_2:def.8">Def8</a></span>;<br/>
<div><span class="lab"><font color="Green" title="E36">A32</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="38_1_1_5"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c12">o1</font> be   <a href="unialg_2.html#NM5" title="UNIALG_2:NM.5">operation</a> of <font color="Maroon" title="c8">U1</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c10">B</font> <a href="unialg_2.html#R2" title="UNIALG_2:pred.2">is_closed_on</a> <font color="Maroon" title="c12">o1</font></span><br/><span class="kw">consider </span><font color="Maroon" title="c13">n</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a><span class="kw"> such that </span><br/><a NAME="E2:38_1_1_5"/><span class="lab"><font color="Green" title="E37">A33</font></span>: 
<font color="Maroon" title="c13">n</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <font color="Maroon" title="c8">U1</font>
 <span class="kw">and </span><br/><a NAME="E3:38_1_1_5"/><span class="lab"><font color="Green" title="E38">A34</font></span>: 
<font color="Maroon" title="c12">o1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <font color="Maroon" title="c8">U1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c13">n</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_2.html#T11" title="FINSEQ_2:th.11">FINSEQ_2:11</a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c14">o0</font> = the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <font color="Maroon" title="c1">U0</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c13">n</font> as   <a href="unialg_2.html#NM5" title="UNIALG_2:NM.5">operation</a> of <font color="Maroon" title="c1">U0</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E20:38_1_1"><span class="lab"><font color="Green" title="E33">A29</font></span></a>, <a class="txt" href="#E21:38_1_1"><span class="lab"><font color="Green" title="E34">A30</font></span></a>, <a class="txt" href="#E2:38_1_1_5"><span class="lab"><font color="Green" title="E37">A33</font></span></a>, <a class="ref" href="funct_1.html#D5" title="FUNCT_1:def.5">FUNCT_1:def 5</a></span>;<br/><a NAME="E5:38_1_1_5"/><span class="lab"><font color="Green" title="E39">A35</font></span>: 
 <a href="unialg_1.html#K3" title="UNIALG_1:func.3">arity</a> <font color="Maroon" title="c14">o0</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="unialg_1.html#K3" title="UNIALG_1:func.3">arity</a> <font color="Maroon" title="c12">o1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:38_1_1_5"><span class="lab"><font color="Green" title="E37">A33</font></span></a>, <a class="txt" href="#E3:38_1_1_5"><span class="lab"><font color="Green" title="E38">A34</font></span></a>, <a class="ref" href="unialg_2.html#T9" target="_self" title="UNIALG_2:th.9">Th9</a></span>;<br/><a NAME="E6:38_1_1_5"/><span class="lab"><font color="Green" title="E40">A36</font></span>: 
<font color="Maroon" title="c11">u11</font> <a href="unialg_2.html#R2" title="UNIALG_2:pred.2">is_closed_on</a> <font color="Maroon" title="c14">o0</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E22:38_1_1"><span class="lab"><font color="Green" title="E35">A31</font></span></a>, <a class="ref" href="unialg_2.html#D5" target="_self" title="UNIALG_2:def.5">Def5</a></span>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="38_1_1_5_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c15">s</font> be    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of <font color="Maroon" title="c10">B</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c15">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="unialg_1.html#K3" title="UNIALG_1:func.3">arity</a> <font color="Maroon" title="c12">o1</font> implies <font color="Maroon" title="c12">o1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c15">s</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">B</font> )</span><br/><a NAME="E1:38_1_1_5_1"/><span class="lab"><font color="Green" title="E41">A37</font></span>: 
<font color="Maroon" title="c6">P</font> <a href="unialg_2.html#R2" title="UNIALG_2:pred.2">is_closed_on</a> <font color="Maroon" title="c14">o0</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:38_1_1"><span class="lab"><font color="Green" title="E27">A6</font></span></a>, <a class="ref" href="unialg_2.html#D5" target="_self" title="UNIALG_2:def.5">Def5</a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c16">sE</font> = <font color="Maroon" title="c15">s</font> as    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <font color="Maroon" title="c6">P</font> <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a>  <span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:38_1_1"><span class="lab"><font color="Green" title="E28">A10</font></span></a>, <a class="txt" href="#E18:38_1_1"><span class="lab"><font color="Green" title="E32">A28</font></span></a>, <a class="ref" href="finseq_1.html#D11" title="FINSEQ_1:def.11">FINSEQ_1:def 11</a></span>;<br/><a NAME="E3:38_1_1_5_1"/>
