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

<span class="kw">let </span><font color="Maroon" title="c1">S</font> be   non  <a href="struct_0.html#V11" title="STRUCT_0:attr.11">void</a>  <a href="catalg_1.html#NM1" title="CATALG_1:NM.1">Signature</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">X</font>, <font color="Olive" title="b2">Y</font> being  <a href="relat_1.html#V2" title="RELAT_1:attr.2">V5</a>() <a href="pboole.html#NM1" title="PBOOLE:NM.1">ManySortedSet</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">S</font><br/>  for <font color="Olive" title="b3">A</font> being    <a href="msualg_2.html#M1" title="MSUALG_2:mode.1">MSSubAlgebra</a> of  <a href="msafree.html#K11" title="MSAFREE:func.11">FreeMSA</a> <font color="Olive" title="b1">X</font><br/>  for <font color="Olive" title="b4">B</font> being    <a href="msualg_2.html#M1" title="MSUALG_2:mode.1">MSSubAlgebra</a> of  <a href="msafree.html#K11" title="MSAFREE:func.11">FreeMSA</a> <font color="Olive" title="b2">Y</font>  st  the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Olive" title="b3">A</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Olive" title="b4">B</font> holds <br/> <a href="msualg_1.html#G3" title="MSUALG_1:aggr.3">MSAlgebra</a>(#  the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Olive" title="b3">A</font>, the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Charact</a> of <font color="Olive" title="b3">A</font> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="msualg_1.html#G3" title="MSUALG_1:aggr.3">MSAlgebra</a>(#  the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Olive" title="b4">B</font>, the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Charact</a> of <font color="Olive" title="b4">B</font> #)</span><br/><span class="kw">let </span><font color="Maroon" title="c2">X</font>, <font color="Maroon" title="c3">Y</font> be  <a href="relat_1.html#V2" title="RELAT_1:attr.2">V5</a>() <a href="pboole.html#NM1" title="PBOOLE:NM.1">ManySortedSet</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">S</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">A</font> being    <a href="msualg_2.html#M1" title="MSUALG_2:mode.1">MSSubAlgebra</a> of  <a href="msafree.html#K11" title="MSAFREE:func.11">FreeMSA</a> <font color="Maroon" title="c2">X</font><br/>  for <font color="Olive" title="b2">B</font> being    <a href="msualg_2.html#M1" title="MSUALG_2:mode.1">MSSubAlgebra</a> of  <a href="msafree.html#K11" title="MSAFREE:func.11">FreeMSA</a> <font color="Maroon" title="c3">Y</font>  st  the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Olive" title="b1">A</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Olive" title="b2">B</font> holds <br/> <a href="msualg_1.html#G3" title="MSUALG_1:aggr.3">MSAlgebra</a>(#  the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Olive" title="b1">A</font>, the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Charact</a> of <font color="Olive" title="b1">A</font> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="msualg_1.html#G3" title="MSUALG_1:aggr.3">MSAlgebra</a>(#  the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Olive" title="b2">B</font>, the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Charact</a> of <font color="Olive" title="b2">B</font> #)</span><br/><span class="kw">let </span><font color="Maroon" title="c4">A</font> be    <a href="msualg_2.html#M1" title="MSUALG_2:mode.1">MSSubAlgebra</a> of  <a href="msafree.html#K11" title="MSAFREE:func.11">FreeMSA</a> <font color="Maroon" title="c2">X</font>; <a class="txt" 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    <a href="msualg_2.html#M1" title="MSUALG_2:mode.1">MSSubAlgebra</a> of  <a href="msafree.html#K11" title="MSAFREE:func.11">FreeMSA</a> <font color="Maroon" title="c3">Y</font>  st  the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c4">A</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Olive" title="b1">B</font> holds <br/> <a href="msualg_1.html#G3" title="MSUALG_1:aggr.3">MSAlgebra</a>(#  the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c4">A</font>, the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Charact</a> of <font color="Maroon" title="c4">A</font> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="msualg_1.html#G3" title="MSUALG_1:aggr.3">MSAlgebra</a>(#  the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Olive" title="b1">B</font>, the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Charact</a> of <font color="Olive" title="b1">B</font> #)</span><br/><span class="kw">let </span><font color="Maroon" title="c5">B</font> be    <a