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<span class="kw">let </span><font color="Maroon" title="c1">U0</font>, <font color="Maroon" title="c2">U1</font>, <font color="Maroon" title="c3">U2</font> be   <a href="unialg_1.html#NM1" title="UNIALG_1:NM.1">Universal_Algebra</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">U0</font> is    <a href="unialg_2.html#M1" title="UNIALG_2:mode.1">SubAlgebra</a> of <font color="Maroon" title="c2">U1</font> &amp; <font color="Maroon" title="c2">U1</font> is    <a href="unialg_2.html#M1" title="UNIALG_2:mode.1">SubAlgebra</a> of <font color="Maroon" title="c3">U2</font> implies <font color="Maroon" title="c1">U0</font> is    <a href="unialg_2.html#M1" title="UNIALG_2:mode.1">SubAlgebra</a> of <font color="Maroon" title="c3">U2</font> )</span><br/>





<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:18"/><span class="lab"><font color="Green" title="E7">A1</font></span>: 
<font color="Maroon" title="c1">U0</font> is    <a href="unialg_2.html#M1" title="UNIALG_2:mode.1">SubAlgebra</a> of <font color="Maroon" title="c2">U1</font>
 <span class="kw">and </span><br/><a NAME="E2:18"/><span class="lab"><font color="Green" title="E8">A2</font></span>: 
<font color="Maroon" title="c2">U1</font> is    <a href="unialg_2.html#M1" title="UNIALG_2:mode.1">SubAlgebra</a> of <font color="Maroon" title="c3">U2</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c1">U0</font> is    <a href="unialg_2.html#M1" title="UNIALG_2:mode.1">SubAlgebra</a> of <font color="Maroon" title="c3">U2</font></span><br/>

<a NAME="E3:18"/><span class="lab"><font color="Green" title="E9">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> is   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c2">U1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:18"><span class="lab"><font color="Green" title="E7">A1</font></span></a>, <a class="ref" href="unialg_2.html#D7" target="_self" onmouseover="rs('unialg_2/D7')" onmouseout="rh()">Def7</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c4">B2</font> =  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">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="c3">U2</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:18"><span class="lab"><font color="Green" title="E8">A2</font></span></a>, <a class="ref" href="unialg_2.html#D7" target="_self" onmouseover="rs('unialg_2/D7')" onmouseout="rh()">Def7</a></span>;<br/>
<a NAME="E5:18"/><span class="lab"><font color="Green" title="E10">A4</font></span>: 
 the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <font color="Maroon" title="c2">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="c3">U2</font>,<font color="Maroon" title="c4">B2</font>)
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:18"><span class="lab"><font color="Green" title="E8">A2</font></span></a>, <a class="ref" href="unialg_2.html#D7" target="_self" onmouseover="rs('unialg_2/D7')" onmouseout="rh()">Def7</a></span>;<br/>
<a NAME="E6:18"/>
 the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">U1</font> is   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c3">U2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:18"><span class="lab"><font color="Green" title="E8">A2</font></span></a>, <a class="ref" href="unialg_2.html#D7" target="_self" onmouseover="rs('unialg_2/D7')" onmouseout="rh()">Def7</a></span>;<br/>
<span class="kw">hence </span><a NAME="E7:18"/>
 the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">U0</font> is   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c3">U2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:18"><span class="lab"><font color="Green" title="E9">A3</font></span></a>, <a class="ref" href="xboole_1.html#T1" onmouseover="rs('xboole_1/T1')" onmouseout="rh()">XBOOLE_1:1</a></span>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="unialg_2.html#D7" target="_self" onmouseover="rs('unialg_2/D7')" onmouseout="rh()">UNIALG_2:def 7</a> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  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="c3">U2</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/>(  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="unialg_2.html#K3" title="UNIALG_2:func.3">Opers</a> (<font color="Maroon" title="c3">U2</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="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 <font color="Maroon" title="c3">U2</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <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 <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="c1">U0</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="c3">U2</font>,<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/>

<span class="kw">assume </span><a NAME="E8:18"/><span class="lab"><font color="Green" title="E11">A5</font></span>: 
<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 <font color="Maroon" title="c1">U0</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  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="c1">U0</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="c3">U2</font>,<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/>

<span class="kw">reconsider </span><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">U0</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">U1</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:18"><span class="lab"><font color="Green" title="E7">A1</font></span></a>, <a class="ref" href="unialg_2.html#D7" target="_self" onmouseover="rs('unialg_2/D7')" onmouseout="rh()">Def7</a></span>;<br/>