<font color="Maroon" title="c15">s</font> is    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of <font color="Maroon" title="c11">u11</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_2.html#T27" title="FINSEQ_2:th.27">FINSEQ_2:27</a></span>;<br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c17">s1</font> = <font color="Maroon" title="c15">s</font> as    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <font color="Maroon" title="c11">u11</font> <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a>  <span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#D11" title="FINSEQ_1:def.11">FINSEQ_1:def 11</a></span>;<br/><span class="lab"><font color="Green" title="E42">A38</font></span>:  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c14">o0</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="unialg_1.html#K3" title="UNIALG_1:func.3">arity</a> <font color="Maroon" title="c14">o0</font></span>)</span> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <font color="Maroon" title="c11">u11</font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c14">o0</font></span>)</span> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="unialg_1.html#K3" title="UNIALG_1:func.3">arity</a> <font color="Maroon" title="c14">o0</font></span>)</span> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <font color="Maroon" title="c11">u11</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#T90" title="RELAT_1:th.90">RELAT_1:90</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="unialg_1.html#K3" title="UNIALG_1:func.3">arity</a> <font color="Maroon" title="c14">o0</font></span>)</span> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">U0</font></span>)</span> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="unialg_1.html#K3" title="UNIALG_1:func.3">arity</a> <font color="Maroon" title="c14">o0</font></span>)</span> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <font color="Maroon" title="c11">u11</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="unialg_2.html#T2" target="_self" title="UNIALG_2:th.2">Th2</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="unialg_1.html#K3" title="UNIALG_1:func.3">arity</a> <font color="Maroon" title="c14">o0</font></span>)</span> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <font color="Maroon" title="c11">u11</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="unialg_2.html#T1" target="_self" title="UNIALG_2:th.1">Th1</a></span>
;<br/><span class="kw">assume </span><a NAME="E6:38_1_1_5_1"/><span class="lab"><font color="Green" title="E43">A39</font></span>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c15">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="unialg_1.html#K3" title="UNIALG_1:func.3">arity</a> <font color="Maroon" title="c12">o1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c12">o1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c15">s</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">B</font></span><br/><a NAME="E7:38_1_1_5_1"/><span class="kw">then </span>
<font color="Maroon" title="c17">s1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <font color="Olive" title="b1">q</font> where <font color="Olive" title="b1">q</font> is    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <font color="Maroon" title="c11">u11</font> <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a>  :  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b1">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="unialg_1.html#K3" title="UNIALG_1:func.3">arity</a> <font color="Maroon" title="c14">o0</font> </span>}</span> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:38_1_1_5"><span class="lab"><font color="Green" title="E39">A35</font></span></a></span>;<br/><a NAME="E8:38_1_1_5_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E44">A40</font></span>: 
<font color="Maroon" title="c17">s1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c14">o0</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="unialg_1.html#K3" title="UNIALG_1:func.3">arity</a> <font color="Maroon" title="c14">o0</font></span>)</span> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <font color="Maroon" title="c11">u11</font></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:38_1_1_5_1"><span class="lab"><font color="Green" title="E42">A38</font></span></a>, <a class="ref" href="finseq_2.html#D4" title="FINSEQ_2:def.4">FINSEQ_2:def 4</a></span>;<br/><font color="Maroon" title="c12">o1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c15">s</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c14">o0</font> <a href="unialg_2.html#K2" title="UNIALG_2:func.2">/.