href="msualg_2.html#M1" title="MSUALG_2:mode.1">MSSubAlgebra</a> of  <a href="msafree.html#K11" title="MSAFREE:func.11">FreeMSA</a> <font color="Maroon" title="c3">Y</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c4">A</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c5">B</font> implies  <a href="msualg_1.html#G3" title="MSUALG_1:aggr.3">MSAlgebra</a>(#  the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c4">A</font>, the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Charact</a> of <font color="Maroon" title="c4">A</font> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="msualg_1.html#G3" title="MSUALG_1:aggr.3">MSAlgebra</a>(#  the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c5">B</font>, the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Charact</a> of <font color="Maroon" title="c5">B</font> #) )</span><br/>







<span class="kw">assume </span><a NAME="E1:38"/><span class="lab"><font color="Green" title="E27">A1</font></span>: 
 the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c4">A</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c5">B</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="msualg_1.html#G3" title="MSUALG_1:aggr.3">MSAlgebra</a>(#  the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c4">A</font>, the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Charact</a> of <font color="Maroon" title="c4">A</font> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="msualg_1.html#G3" title="MSUALG_1:aggr.3">MSAlgebra</a>(#  the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c5">B</font>, the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Charact</a> of <font color="Maroon" title="c5">B</font> #)</span><br/>

<span class="kw">reconsider </span><font color="Maroon" title="c6">SB</font> =  the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c5">B</font> as   <a href="msualg_2.html#NM1" title="MSUALG_2:NM.1">MSSubset</a> of <span class="p1">(<span class="default"><a href="msafree.html#K11" title="MSAFREE:func.11">FreeMSA</a> <font color="Maroon" title="c3">Y</font></span>)</span> <span class="kw">by</span> <span class="lab"><a class="ref" href="msualg_2.html#D9" title="MSUALG_2:def.9">MSUALG_2:def 9</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c7">SA</font> =  the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c4">A</font> as   <a href="msualg_2.html#NM1" title="MSUALG_2:NM.1">MSSubset</a> of <span class="p1">(<span class="default"><a href="msafree.html#K11" title="MSAFREE:func.11">FreeMSA</a> <font color="Maroon" title="c2">X</font></span>)</span> <span class="kw">by</span> <span class="lab"><a class="ref" href="msualg_2.html#D9" title="MSUALG_2:def.9">MSUALG_2:def 9</a></span>;<br/>
<a NAME="E4:38"/><span class="lab"><font color="Green" title="E28">A2</font></span>: 
<font color="Maroon" title="c7">SA</font> is  <a href="msualg_2.html#V3" title="MSUALG_2:attr.3">opers_closed</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="msualg_2.html#D9" title="MSUALG_2:def.9">MSUALG_2:def 9</a></span>;<br/>
<a NAME="E5:38"/><span class="lab"><font color="Green" title="E29">A3</font></span>: 
<font color="Maroon" title="c6">SB</font> is  <a href="msualg_2.html#V3" title="MSUALG_2:attr.3">opers_closed</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="msualg_2.html#D9" title="MSUALG_2:def.9">MSUALG_2:def 9</a></span>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="38_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c8">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="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c1">S</font> implies  the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Charact</a> of <font color="Maroon" title="c4">A</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Charact</a> of <font color="Maroon" title="c5">B</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font> )</span><br/><a NAME="E1:38_1"/><span class="lab"><font color="Green" title="E30">A4</font></span>: 
( <font color="Maroon" title="c7">SA</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a>  the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <span class="p1">(<span class="default"><a href="msafree.html#K11" title="MSAFREE:func.11">FreeMSA</a> <font color="Maroon" title="c2">X</font></span>)</span> &amp;  the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <span class="p1">(<span class="default"><a href="msafree.html#K11" title="MSAFREE:func.11">FreeMSA</a> <font color="Maroon" title="c2">X</font></span>)</span> is   <a href="msualg_2.html#NM1" title="MSUALG_2:NM.1">MSSubset</a> of <span class="p1">(<span class="default"><a href="msafree.html#K11" title="MSAFREE:func.11">FreeMSA</a> <font color="Maroon" title="c2">X</font></span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="pboole.html#D18" title="PBOOLE:def.18">PBOOLE:def 18</a></span>;<br/><span class="kw">assume </span><a NAME="E2:38_1"/>