<a NAME="E10:18"/><span class="lab"><font color="Green" title="E12">A6</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="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="c2">U1</font>,<font color="Maroon" title="c6">B1</font>)
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:18"><span class="lab"><font color="Green" title="E7">A1</font></span></a>, <a class="ref" href="unialg_2.html#D7" target="_self" onmouseover="rs('unialg_2/D7')" onmouseout="rh()">Def7</a></span>;<br/>
<a NAME="E11:18"/><span class="lab"><font color="Green" title="E13">A7</font></span>: 
<font color="Maroon" title="c4">B2</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="#E2:18"><span class="lab"><font color="Green" title="E8">A2</font></span></a>, <a class="ref" href="unialg_2.html#D7" target="_self" onmouseover="rs('unialg_2/D7')" onmouseout="rh()">Def7</a></span>;<br/>
<span class="lab"><font color="Green" title="E14">A8</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="c2">U1</font> = 
 <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="c3">U2</font>,<font color="Maroon" title="c4">B2</font>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:18"><span class="lab"><font color="Green" title="E8">A2</font></span></a>, <a class="ref" href="unialg_2.html#D7" target="_self" onmouseover="rs('unialg_2/D7')" onmouseout="rh()">Def7</a></span>
<br/>.= 
 <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">U2</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="unialg_2.html#D6" target="_self" onmouseover="rs('unialg_2/D6')" onmouseout="rh()">Def6</a></span>
;<br/>
<a NAME="E13:18"/><span class="lab"><font color="Green" title="E15">A9</font></span>: 
<font color="Maroon" title="c6">B1</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="#E1:18"><span class="lab"><font color="Green" title="E7">A1</font></span></a>, <a class="ref" href="unialg_2.html#D7" target="_self" onmouseover="rs('unialg_2/D7')" onmouseout="rh()">Def7</a></span>;<br/>
<div><span class="lab"><font color="Green" title="E16">A10</font></span>: <a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="18_2"><span class="kw">now </span> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">o2</font> being   <a href="unialg_2.html#NM3" title="UNIALG_2:NM.3">operation</a> of <font color="Maroon" title="c3">U2</font> 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">o2</font></span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c7">o2</font> be   <a href="unialg_2.html#NM3" title="UNIALG_2:NM.3">operation</a> of <font color="Maroon" title="c3">U2</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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="c7">o2</font></span><br/><span class="kw">consider </span><font color="Maroon" title="c8">n</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a><span class="kw"> such that </span><br/><a NAME="E2:18_2"/><span class="lab"><font color="Green" title="E17">A11</font></span>: 
<font color="Maroon" title="c8">n</font> <a href="tarski.html#R2" title="TARSKI: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="c3">U2</font>
 <span class="kw">and </span><br/><a NAME="E3:18_2"/><span class="lab"><font color="Green" title="E18">A12</font></span>: 
 the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <font color="Maroon" title="c3">U2</font> <a href="partfun1.html#K8" title="PARTFUN1:func.8">.</a> <font color="Maroon" title="c8">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">o2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_2.html#T10" onmouseover="rs('finseq_2/T10')" onmouseout="rh()">FINSEQ_2:10</a></span>;<br/><a NAME="E4:18_2"/><span class="lab"><font color="Green" title="E19">A13</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="c3">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="c3">U2</font>,<font color="Maroon" title="c4">B2</font>)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="unialg_2.html#D6" target="_self" onmouseover="rs('unialg_2/D6')" onmouseout="rh()">Def6</a></span>;<br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c9">o21</font> =  the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <font color="Maroon" title="c2">U1</font> <a href="partfun1.html#K8" title="PARTFUN1:func.8">.</a> <font color="Maroon" title="c8">n</font> as   <a href="unialg_2.html#NM3" title="UNIALG_2:NM.3">operation</a> of <font color="Maroon" title="c2">U1</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:18"><span class="lab"><font color="Green" title="E10">A4</font></span></a>, <a class="txt" href="#E2:18_2"><span class="lab"><font color="Green" title="E17">A11</font></span></a>, <a class="ref" href="funct_1.html#D3" onmouseover="rs('funct_1/D3')" onmouseout="rh()">FUNCT_1:def 3</a></span>;<br/><a NAME="E6:18_2"/><span class="lab"><font color="Green" title="E20">A14</font></span>: 