</a> <font color="Maroon" title="c11">u11</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c17">s1</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E20:38_1_1"><span class="lab"><font color="Green" title="E33">A29</font></span></a>, <a class="txt" href="#E2:38_1_1_5"><span class="lab"><font color="Green" title="E37">A33</font></span></a>, <a class="txt" href="#E3:38_1_1_5"><span class="lab"><font color="Green" title="E38">A34</font></span></a>, <a class="ref" href="unialg_2.html#D7" target="_self" title="UNIALG_2:def.7">Def7</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c14">o0</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="unialg_1.html#K3" title="UNIALG_1:func.3">arity</a> <font color="Maroon" title="c14">o0</font></span>)</span> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <font color="Maroon" title="c11">u11</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c17">s1</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:38_1_1_5"><span class="lab"><font color="Green" title="E40">A36</font></span></a>, <a class="ref" href="unialg_2.html#D6" target="_self" title="UNIALG_2:def.6">Def6</a></span>
<br/>.= 
<font color="Maroon" title="c14">o0</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c16">sE</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:38_1_1_5_1"><span class="lab"><font color="Green" title="E44">A40</font></span></a>, <a class="ref" href="funct_1.html#T70" title="FUNCT_1:th.70">FUNCT_1:70</a></span>
;<br/><span class="kw">hence </span><a NAME="E10:38_1_1_5_1"/>
<font color="Maroon" title="c12">o1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c15">s</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">B</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:38_1_1"><span class="lab"><font color="Green" title="E28">A10</font></span></a>, <a class="txt" href="#E18:38_1_1"><span class="lab"><font color="Green" title="E32">A28</font></span></a>, <a class="txt" href="#E5:38_1_1_5"><span class="lab"><font color="Green" title="E39">A35</font></span></a>, <a class="txt" href="#E6:38_1_1_5_1"><span class="lab"><font color="Green" title="E43">A39</font></span></a>, <a class="txt" href="#E1:38_1_1_5_1"><span class="lab"><font color="Green" title="E41">A37</font></span></a>, <a class="ref" href="unialg_2.html#D4" target="_self" title="UNIALG_2:def.4">Def4</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><span class="kw">hence </span><a NAME="E8:38_1_1_5"/>
<font color="Maroon" title="c10">B</font> <a href="unialg_2.html#R2" title="UNIALG_2:pred.2">is_closed_on</a> <font color="Maroon" title="c12">o1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="unialg_2.html#D4" target="_self" title="UNIALG_2:def.4">Def4</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<a NAME="E24:38_1_1"/><span class="lab"><font color="Green" title="E37">A41</font></span>: 
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="unialg_2.html#K3" title="UNIALG_2:func.3">Opers</a> <font color="Maroon" title="c8">U1</font>,<font color="Maroon" title="c10">B</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <font color="Maroon" title="c8">U1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="unialg_2.html#D7" target="_self" title="UNIALG_2:def.7">Def7</a></span>;<br/>
<a NAME="E25:38_1_1"/><span class="lab"><font color="Green" title="E38">A42</font></span>: 
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <font color="Maroon" title="c1">U0</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="unialg_2.html#K3" title="UNIALG_2:func.3">Opers</a> <font color="Maroon" title="c1">U0</font>,<font color="Maroon" title="c6">P</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="unialg_2.html#D7" target="_self" title="UNIALG_2:def.7">Def7</a></span>;<br/>
<a NAME="E26:38_1_1"/><span class="lab"><font color="Green" title="E39">A43</font></span>: 
<font color="Maroon" title="c6">P</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c8">U1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E16:38_1_1"><span class="lab"><font color="Green" title="E31">A27</font></span></a>, <a class="ref" href="setfam_1.html#T4" title="SETFAM_1:th.4">SETFAM_1:4</a></span>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="38_1_1_6"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c12">n</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c12">n</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <font color="Maroon" title="c1">U0</font> implies the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <font color="Maroon" title="c7">E</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c12">n</font> <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> <font color="Maroon" title="c8">U1</font>,<font color="Maroon" title="c10">B</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c12">n</font> )</span><br/><span class="kw">assume </span><a NAME="E1:38_1_1_6"/><span class="lab"><font color="Green" title="E40">A44</font></span>: 