<font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c1">S</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Charact</a> of <font color="Maroon" title="c4">A</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Charact</a> of <font color="Maroon" title="c5">B</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font></span><br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c9">o</font> = <font color="Maroon" title="c8">x</font> as   <a href="msualg_1.html#NM2" title="MSUALG_1:NM.2">OperSymbol</a> of <font color="Maroon" title="c1">S</font> ;<br/><a NAME="E4:38_1"/><span class="lab"><font color="Green" title="E31">A5</font></span>: 
<font color="Maroon" title="c7">SA</font> <a href="msualg_2.html#R1" title="MSUALG_2:pred.1">is_closed_on</a> <font color="Maroon" title="c9">o</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:38"><span class="lab"><font color="Green" title="E28">A2</font></span></a>, <a class="ref" href="msualg_2.html#D6" title="MSUALG_2:def.6">MSUALG_2:def 6</a></span>;<br/><span class="lab"><font color="Green" title="E32">A6</font></span>:  the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Charact</a> of <font color="Maroon" title="c4">A</font> <a href="msualg_3.html#K1" title="MSUALG_3:func.1">.</a> <font color="Maroon" title="c9">o</font> = 
<span class="p1">(<span class="default"><a href="msualg_2.html#K4" title="MSUALG_2:func.4">Opers</a> (<span class="p2">(<span class="default"><a href="msafree.html#K11" title="MSAFREE:func.11">FreeMSA</a> <font color="Maroon" title="c2">X</font></span>)</span>,<font color="Maroon" title="c7">SA</font>)</span>)</span> <a href="msualg_3.html#K1" title="MSUALG_3:func.1">.</a> <font color="Maroon" title="c9">o</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="msualg_2.html#D9" title="MSUALG_2:def.9">MSUALG_2:def 9</a></span>
<br/>.= 
<font color="Maroon" title="c9">o</font> <a href="msualg_2.html#K3" title="MSUALG_2:func.3">/.</a> <font color="Maroon" title="c7">SA</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="msualg_2.html#D8" title="MSUALG_2:def.8">MSUALG_2:def 8</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="msualg_1.html#K5" title="MSUALG_1:func.5">Den</a> (<font color="Maroon" title="c9">o</font>,<span class="p2">(<span class="default"><a href="msafree.html#K11" title="MSAFREE:func.11">FreeMSA</a> <font color="Maroon" title="c2">X</font></span>)</span>)</span>)</span> <a href="relset_1.html#K5" title="RELSET_1:func.5">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c7">SA</font> <a href="finseq_2.html#K6" title="FINSEQ_2:func.6">#</a></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a>  the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">Arity</a> of <font color="Maroon" title="c1">S</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">o</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:38_1"><span class="lab"><font color="Green" title="E31">A5</font></span></a>, <a class="ref" href="msualg_2.html#D7" title="MSUALG_2:def.7">MSUALG_2:def 7</a></span>
;<br/><a NAME="E6:38_1"/>
 <a href="msualg_1.html#K3" title="MSUALG_1:func.3">Args</a> (<font color="Maroon" title="c9">o</font>,<span class="p1">(<span class="default"><a href="msafree.html#K11" title="MSAFREE:func.11">FreeMSA</a> <font color="Maroon" title="c2">X</font></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"> the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <span class="p3">(<span class="default"><a href="msafree.html#K11" title="MSAFREE:func.11">FreeMSA</a> <font color="Maroon" title="c2">X</font></span>)</span> <a href="finseq_2.html#K6" title="FINSEQ_2:func.6">#</a></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a>  the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">Arity</a> of <font color="Maroon" title="c1">S</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">o</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="msualg_1.html#D4" title="MSUALG_1:def.4">MSUALG_1:def 4</a></span>;<br/><a NAME="E7:38_1"/><span class="kw">then </span>