 <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Maroon" title="c9">o21</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="margrel1.html#K18" title="MARGREL1:func.18">arity</a> <font color="Maroon" title="c9">o21</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">U1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="margrel1.html#T22" onmouseover="rs('margrel1/T22')" onmouseout="rh()">MARGREL1:22</a></span>;<br/><a NAME="E7:18_2"/><span class="lab"><font color="Green" title="E21">A15</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="c2">U1</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">U1</font>,<font color="Maroon" title="c6">B1</font>)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="unialg_2.html#D6" target="_self" onmouseover="rs('unialg_2/D6')" onmouseout="rh()">Def6</a></span>;<br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c10">o20</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="partfun1.html#K8" title="PARTFUN1:func.8">.</a> <font color="Maroon" title="c8">n</font> as   <a href="unialg_2.html#NM3" title="UNIALG_2:NM.3">operation</a> of <font color="Maroon" title="c1">U0</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:18"><span class="lab"><font color="Green" title="E12">A6</font></span></a>, <a class="txt" href="#E5:18"><span class="lab"><font color="Green" title="E10">A4</font></span></a>, <a class="txt" href="#E2:18_2"><span class="lab"><font color="Green" title="E17">A11</font></span></a>, <a class="txt" href="#E4:18_2"><span class="lab"><font color="Green" title="E19">A13</font></span></a>, <a class="ref" href="funct_1.html#D3" onmouseover="rs('funct_1/D3')" onmouseout="rh()">FUNCT_1:def 3</a></span>;<br/><a NAME="E9:18_2"/><span class="lab"><font color="Green" title="E22">A16</font></span>: 
 <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Maroon" title="c10">o20</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="margrel1.html#K18" title="MARGREL1:func.18">arity</a> <font color="Maroon" title="c10">o20</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 class="kw">by</span> <span class="lab"><a class="ref" href="margrel1.html#T22" onmouseover="rs('margrel1/T22')" onmouseout="rh()">MARGREL1:22</a></span>;<br/><a NAME="E10:18_2"/><span class="lab"><font color="Green" title="E23">A17</font></span>: 
(  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Maroon" title="c7">o2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="margrel1.html#K18" title="MARGREL1:func.18">arity</a> <font color="Maroon" title="c7">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="c3">U2</font> &amp;  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">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="margrel1.html#K18" title="MARGREL1:func.18">arity</a> <font color="Maroon" title="c7">o2</font></span>)</span> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <font color="Maroon" title="c4">B2</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Maroon" title="c7">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="margrel1.html#K18" title="MARGREL1:func.18">arity</a> <font color="Maroon" title="c7">o2</font></span>)</span> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <font color="Maroon" title="c4">B2</font></span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="margrel1.html#T22" onmouseover="rs('margrel1/T22')" onmouseout="rh()">MARGREL1:22</a>, <a class="ref" href="relat_1.html#T61" onmouseover="rs('relat_1/T61')" onmouseout="rh()">RELAT_1:61</a></span>;<br/><a NAME="E11:18_2"/><span class="lab"><font color="Green" title="E24">A18</font></span>: 
<font color="Maroon" title="c4">B2</font> <a href="unialg_2.html#R2" title="UNIALG_2:pred.2">is_closed_on</a> <font color="Maroon" title="c7">o2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:18"><span class="lab"><font color="Green" title="E13">A7</font></span></a></span>;<br/><a NAME="E12:18_2"/><span class="lab"><font color="Green" title="E25">A19</font></span>: 
<font color="Maroon" title="c9">o21</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">o2</font> <a href="unialg_2.html#K2" title="UNIALG_2:func.2">/.</a> <font color="Maroon" title="c4">B2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:18"><span class="lab"><font color="Green" title="E10">A4</font></span></a>, <a class="txt" href="#E2:18_2"><span class="lab"><font color="Green" title="E17">A11</font></span></a>, <a class="txt" href="#E3:18_2"><span class="lab"><font color="Green" title="E18">A12</font></span></a>, <a class="txt" href="#E4:18_2"><span class="lab"><font color="Green" title="E19">A13</font></span></a>, <a class="ref" href="unialg_2.html#D6" target="_self" onmouseover="rs('unialg_2/D6')" onmouseout="rh()">Def6</a></span>;<br/><a NAME="E13:18_2"/><span class="kw">then </span>
<font color="Maroon" title="c9">o21</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">o2</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="margrel1.html#K18" title="MARGREL1:func.18">arity</a> <font color="Maroon" title="c7">o2</font></span>)</span> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <font color="Maroon" title="c4">B2</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:18_2"><span class="lab"><font color="Green" title="E24">A18</font></span></a>, <a class="ref" href="unialg_2.html#D5" target="_self" onmouseover="rs('unialg_2/D5')" onmouseout="rh()">Def5</a></span>;<br/><a NAME="E14:18_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E26">A20</font></span>: 
 <a href="margrel1.html#K18" title="MARGREL1:func.18">arity</a> <font color="Maroon" title="c7">o2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K18" title="MARGREL1:func.18">arity</a> <font color="Maroon" title="c9">o21</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:18_2"><span class="lab"><font color="Green" title="E20">A14</font></span></a>, <a class="txt" href="#E10:18_2"><span class="lab"><font color="Green" title="E23">A17</font></span></a>, <a class="ref" href="finseq_2.html#T110" onmouseover="rs('finseq_2/T110')" onmouseout="rh()">FINSEQ_2:110</a>, <a class="ref" href="margrel1.html#T21" onmouseover="rs('margrel1/T21')" onmouseout="rh()">MARGREL1:21</a></span>;<br/><a NAME="E15:18_2"/><span class="lab"><font color="Green" title="E27">A21</font></span>: 