<font color="Maroon" title="c12">n</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <font color="Maroon" title="c1">U0</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <font color="Maroon" title="c7">E</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c12">n</font> <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> <font color="Maroon" title="c8">U1</font>,<font color="Maroon" title="c10">B</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c12">n</font></span><br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c13">o0</font> = the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <font color="Maroon" title="c1">U0</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c12">n</font> as   <a href="unialg_2.html#NM5" title="UNIALG_2:NM.5">operation</a> of <font color="Maroon" title="c1">U0</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_1.html#D5" title="FUNCT_1:def.5">FUNCT_1:def 5</a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c14">o1</font> = the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <font color="Maroon" title="c8">U1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c12">n</font> as   <a href="unialg_2.html#NM5" title="UNIALG_2:NM.5">operation</a> of <font color="Maroon" title="c8">U1</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E20:38_1_1"><span class="lab"><font color="Green" title="E33">A29</font></span></a>, <a class="txt" href="#E21:38_1_1"><span class="lab"><font color="Green" title="E34">A30</font></span></a>, <a class="txt" href="#E1:38_1_1_6"><span class="lab"><font color="Green" title="E40">A44</font></span></a>, <a class="ref" href="funct_1.html#D5" title="FUNCT_1:def.5">FUNCT_1:def 5</a></span>;<br/><a NAME="E4:38_1_1_6"/><span class="lab"><font color="Green" title="E41">A45</font></span>: 
<font color="Maroon" title="c11">u11</font> <a href="unialg_2.html#R2" title="UNIALG_2:pred.2">is_closed_on</a> <font color="Maroon" title="c13">o0</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E22:38_1_1"><span class="lab"><font color="Green" title="E35">A31</font></span></a>, <a class="ref" href="unialg_2.html#D5" target="_self" title="UNIALG_2:def.5">Def5</a></span>;<br/><a NAME="E5:38_1_1_6"/><span class="lab"><font color="Green" title="E42">A46</font></span>: 
<font color="Maroon" title="c6">P</font> <a href="unialg_2.html#R2" title="UNIALG_2:pred.2">is_closed_on</a> <font color="Maroon" title="c13">o0</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:38_1_1"><span class="lab"><font color="Green" title="E27">A6</font></span></a>, <a class="ref" href="unialg_2.html#D5" target="_self" title="UNIALG_2:def.5">Def5</a></span>;<br/><span class="kw">thus </span>the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <font color="Maroon" title="c7">E</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c12">n</font> = 
<font color="Maroon" title="c13">o0</font> <a href="unialg_2.html#K2" title="UNIALG_2:func.2">/.</a> <font color="Maroon" title="c6">P</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:38_1_1"><span class="lab"><font color="Green" title="E28">A10</font></span></a>, <a class="txt" href="#E25:38_1_1"><span class="lab"><font color="Green" title="E38">A42</font></span></a>, <a class="txt" href="#E1:38_1_1_6"><span class="lab"><font color="Green" title="E40">A44</font></span></a>, <a class="ref" href="unialg_2.html#D7" target="_self" title="UNIALG_2:def.7">Def7</a></span>
<br/>.= 
<font color="Maroon" title="c13">o0</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="unialg_1.html#K3" title="UNIALG_1:func.3">arity</a> <font color="Maroon" title="c13">o0</font></span>)</span> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <font color="Maroon" title="c6">P</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:38_1_1_6"><span class="lab"><font color="Green" title="E42">A46</font></span></a>, <a class="ref" href="unialg_2.html#D6" target="_self" title="UNIALG_2:def.6">Def6</a></span>
<br/>.= 
<font color="Maroon" title="c13">o0</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="unialg_1.html#K3" title="UNIALG_1:func.3">arity</a> <font color="Maroon" title="c13">o0</font></span>)</span> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <font color="Maroon" title="c11">u11</font></span>)</span> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="unialg_1.html#K3" title="UNIALG_1:func.3">arity</a> <font color="Maroon" title="c13">o0</font></span>)</span> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <font color="Maroon" title="c6">P</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E26:38_1_1"><span class="lab"><font color="Green" title="E39">A43</font></span></a>, <a class="ref" href="unialg_2.html#T1" target="_self" title="UNIALG_2:th.1">Th1</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c13">o0</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="unialg_1.html#K3" title="UNIALG_1:func.3">arity</a> <font color="Maroon" title="c13">o0</font></span>)</span> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <font color="Maroon" title="c11">u11</font></span>)</span></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="unialg_1.html#K3" title="UNIALG_1:func.3">arity</a> <font color="Maroon" title="c13">o0</font></span>)</span> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <font color="Maroon" title="c6">P</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#T100" title="RELAT_1:th.100">RELAT_1:100</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c13">o0</font> <a href="unialg_2.html#K2" title="UNIALG_2:func.2">/.