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="msualg_1.html#K5" title="MSUALG_1:func.5">Den</a> (<font color="Maroon" title="c9">o</font>,<span class="p2">(<span class="default"><a href="msafree.html#K11" title="MSAFREE:func.11">FreeMSA</a> <font color="Maroon" title="c2">X</font></span>)</span>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"> the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <span class="p3">(<span class="default"><a href="msafree.html#K11" title="MSAFREE:func.11">FreeMSA</a> <font color="Maroon" title="c2">X</font></span>)</span> <a href="finseq_2.html#K6" title="FINSEQ_2:func.6">#</a></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a>  the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">Arity</a> of <font color="Maroon" title="c1">S</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">o</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></span>;<br/><a NAME="E8:38_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E33">A7</font></span>: 
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"> the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Charact</a> of <font color="Maroon" title="c4">A</font> <a href="msualg_3.html#K1" title="MSUALG_3:func.1">.</a> <font color="Maroon" title="c9">o</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c7">SA</font> <a href="finseq_2.html#K6" title="FINSEQ_2:func.6">#</a></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a>  the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">Arity</a> of <font color="Maroon" title="c1">S</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">o</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:38_1"><span class="lab"><font color="Green" title="E32">A6</font></span></a>, <a class="txt" href="#E1:38_1"><span class="lab"><font color="Green" title="E30">A4</font></span></a>, <a class="ref" href="msualg_2.html#T2" title="MSUALG_2:th.2">MSUALG_2:2</a>, <a class="ref" href="relat_1.html#T62" title="RELAT_1:th.62">RELAT_1:62</a></span>;<br/><a NAME="E9:38_1"/><span class="lab"><font color="Green" title="E34">A8</font></span>: 
( <font color="Maroon" title="c6">SB</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a>  the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <span class="p1">(<span class="default"><a href="msafree.html#K11" title="MSAFREE:func.11">FreeMSA</a> <font color="Maroon" title="c3">Y</font></span>)</span> &amp;  the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <span class="p1">(<span class="default"><a href="msafree.html#K11" title="MSAFREE:func.11">FreeMSA</a> <font color="Maroon" title="c3">Y</font></span>)</span> is   <a href="msualg_2.html#NM1" title="MSUALG_2:NM.1">MSSubset</a> of <span class="p1">(<span class="default"><a href="msafree.html#K11" title="MSAFREE:func.11">FreeMSA</a> <font color="Maroon" title="c3">Y</font></span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="pboole.html#D18" title="PBOOLE:def.18">PBOOLE:def 18</a></span>;<br/><a NAME="E10:38_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E35">A9</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">SB</font> <a href="finseq_2.html#K6" title="FINSEQ_2:func.6">#</a></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a>  the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">Arity</a> of <font color="Maroon" title="c1">S</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">o</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"> the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <span class="p3">(<span class="default"><a href="msafree.html#K11" title="MSAFREE:func.11">FreeMSA</a> <font color="Maroon" title="c3">Y</font></span>)</span> <a href="finseq_2.html#K6" title="FINSEQ_2:func.6">#</a></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a>  the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">Arity</a> of <font color="Maroon" title="c1">S</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">o</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="msualg_2.html#T2" title="MSUALG_2:th.2">MSUALG_2:2</a></span>;<br/><a NAME="E11:38_1"/><span class="lab"><font color="Green" title="E36">A10</font></span>: 
<font color="Maroon" title="c6">SB</font> <a href="msualg_2.html#R1" title="MSUALG_2:pred.1">is_closed_on</a> <font color="Maroon" title="c9">o</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:38"><span class="lab"><font color="Green" title="E29">A3</font></span></a>, <a class="ref" href="msualg_2.html#D6" title="MSUALG_2:def.6">MSUALG_2:def 6</a></span>;<br/><span class="lab"><font color="Green" title="E37">A11</font></span>:  the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Charact</a> of <font color="Maroon" title="c5">B</font> <a href="msualg_3.html#K1" title="MSUALG_3:func.1">.</a> <font color="Maroon" title="c9">o</font> = 