<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">o21</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:18"><span class="lab"><font color="Green" title="E15">A9</font></span></a></span>;<br/><a NAME="E16:18_2"/><span class="lab"><font color="Green" title="E28">A22</font></span>: 
<font color="Maroon" title="c10">o20</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">o21</font> <a href="unialg_2.html#K2" title="UNIALG_2:func.2">/.</a> <font color="Maroon" title="c6">B1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:18"><span class="lab"><font color="Green" title="E12">A6</font></span></a>, <a class="txt" href="#E5:18"><span class="lab"><font color="Green" title="E10">A4</font></span></a>, <a class="txt" href="#E2:18_2"><span class="lab"><font color="Green" title="E17">A11</font></span></a>, <a class="txt" href="#E4:18_2"><span class="lab"><font color="Green" title="E19">A13</font></span></a>, <a class="txt" href="#E7:18_2"><span class="lab"><font color="Green" title="E21">A15</font></span></a>, <a class="ref" href="unialg_2.html#D6" target="_self" onmouseover="rs('unialg_2/D6')" onmouseout="rh()">Def6</a></span>;<br/><a NAME="E17:18_2"/><span class="kw">then </span>
<font color="Maroon" title="c10">o20</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">o21</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="margrel1.html#K18" title="MARGREL1:func.18">arity</a> <font color="Maroon" title="c9">o21</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 class="kw">by</span> <span class="lab"><a class="txt" href="#E15:18_2"><span class="lab"><font color="Green" title="E27">A21</font></span></a>, <a class="ref" href="unialg_2.html#D5" target="_self" onmouseover="rs('unialg_2/D5')" onmouseout="rh()">Def5</a></span>;<br/><a NAME="E18:18_2"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="margrel1.html#K18" title="MARGREL1:func.18">arity</a> <font color="Maroon" title="c10">o20</font></span>)</span> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <font color="Maroon" title="c6">B1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="margrel1.html#K18" title="MARGREL1:func.18">arity</a> <font color="Maroon" title="c9">o21</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">U1</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="margrel1.html#K18" title="MARGREL1:func.18">arity</a> <font color="Maroon" title="c9">o21</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 class="kw">by</span> <span class="lab"><a class="txt" href="#E9:18_2"><span class="lab"><font color="Green" title="E22">A16</font></span></a>, <a class="txt" href="#E6:18_2"><span class="lab"><font color="Green" title="E20">A14</font></span></a>, <a class="ref" href="relat_1.html#T61" onmouseover="rs('relat_1/T61')" onmouseout="rh()">RELAT_1:61</a></span>;<br/><a NAME="E19:18_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E29">A23</font></span>: 
 <a href="margrel1.html#K18" title="MARGREL1:func.18">arity</a> <font color="Maroon" title="c10">o20</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K18" title="MARGREL1:func.18">arity</a> <font color="Maroon" title="c9">o21</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_2.html#T110" onmouseover="rs('finseq_2/T110')" onmouseout="rh()">FINSEQ_2:110</a>, <a class="ref" href="margrel1.html#T21" onmouseover="rs('margrel1/T21')" onmouseout="rh()">MARGREL1:21</a></span>;<br/><div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="18_2_1"><span class="kw">now </span> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">s</font> being    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of <font color="Maroon" title="c5">B</font>  st  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b1">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K18" title="MARGREL1:func.18">arity</a> <font color="Maroon" title="c7">o2</font> holds <br/><font color="Maroon" title="c7">o2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">s</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c5">B</font></span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c11">s</font> be    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of <font color="Maroon" title="c5">B</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c11">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K18" title="MARGREL1:func.18">arity</a> <font color="Maroon" title="c7">o2</font> implies <font color="Maroon" title="c7">o2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">s</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c5">B</font> )</span><br/><span class="kw">reconsider </span><font color="Maroon" title="c12">s1</font> = <font color="Maroon" title="c11">s</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>  <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:18"><span class="lab"><font color="Green" title="E11">A5</font></span></a>, <a class="ref" href="finseq_1.html#D11" onmouseover="rs('finseq_1/D11')" onmouseout="rh()">FINSEQ_1:def 11</a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c13">s0</font> = <font color="Maroon" title="c11">s</font> as    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">U0</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="#E8:18"><span class="lab"><font color="Green" title="E11">A5</font></span></a>, <a class="ref" href="finseq_1.html#D11" onmouseover="rs('finseq_1/D11')" onmouseout="rh()">FINSEQ_1:def 11</a></span>;<br/><a NAME="E3:18_2_1"/><span class="lab"><font color="Green" title="E30">A24</font></span>: 
