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<a NAME="E1:24_1_1"/>
<font color="Maroon" title="c2">r2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"> { <span class="default"> <font color="Olive" title="b1">r</font> where <font color="Olive" title="b1">r</font> is   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a> : ( <font color="Maroon" title="c1">r1</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b1">r</font> &amp; <font color="Olive" title="b1">r</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c2">r2</font> ) </span> } </span> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:24"><span class="lab"><font color="Green" title="E18">A1</font></span></a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c3">A</font> = <span class="p1"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><font color="Maroon" title="c1">r1</font>,<font color="Maroon" title="c2">r2</font></span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span> as   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  <span class="kw">by</span> <span class="lab"><a class="ref" href="rcomp_1.html#D1" title="RCOMP_1:def.1">RCOMP_1:def 1</a></span>;<br/>
<a NAME="E3:24_1_1"/>
<span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Maroon" title="c3">A</font>,<font color="Maroon" title="c3">A</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>,<a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="zfmisc_1.html#T96" title="ZFMISC_1:th.96">ZFMISC_1:96</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c4">Ma</font> = <a href="real_lat.html#K2" title="REAL_LAT:func.2">maxreal</a> <a href="realset1.html#K1" title="REALSET1:func.1">||</a> <font color="Maroon" title="c3">A</font>, <font color="Maroon" title="c5">Mi</font> = <a href="real_lat.html#K1" title="REAL_LAT:func.1">minreal</a> <a href="realset1.html#K1" title="REALSET1:func.1">||</a> <font color="Maroon" title="c3">A</font> as   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Maroon" title="c3">A</font>,<font color="Maroon" title="c3">A</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>,<a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#T32" title="FUNCT_2:th.32">FUNCT_2:32</a></span>;<br/>
<a NAME="E5:24_1_1"/><span class="lab"><font color="Green" title="E19">A2</font></span>: 
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c5">Mi</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Maroon" title="c3">A</font>,<font color="Maroon" title="c3">A</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 
<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/>
<div><span class="lab"><font color="Green" title="E20">A3</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="24_1_1_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c6">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c5">Mi</font> implies <font color="Maroon" title="c5">Mi</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">A</font> )</span><br/><span class="kw">assume </span><a NAME="E1:24_1_1_1"/><span class="lab"><font color="Green" title="E21">A4</font></span>: 
<font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c5">Mi</font>
 ; <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="c5">Mi</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">A</font></span><br/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c7">x1</font>, <font color="Maroon" title="c8">x2</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <span class="kw"> such that </span><br/><a NAME="E3:24_1_1_1"/><span class="lab"><font color="Green" title="E22">A5</font></span>: 
<font color="Maroon" title="c6">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c7">x1</font>,<font color="Maroon" title="c8">x2</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#D1" title="RELAT_1:def.1">RELAT_1:def 1</a></span>;<br/><a NAME="E4:24_1_1_1"/>
<font color="Maroon" title="c8">x2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">A</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:24_1_1_1"><span class="lab"><font color="Green" title="E21">A4</font></span></a>, <a class="txt" href="#E3:24_1_1_1"><span class="lab"><font color="Green" title="E22">A5</font></span></a>, <a class="ref" href="zfmisc_1.html#T87" title="ZFMISC_1:th.87">ZFMISC_1:87</a></span>;<br/><a NAME="E5:24_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c8">x2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"> { <span class="default"> <font color="Olive" title="b1">r</font> where <font color="Olive" title="b1">r</font> is   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a> : ( <font color="Maroon" title="c1">r1</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b1">r</font> &amp; <font color="Olive" title="b1">r</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c2">r2</font> ) </span> } </span> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="rcomp_1.html#D1" title="RCOMP_1:def.1">RCOMP_1:def 1</a></span>;<br/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c9">y2</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> <span class="kw"> such that </span><br/><a NAME="E7:24_1_1_1"/><span class="lab"><font color="Green" title="E23">A6</font></span>: 
<font color="Maroon" title="c8">x2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">y2</font>
 <span class="kw">and </span><br/><a NAME="E8:24_1_1_1"/><span class="lab"><font color="Green" title="E24">A7</font></span>: 