<span class="p1">(<span class="default"><a href="msualg_2.html#K4" title="MSUALG_2:func.4">Opers</a> (<span class="p2">(<span class="default"><a href="msafree.html#K11" title="MSAFREE:func.11">FreeMSA</a> <font color="Maroon" title="c3">Y</font></span>)</span>,<font color="Maroon" title="c6">SB</font>)</span>)</span> <a href="msualg_3.html#K1" title="MSUALG_3:func.1">.</a> <font color="Maroon" title="c9">o</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="msualg_2.html#D9" title="MSUALG_2:def.9">MSUALG_2:def 9</a></span>
<br/>.= 
<font color="Maroon" title="c9">o</font> <a href="msualg_2.html#K3" title="MSUALG_2:func.3">/.</a> <font color="Maroon" title="c6">SB</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="msualg_2.html#D8" title="MSUALG_2:def.8">MSUALG_2:def 8</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="msualg_1.html#K5" title="MSUALG_1:func.5">Den</a> (<font color="Maroon" title="c9">o</font>,<span class="p2">(<span class="default"><a href="msafree.html#K11" title="MSAFREE:func.11">FreeMSA</a> <font color="Maroon" title="c3">Y</font></span>)</span>)</span>)</span> <a href="relset_1.html#K5" title="RELSET_1:func.5">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c6">SB</font> <a href="finseq_2.html#K6" title="FINSEQ_2:func.6">#</a></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a>  the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">Arity</a> of <font color="Maroon" title="c1">S</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">o</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:38_1"><span class="lab"><font color="Green" title="E36">A10</font></span></a>, <a class="ref" href="msualg_2.html#D7" title="MSUALG_2:def.7">MSUALG_2:def 7</a></span>
;<br/><a NAME="E13:38_1"/>
 <a href="msualg_1.html#K3" title="MSUALG_1:func.3">Args</a> (<font color="Maroon" title="c9">o</font>,<span class="p1">(<span class="default"><a href="msafree.html#K11" title="MSAFREE:func.11">FreeMSA</a> <font color="Maroon" title="c3">Y</font></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"> the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <span class="p3">(<span class="default"><a href="msafree.html#K11" title="MSAFREE:func.11">FreeMSA</a> <font color="Maroon" title="c3">Y</font></span>)</span> <a href="finseq_2.html#K6" title="FINSEQ_2:func.6">#</a></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a>  the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">Arity</a> of <font color="Maroon" title="c1">S</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">o</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="msualg_1.html#D4" title="MSUALG_1:def.4">MSUALG_1:def 4</a></span>;<br/><a NAME="E14:38_1"/><span class="kw">then </span>
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="msualg_1.html#K5" title="MSUALG_1:func.5">Den</a> (<font color="Maroon" title="c9">o</font>,<span class="p2">(<span class="default"><a href="msafree.html#K11" title="MSAFREE:func.11">FreeMSA</a> <font color="Maroon" title="c3">Y</font></span>)</span>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"> the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <span class="p3">(<span class="default"><a href="msafree.html#K11" title="MSAFREE:func.11">FreeMSA</a> <font color="Maroon" title="c3">Y</font></span>)</span> <a href="finseq_2.html#K6" title="FINSEQ_2:func.6">#</a></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a>  the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">Arity</a> of <font color="Maroon" title="c1">S</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">o</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></span>;<br/><a NAME="E15:38_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E38">A12</font></span>: 
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"> the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Charact</a> of <font color="Maroon" title="c5">B</font> <a href="msualg_3.html#K1" title="MSUALG_3:func.1">.</a> <font color="Maroon" title="c9">o</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">SB</font> <a href="finseq_2.html#K6" title="FINSEQ_2:func.6">#</a></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a>  the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">Arity</a> of <font color="Maroon" title="c1">S</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">o</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:38_1"><span class="lab"><font color="Green" title="E37">A11</font></span></a>, <a class="txt" href="#E9:38_1"><span class="lab"><font color="Green" title="E34">A8</font></span></a>, <a class="ref" href="msualg_2.html#T2" title="MSUALG_2:th.2">MSUALG_2:2</a>, <a class="ref" href="relat_1.html#T62" title="RELAT_1:th.62">RELAT_1:62</a></span>;<br/><a NAME="E16:38_1"/><span class="lab"><font