 <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <font color="Maroon" title="c10">o20</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c5">B</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:18"><span class="lab"><font color="Green" title="E11">A5</font></span></a>, <a class="ref" href="relat_1.html#D19" onmouseover="rs('relat_1/D19')" onmouseout="rh()">RELAT_1:def 19</a></span>;<br/><a NAME="E4:18_2_1"/>
 <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <font color="Maroon" title="c11">s</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c5">B</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#D4" onmouseover="rs('finseq_1/D4')" onmouseout="rh()">FINSEQ_1:def 4</a></span>;<br/><a NAME="E5:18_2_1"/><span class="kw">then </span>
 <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <font color="Maroon" title="c11">s</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">B2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:18"><span class="lab"><font color="Green" title="E9">A3</font></span></a>, <a class="txt" href="#E8:18"><span class="lab"><font color="Green" title="E11">A5</font></span></a>, <a class="ref" href="xboole_1.html#T1" onmouseover="rs('xboole_1/T1')" onmouseout="rh()">XBOOLE_1:1</a></span>;<br/><a NAME="E6:18_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c11">s</font> is    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of <font color="Maroon" title="c4">B2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#D4" onmouseover="rs('finseq_1/D4')" onmouseout="rh()">FINSEQ_1:def 4</a></span>;<br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c14">s2</font> = <font color="Maroon" title="c11">s</font> as    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <font color="Maroon" title="c4">B2</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" onmouseover="rs('finseq_1/D11')" onmouseout="rh()">FINSEQ_1:def 11</a></span>;<br/><span class="kw">assume </span><a NAME="E8:18_2_1"/><span class="lab"><font color="Green" title="E31">A25</font></span>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c11">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K18" title="MARGREL1:func.18">arity</a> <font color="Maroon" title="c7">o2</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c7">o2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">s</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c5">B</font></span><br/><a NAME="E9:18_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c14">s2</font> <a href="tarski.html#R2" title="TARSKI: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 <font color="Maroon" title="c4">B2</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">w</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K18" title="MARGREL1:func.18">arity</a> <font color="Maroon" title="c7">o2</font> </span> } </span> 
 ;<br/><a NAME="E10:18_2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E32">A26</font></span>: 
<font color="Maroon" title="c14">s2</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <span class="p1">(<span class="default"><a href="margrel1.html#K18" title="MARGREL1:func.18">arity</a> <font color="Maroon" title="c7">o2</font></span>)</span> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <font color="Maroon" title="c4">B2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_2.html#D4" onmouseover="rs('finseq_2/D4')" onmouseout="rh()">FINSEQ_2:def 4</a></span>;<br/><a NAME="E11:18_2_1"/>
<font color="Maroon" title="c13">s0</font> <a href="tarski.html#R2" title="TARSKI: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  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">U0</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">w</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K18" title="MARGREL1:func.18">arity</a> <font color="Maroon" title="c10">o20</font> </span> } </span> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:18_2"><span class="lab"><font color="Green" title="E29">A23</font></span></a>, <a class="txt" href="#E14:18_2"><span class="lab"><font color="Green" title="E26">A20</font></span></a>, <a class="txt" href="#E8:18_2_1"><span class="lab"><font color="Green" title="E31">A25</font></span></a></span>;<br/><a NAME="E12:18_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c13">s0</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <span class="p1">(<span class="default"><a href="margrel1.html#K18" title="MARGREL1:func.18">arity</a> <font color="Maroon" title="c10">o20</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 class="kw">by</span> <span class="lab"><a class="ref" href="finseq_2.html#D4" onmouseover="rs('finseq_2/D4')" onmouseout="rh()">FINSEQ_2:def 4</a></span>;<br/><a NAME="E13:18_2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E33">A27</font></span>: 
<font color="Maroon" title="c10">o20</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c13">s0</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <font color="Maroon" title="c10">o20</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:18_2"><span class="lab"><font color="Green" title="E22">A16</font></span></a>, <a class="ref" href="funct_1.html#D3" onmouseover="rs('funct_1/D3')" onmouseout="rh()">FUNCT_1:def 3</a></span>;<br/><a NAME="E14:18_2_1"/>
<font color="Maroon" title="c12">s1</font> <a href="tarski.html#R2" title="TARSKI: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 <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">w</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K18" title="MARGREL1:func.18">arity</a> <font color="Maroon" title="c9">o21</font> </span> } </span> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:18_2"><span class="lab"><font color="Green" title="E26">A20</font></span></a>, <a class="txt" href="#E8:18_2_1"><span class="lab"><font color="Green" title="E31">A25</font></span></a></span>;<br/><a NAME="E15:18_2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E34">A28</font></span>: 