</a> <font color="Maroon" title="c11">u11</font></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="unialg_1.html#K3" title="UNIALG_1:func.3">arity</a> <font color="Maroon" title="c13">o0</font></span>)</span> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <font color="Maroon" title="c6">P</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:38_1_1_6"><span class="lab"><font color="Green" title="E41">A45</font></span></a>, <a class="ref" href="unialg_2.html#D6" target="_self" title="UNIALG_2:def.6">Def6</a></span>
<br/>.= 
<font color="Maroon" title="c14">o1</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="unialg_1.html#K3" title="UNIALG_1:func.3">arity</a> <font color="Maroon" title="c13">o0</font></span>)</span> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <font color="Maroon" title="c6">P</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E20:38_1_1"><span class="lab"><font color="Green" title="E33">A29</font></span></a>, <a class="txt" href="#E21:38_1_1"><span class="lab"><font color="Green" title="E34">A30</font></span></a>, <a class="txt" href="#E1:38_1_1_6"><span class="lab"><font color="Green" title="E40">A44</font></span></a>, <a class="ref" href="unialg_2.html#D7" target="_self" title="UNIALG_2:def.7">Def7</a></span>
<br/>.= 
<font color="Maroon" title="c14">o1</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="unialg_1.html#K3" title="UNIALG_1:func.3">arity</a> <font color="Maroon" title="c14">o1</font></span>)</span> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <font color="Maroon" title="c10">B</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:38_1_1"><span class="lab"><font color="Green" title="E28">A10</font></span></a>, <a class="txt" href="#E18:38_1_1"><span class="lab"><font color="Green" title="E32">A28</font></span></a>, <a class="txt" href="#E20:38_1_1"><span class="lab"><font color="Green" title="E33">A29</font></span></a>, <a class="txt" href="#E21:38_1_1"><span class="lab"><font color="Green" title="E34">A30</font></span></a>, <a class="txt" href="#E1:38_1_1_6"><span class="lab"><font color="Green" title="E40">A44</font></span></a>, <a class="ref" href="unialg_2.html#T9" target="_self" title="UNIALG_2:th.9">Th9</a></span>
<br/>.= 
<font color="Maroon" title="c14">o1</font> <a href="unialg_2.html#K2" title="UNIALG_2:func.2">/.</a> <font color="Maroon" title="c10">B</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E23:38_1_1"><span class="lab"><font color="Green" title="E36">A32</font></span></a>, <a class="ref" href="unialg_2.html#D6" target="_self" title="UNIALG_2:def.6">Def6</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="unialg_2.html#K3" title="UNIALG_2:func.3">Opers</a> <font color="Maroon" title="c8">U1</font>,<font color="Maroon" title="c10">B</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c12">n</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E20:38_1_1"><span class="lab"><font color="Green" title="E33">A29</font></span></a>, <a class="txt" href="#E21:38_1_1"><span class="lab"><font color="Green" title="E34">A30</font></span></a>, <a class="txt" href="#E24:38_1_1"><span class="lab"><font color="Green" title="E37">A41</font></span></a>, <a class="txt" href="#E1:38_1_1_6"><span class="lab"><font color="Green" title="E40">A44</font></span></a>, <a class="ref" href="unialg_2.html#D7" target="_self" title="UNIALG_2:def.7">Def7</a></span>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E28:38_1_1"/>
( the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <font color="Maroon" title="c7">E</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="unialg_2.html#K3" title="UNIALG_2:func.3">Opers</a> <font color="Maroon" title="c8">U1</font>,<font color="Maroon" title="c10">B</font> &amp; <font color="Maroon" title="c10">B</font> is  <a href="unialg_2.html#V1" title="UNIALG_2:attr.1">opers_closed</a>  )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:38_1_1"><span class="lab"><font color="Green" title="E28">A10</font></span></a>, <a class="txt" href="#E20:38_1_1"><span class="lab"><font color="Green" title="E33">A29</font></span></a>, <a class="txt" href="#E25:38_1_1"><span class="lab"><font color="Green" title="E38">A42</font></span></a>, <a class="txt" href="#E21:38_1_1"><span class="lab"><font color="Green" title="E34">A30</font></span></a>, <a class="txt" href="#E23:38_1_1"><span class="lab"><font color="Green" title="E36">A32</font></span></a>, <a class="txt" href="#E24:38_1_1"><span class="lab"><font color="Green" title="E37">A41</font></span></a>, <a class="ref" href="unialg_2.html#D5" target="_self" title="UNIALG_2:def.5">Def5</a>, <a class="ref" href="finseq_1.html#T17" title="FINSEQ_1:th.17">FINSEQ_1:17</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