color="Green" title="E39">A13</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c7">SA</font> <a href="finseq_2.html#K6" title="FINSEQ_2:func.6">#</a></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a>  the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">Arity</a> of <font color="Maroon" title="c1">S</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">o</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"> the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <span class="p3">(<span class="default"><a href="msafree.html#K11" title="MSAFREE:func.11">FreeMSA</a> <font color="Maroon" title="c2">X</font></span>)</span> <a href="finseq_2.html#K6" title="FINSEQ_2:func.6">#</a></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a>  the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">Arity</a> of <font color="Maroon" title="c1">S</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">o</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:38_1"><span class="lab"><font color="Green" title="E30">A4</font></span></a>, <a class="ref" href="msualg_2.html#T2" title="MSUALG_2:th.2">MSUALG_2:2</a></span>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="38_1_3"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c10">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="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c10">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c7">SA</font> <a href="finseq_2.html#K6" title="FINSEQ_2:func.6">#</a></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a>  the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">Arity</a> of <font color="Maroon" title="c1">S</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">o</font> implies <span class="p1">(<span class="default"> the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Charact</a> of <font color="Maroon" title="c4">A</font> <a href="msualg_3.html#K1" title="MSUALG_3:func.1">.</a> <font color="Maroon" title="c9">o</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"> the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Charact</a> of <font color="Maroon" title="c5">B</font> <a href="msualg_3.html#K1" title="MSUALG_3:func.1">.</a> <font color="Maroon" title="c9">o</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">x</font> )</span><br/><span class="kw">assume </span><a NAME="E1:38_1_3"/><span class="lab"><font color="Green" title="E40">A14</font></span>: 
<font color="Maroon" title="c10">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c7">SA</font> <a href="finseq_2.html#K6" title="FINSEQ_2:func.6">#</a></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a>  the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">Arity</a> of <font color="Maroon" title="c1">S</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">o</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"> the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Charact</a> of <font color="Maroon" title="c4">A</font> <a href="msualg_3.html#K1" title="MSUALG_3:func.1">.</a> <font color="Maroon" title="c9">o</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"> the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Charact</a> of <font color="Maroon" title="c5">B</font> <a href="msualg_3.html#K1" title="MSUALG_3:func.1">.</a> <font color="Maroon" title="c9">o</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">x</font></span><br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c11">p1</font> = <font color="Maroon" title="c10">x</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="msualg_1.html#K3" title="MSUALG_1:func.3">Args</a> (<font color="Maroon" title="c9">o</font>,<span class="p1">(<span class="default"><a href="msafree.html#K11" title="MSAFREE:func.11">FreeMSA</a> <font color="Maroon" title="c2">X</font></span>)</span>) <span class="kw">by</span> <span class="lab"><a class="txt" href="#E16:38_1"><span class="lab"><font color="Green" title="E39">A13</font></span></a>, <a class="ref" href="msualg_1.html#D4" title="MSUALG_1:def.4">MSUALG_1:def 4</a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c12">p2</font> = <font color="Maroon" title="c10">x</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="msualg_1.html#K3" title="MSUALG_1:func.3">Args</a> (<font color="Maroon" title="c9">o</font>,<span class="p1">(<span class="default"><a href="msafree.html#K11" title="MSAFREE:func.11">FreeMSA</a> <font color="Maroon" title="c3">Y</font></span>)</span>) <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:38"><span class="lab"><font color="Green" title="E27">A1</font></span></a>, <a class="txt" href="#E10:38_1"><span class="lab"><font color="Green" title="E35">A9</font></span></a>, <a class="txt" href="#E1:38_1_3"><span class="lab"><font color="Green" title="E40">A14</font></span></a>, <a class="ref" href="msualg_1.html#D4" title="MSUALG_1:def.4">MSUALG_1:def 4</a></span>;<br/><span class="kw">thus </span><span class="p1">(<span class="default"> the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Charact</a> of <font color="Maroon" title="c4">A</font> <a href="msualg_3.html#K1" title="MSUALG_3:func.1">.</a> <font color="Maroon" title="c9">o</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">x</font> = 