<font color="Maroon" title="c12">s1</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <span class="p1">(<span class="default"><a href="margrel1.html#K18" title="MARGREL1:func.18">arity</a> <font color="Maroon" title="c9">o21</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 class="kw">by</span> <span class="lab"><a class="ref" href="finseq_2.html#D4" onmouseover="rs('finseq_2/D4')" onmouseout="rh()">FINSEQ_2:def 4</a></span>;<br/><font color="Maroon" title="c10">o20</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c13">s0</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c9">o21</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="margrel1.html#K18" title="MARGREL1:func.18">arity</a> <font color="Maroon" title="c9">o21</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="c12">s1</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E15:18_2"><span class="lab"><font color="Green" title="E27">A21</font></span></a>, <a class="txt" href="#E16:18_2"><span class="lab"><font color="Green" title="E28">A22</font></span></a>, <a class="ref" href="unialg_2.html#D5" target="_self" onmouseover="rs('unialg_2/D5')" onmouseout="rh()">Def5</a></span>
<br/>.= 
<font color="Maroon" title="c9">o21</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c12">s1</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E15:18_2_1"><span class="lab"><font color="Green" title="E34">A28</font></span></a>, <a class="ref" href="funct_1.html#T49" onmouseover="rs('funct_1/T49')" onmouseout="rh()">FUNCT_1:49</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c7">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="margrel1.html#K18" title="MARGREL1:func.18">arity</a> <font color="Maroon" title="c7">o2</font></span>)</span> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <font color="Maroon" title="c4">B2</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c14">s2</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:18_2"><span class="lab"><font color="Green" title="E24">A18</font></span></a>, <a class="txt" href="#E12:18_2"><span class="lab"><font color="Green" title="E25">A19</font></span></a>, <a class="ref" href="unialg_2.html#D5" target="_self" onmouseover="rs('unialg_2/D5')" onmouseout="rh()">Def5</a></span>
<br/>.= 
<font color="Maroon" title="c7">o2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">s</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:18_2_1"><span class="lab"><font color="Green" title="E32">A26</font></span></a>, <a class="ref" href="funct_1.html#T49" onmouseover="rs('funct_1/T49')" onmouseout="rh()">FUNCT_1:49</a></span>
;<br/><span class="kw">hence </span><a NAME="E17:18_2_1"/>
<font color="Maroon" title="c7">o2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">s</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c5">B</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:18_2_1"><span class="lab"><font color="Green" title="E33">A27</font></span></a>, <a class="txt" href="#E3:18_2_1"><span class="lab"><font color="Green" title="E30">A24</font></span></a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><span class="kw">hence </span><a NAME="E21:18_2"/>
<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="c7">o2</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="lab"><font color="Green" title="E17">A29</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="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">U1</font>,<font color="Maroon" title="c6">B1</font>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:18"><span class="lab"><font color="Green" title="E7">A1</font></span></a>, <a class="ref" href="unialg_2.html#D7" target="_self" onmouseover="rs('unialg_2/D7')" onmouseout="rh()">Def7</a></span>
<br/>.= 
 <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">U1</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="unialg_2.html#D6" target="_self" onmouseover="rs('unialg_2/D6')" onmouseout="rh()">Def6</a></span>
;<br/>
<a NAME="E16:18"/><span class="lab"><font color="Green" title="E18">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="c3">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="c3">U2</font>,<font color="Maroon" title="c5">B</font>)</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="unialg_2.html#D6" target="_self" onmouseover="rs('unialg_2/D6')" onmouseout="rh()">Def6</a></span>;<br/>
<a NAME="E17:18"/><span class="lab"><font color="Green" title="E19">A31</font></span>: 
<font color="Maroon" title="c5">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">B1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:18"><span class="lab"><font color="Green" title="E11">A5</font></span></a></span>;<br/>
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="18_4"><span class="kw">now </span> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">n</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st <font color="Olive" title="b1">n</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</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="c3">U2</font>,<font color="Maroon" title="c5">B</font>)</span>)</span> holds <br/><span class="p1">(<span class="default"><a href="unialg_2.html#K3" title="UNIALG_2:func.3">Opers</a> (<font color="Maroon" title="c3">U2</font>,<font color="Maroon" title="c5">B</font>)</span>)</span> <a href="partfun1.html#K8" title="PARTFUN1:func.8">.</a> <font color="Olive" title="b1">n</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="c1">U0</font> <a href="partfun1.html#K8" title="PARTFUN1:func.8">.</a> <font color="Olive" title="b1">n</font></span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c7">n</font> be   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c7">n</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</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="c3">U2</font>,<font color="Maroon" title="c5">B</font>)</span>)</span> implies <span class="p1">(<span class="default"><a href="unialg_2.html#K3" title="UNIALG_2:func.3">Opers</a> (<font color="Maroon" title="c3">U2</font>,<font color="Maroon" title="c5">B</font>)</span>)</span> <a href="partfun1.html#K8" title="PARTFUN1:func.8">.</a> <font color="Maroon" title="c7">n</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="c1">U0</font> <a href="partfun1.html#K8" title="PARTFUN1:func.8">.</a> <font color="Maroon" title="c7">n</font> )</span><br/><span class="kw">assume </span><a NAME="E1:18_4"/><span class="lab"><font color="Green" title="E20">A32</font></span>: 
<font color="Maroon" title="c7">n</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</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="c3">U2</font>,<font color="Maroon" title="c5">B</font>)</span>)</span>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="unialg_2.html#K3" title="UNIALG_2:func.3">Opers</a> (<font color="Maroon" title="c3">U2</font>,<font color="Maroon" title="c5">B</font>)</span>)</span> <a href="partfun1.html#K8" title="PARTFUN1:func.8">.</a> <font color="Maroon" title="c7">n</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="c1">U0</font> <a href="partfun1.html#K8" title="PARTFUN1:func.8">.</a> <font color="Maroon" title="c7">n</font></span><br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c8">o2</font> =  the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <font color="Maroon" title="c3">U2</font> <a href="partfun1.html#K8" title="PARTFUN1:func.8">.</a> <font color="Maroon" title="c7">n</font> as   <a href="unialg_2.html#NM3" title="UNIALG_2:NM.3">operation</a> of <font color="Maroon" title="c3">U2</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E16:18"><span class="lab"><font color="Green" title="E18">A30</font></span></a>, <a class="ref" href="funct_1.html#D3" onmouseover="rs('funct_1/D3')" onmouseout="rh()">FUNCT_1:def 3</a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c9">o21</font> =  the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <font color="Maroon" title="c2">U1</font> <a href="partfun1.html#K8" title="PARTFUN1:func.8">.</a> <font color="Maroon" title="c7">n</font> as   <a href="unialg_2.html#NM3" title="UNIALG_2:NM.3">operation</a> of <font color="Maroon" title="c2">U1</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:18"><span class="lab"><font color="Green" title="E14">A8</font></span></a>, <a class="txt" href="#E16:18"><span class="lab"><font color="Green" title="E18">A30</font></span></a>, <a class="txt" href="#E1:18_4"><span class="lab"><font color="Green" title="E20">A32</font></span></a>, <a class="ref" href="funct_1.html#D3" onmouseover="rs('funct_1/D3')" onmouseout="rh()">FUNCT_1:def 3</a></span>;<br/><a NAME="E4:18_4"/><span class="lab"><font color="Green" title="E21">A33</font></span>: 
<font color="Maroon" title="c4">B2</font> <a href="unialg_2.html#R2" title="UNIALG_2:pred.2">is_closed_on</a> <font color="Maroon" title="c8">o2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:18"><span class="lab"><font color="Green" title="E13">A7</font></span></a></span>;<br/><a NAME="E5:18_4"/><span class="lab"><font color="Green" title="E22">A34</font></span>: 
<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">o21</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:18"><span class="lab"><font color="Green" title="E15">A9</font></span></a></span>;<br/><span class="kw">thus </span><span class="p1">(<span class="default"><a href="unialg_2.html#K3" title="UNIALG_2:func.3">Opers</a> (<font color="Maroon" title="c3">U2</font>,<font color="Maroon" title="c5">B</font>)</span>)</span> <a href="partfun1.html#K8" title="PARTFUN1:func.8">.</a> <font color="Maroon" title="c7">n</font> = 
<font color="Maroon" title="c8">o2</font> <a href="unialg_2.html#K2" title="UNIALG_2:func.2">/.</a> <font color="Maroon" title="c5">B</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:18_4"><span class="lab"><font color="Green" title="E20">A32</font></span></a>, <a class="ref" href="unialg_2.html#D6" target="_self" onmouseover="rs('unialg_2/D6')" onmouseout="rh()">Def6</a></span>
<br/>.= 
<font color="Maroon" title="c8">o2</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="margrel1.html#K18" title="MARGREL1:func.18">arity</a> <font color="Maroon" title="c8">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>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:18"><span class="lab"><font color="Green" title="E16">A10</font></span></a>, <a class="ref" href="unialg_2.html#D5" target="_self" onmouseover="rs('unialg_2/D5')" onmouseout="rh()">Def5</a></span>
<br/>.= 