<span class="p1">(<span class="default"><a href="msualg_1.html#K5" title="MSUALG_1:func.5">Den</a> (<font color="Maroon" title="c9">o</font>,<span class="p2">(<span class="default"><a href="msafree.html#K11" title="MSAFREE:func.11">FreeMSA</a> <font color="Maroon" title="c2">X</font></span>)</span>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">p1</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:38_1"><span class="lab"><font color="Green" title="E32">A6</font></span></a>, <a class="txt" href="#E8:38_1"><span class="lab"><font color="Green" title="E33">A7</font></span></a>, <a class="txt" href="#E1:38_1_3"><span class="lab"><font color="Green" title="E40">A14</font></span></a>, <a class="ref" href="funct_1.html#T47" title="FUNCT_1:th.47">FUNCT_1:47</a></span>
<br/>.= 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c9">o</font>, the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">S</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="trees_4.html#K4" title="TREES_4:func.4">-tree</a> <font color="Maroon" title="c11">p1</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="instalg1.html#T3" title="INSTALG1:th.3">INSTALG1:3</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="msualg_1.html#K5" title="MSUALG_1:func.5">Den</a> (<font color="Maroon" title="c9">o</font>,<span class="p2">(<span class="default"><a href="msafree.html#K11" title="MSAFREE:func.11">FreeMSA</a> <font color="Maroon" title="c3">Y</font></span>)</span>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c12">p2</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="instalg1.html#T3" title="INSTALG1:th.3">INSTALG1:3</a></span>
<br/>.= 
<span class="p1">(<span class="default"> the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Charact</a> of <font color="Maroon" title="c5">B</font> <a href="msualg_3.html#K1" title="MSUALG_3:func.1">.</a> <font color="Maroon" title="c9">o</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">x</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:38"><span class="lab"><font color="Green" title="E27">A1</font></span></a>, <a class="txt" href="#E12:38_1"><span class="lab"><font color="Green" title="E37">A11</font></span></a>, <a class="txt" href="#E15:38_1"><span class="lab"><font color="Green" title="E38">A12</font></span></a>, <a class="txt" href="#E1:38_1_3"><span class="lab"><font color="Green" title="E40">A14</font></span></a>, <a class="ref" href="funct_1.html#T47" title="FUNCT_1:th.47">FUNCT_1:47</a></span>
; <a class="txt" 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="E18:38_1"/>
 the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Charact</a> of <font color="Maroon" title="c4">A</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Charact</a> of <font color="Maroon" title="c5">B</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:38"><span class="lab"><font color="Green" title="E27">A1</font></span></a>, <a class="txt" href="#E8:38_1"><span class="lab"><font color="Green" title="E33">A7</font></span></a>, <a class="txt" href="#E15:38_1"><span class="lab"><font color="Green" title="E38">A12</font></span></a>, <a class="ref" href="funct_1.html#T2" title="FUNCT_1:th.2">FUNCT_1:2</a></span>; <a class="txt" 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="E7:38"/>
 <a href="msualg_1.html#G3" title="MSUALG_1:aggr.3">MSAlgebra</a>(#  the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c4">A</font>, the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Charact</a> of <font color="Maroon" title="c4">A</font> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="msualg_1.html#G3" title="MSUALG_1:aggr.3">MSAlgebra</a>(#  the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c5">B</font>, the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Charact</a> of <font color="Maroon" title="c5">B</font> #)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:38"><span class="lab"><font color="Green" title="E27">A1</font></span></a>, <a class="ref" href="pboole.html#T3" title="PBOOLE:th.3">PBOOLE:3</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