<font color="Maroon" title="c8">o2</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="margrel1.html#K18" title="MARGREL1:func.18">arity</a> <font color="Maroon" title="c8">o2</font></span>)</span> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <font color="Maroon" title="c4">B2</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="margrel1.html#K18" title="MARGREL1:func.18">arity</a> <font color="Maroon" title="c8">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></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E17:18"><span class="lab"><font color="Green" title="E19">A31</font></span></a>, <a class="ref" href="margrel1.html#T21" onmouseover="rs('margrel1/T21')" onmouseout="rh()">MARGREL1:21</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c8">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="margrel1.html#K18" title="MARGREL1:func.18">arity</a> <font color="Maroon" title="c8">o2</font></span>)</span> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <font color="Maroon" title="c4">B2</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="margrel1.html#K18" title="MARGREL1:func.18">arity</a> <font color="Maroon" title="c8">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>
<span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#T71" onmouseover="rs('relat_1/T71')" onmouseout="rh()">RELAT_1:71</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c8">o2</font> <a href="unialg_2.html#K2" title="UNIALG_2:func.2">/.</a> <font color="Maroon" title="c4">B2</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="margrel1.html#K18" title="MARGREL1:func.18">arity</a> <font color="Maroon" title="c8">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>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:18_4"><span class="lab"><font color="Green" title="E21">A33</font></span></a>, <a class="ref" href="unialg_2.html#D5" target="_self" onmouseover="rs('unialg_2/D5')" onmouseout="rh()">Def5</a></span>
<br/>.= 
<font color="Maroon" title="c9">o21</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="margrel1.html#K18" title="MARGREL1:func.18">arity</a> <font color="Maroon" title="c8">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>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:18"><span class="lab"><font color="Green" title="E10">A4</font></span></a>, <a class="txt" href="#E12:18"><span class="lab"><font color="Green" title="E14">A8</font></span></a>, <a class="txt" href="#E16:18"><span class="lab"><font color="Green" title="E18">A30</font></span></a>, <a class="txt" href="#E1:18_4"><span class="lab"><font color="Green" title="E20">A32</font></span></a>, <a class="ref" href="unialg_2.html#D6" target="_self" onmouseover="rs('unialg_2/D6')" onmouseout="rh()">Def6</a></span>
<br/>.= 
<font color="Maroon" title="c9">o21</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="margrel1.html#K18" title="MARGREL1:func.18">arity</a> <font color="Maroon" title="c9">o21</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 class="kw">by</span> <span class="lab"><a class="txt" href="#E2:18"><span class="lab"><font color="Green" title="E8">A2</font></span></a>, <a class="txt" href="#E8:18"><span class="lab"><font color="Green" title="E11">A5</font></span></a>, <a class="txt" href="#E12:18"><span class="lab"><font color="Green" title="E14">A8</font></span></a>, <a class="txt" href="#E16:18"><span class="lab"><font color="Green" title="E18">A30</font></span></a>, <a class="txt" href="#E1:18_4"><span class="lab"><font color="Green" title="E20">A32</font></span></a>, <a class="ref" href="unialg_2.html#T6" target="_self" onmouseover="rs('unialg_2/T6')" onmouseout="rh()">Th6</a></span>
<br/>.= 
<font color="Maroon" title="c9">o21</font> <a href="unialg_2.html#K2" title="UNIALG_2:func.2">/.</a> <font color="Maroon" title="c6">B1</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:18_4"><span class="lab"><font color="Green" title="E22">A34</font></span></a>, <a class="ref" href="unialg_2.html#D5" target="_self" onmouseover="rs('unialg_2/D5')" onmouseout="rh()">Def5</a></span>
<br/>.= 
 the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <font color="Maroon" title="c1">U0</font> <a href="partfun1.html#K8" title="PARTFUN1:func.8">.</a> <font color="Maroon" title="c7">n</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:18"><span class="lab"><font color="Green" title="E12">A6</font></span></a>, <a class="txt" href="#E15:18"><span class="lab"><font color="Green" title="E17">A29</font></span></a>, <a class="txt" href="#E12:18"><span class="lab"><font color="Green" title="E14">A8</font></span></a>, <a class="txt" href="#E16:18"><span class="lab"><font color="Green" title="E18">A30</font></span></a>, <a class="txt" href="#E1:18_4"><span class="lab"><font color="Green" title="E20">A32</font></span></a>, <a class="ref" href="unialg_2.html#D6" target="_self" onmouseover="rs('unialg_2/D6')" onmouseout="rh()">Def6</a></span>
; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E19:18"/>
 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="unialg_2.html#K3" title="UNIALG_2:func.3">Opers</a> (<font color="Maroon" title="c3">U2</font>,<font color="Maroon" title="c5">B</font>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E15:18"><span class="lab"><font color="Green" title="E17">A29</font></span></a>, <a class="txt" href="#E12:18"><span class="lab"><font color="Green" title="E14">A8</font></span></a>, <a class="txt" href="#E16:18"><span class="lab"><font color="Green" title="E18">A30</font></span></a>, <a class="ref" href="finseq_1.html#T13" onmouseover="rs('finseq_1/T13')" onmouseout="rh()">FINSEQ_1:13</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c5">B</font> is  <a href="unialg_2.html#V1" title="UNIALG_2:attr.1">opers_closed</a> </span><br/>

<span class="kw">thus </span><a NAME="E20:18"/>
<font color="Maroon" title="c5">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="#E14:18"><span class="lab"><font color="Green" title="E16">A10</font></span></a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