( <font color="Maroon" title="c1">r1</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c9">y2</font> &amp; <font color="Maroon" title="c9">y2</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c2">r2</font> )
 ;<br/><a NAME="E9:24_1_1_1"/>
<font color="Maroon" title="c7">x1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">A</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:24_1_1_1"><span class="lab"><font color="Green" title="E21">A4</font></span></a>, <a class="txt" href="#E3:24_1_1_1"><span class="lab"><font color="Green" title="E22">A5</font></span></a>, <a class="ref" href="zfmisc_1.html#T87" title="ZFMISC_1:th.87">ZFMISC_1:87</a></span>;<br/><a NAME="E10:24_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c7">x1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"> { <span class="default"> <font color="Olive" title="b1">r</font> where <font color="Olive" title="b1">r</font> is   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a> : ( <font color="Maroon" title="c1">r1</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b1">r</font> &amp; <font color="Olive" title="b1">r</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c2">r2</font> ) </span> } </span> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="rcomp_1.html#D1" title="RCOMP_1:def.1">RCOMP_1:def 1</a></span>;<br/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c10">y1</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> <span class="kw"> such that </span><br/><a NAME="E12:24_1_1_1"/><span class="lab"><font color="Green" title="E25">A8</font></span>: 
<font color="Maroon" title="c7">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">y1</font>
 <span class="kw">and </span><br/><a NAME="E13:24_1_1_1"/><span class="lab"><font color="Green" title="E26">A9</font></span>: 
( <font color="Maroon" title="c1">r1</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c10">y1</font> &amp; <font color="Maroon" title="c10">y1</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c2">r2</font> )
 ;<br/><font color="Maroon" title="c5">Mi</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">x</font> = 
<a href="real_lat.html#K1" title="REAL_LAT:func.1">minreal</a> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c7">x1</font>,<font color="Maroon" title="c8">x2</font>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:24_1_1_1"><span class="lab"><font color="Green" title="E21">A4</font></span></a>, <a class="txt" href="#E3:24_1_1_1"><span class="lab"><font color="Green" title="E22">A5</font></span></a>, <a class="ref" href="funct_1.html#T49" title="FUNCT_1:th.49">FUNCT_1:49</a></span>
<br/>.= 
 <a href="xxreal_0.html#K3" title="XXREAL_0:func.3">min</a> (<font color="Maroon" title="c10">y1</font>,<font color="Maroon" title="c9">y2</font>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:24_1_1_1"><span class="lab"><font color="Green" title="E25">A8</font></span></a>, <a class="txt" href="#E7:24_1_1_1"><span class="lab"><font color="Green" title="E23">A6</font></span></a>, <a class="ref" href="real_lat.html#D1" title="REAL_LAT:def.1">REAL_LAT:def 1</a></span>
;<br/><a NAME="E15:24_1_1_1"/><span class="kw">then </span>
( <font color="Maroon" title="c5">Mi</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">y1</font> or <font color="Maroon" title="c5">Mi</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">y2</font> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xxreal_0.html#T15" title="XXREAL_0:th.15">XXREAL_0:15</a></span>;<br/><a NAME="E16:24_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c5">Mi</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"> { <span class="default"> <font color="Olive" title="b1">r</font> where <font color="Olive" title="b1">r</font> is   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a> : ( <font color="Maroon" title="c1">r1</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b1">r</font> &amp; <font color="Olive" title="b1">r</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c2">r2</font> ) </span> } </span> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:24_1_1_1"><span class="lab"><font color="Green" title="E26">A9</font></span></a>, <a class="txt" href="#E8:24_1_1_1"><span class="lab"><font color="Green" title="E24">A7</font></span></a></span>;<br/><span class="kw">hence </span><a NAME="E17:24_1_1_1"/>
<font color="Maroon" title="c5">Mi</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">A</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="rcomp_1.html#D1" title="RCOMP_1:def.1">RCOMP_1:def 1</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>
<div><span class="lab"><font color="Green" title="E21">A10</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="24_1_1_2"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c6">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c4">Ma</font> implies <font color="Maroon" title="c4">Ma</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">A</font> )</span><br/><span class="kw">assume </span><a NAME="E1:24_1_1_2"/><span class="lab"><font color="Green" title="E22">A11</font></span>: 
<font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c4">Ma</font>
 ; <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="c4">Ma</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">A</font></span><br/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c7">x1</font>, <font color="Maroon" title="c8">x2</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <span class="kw"> such that </span><br/><a NAME="E3:24_1_1_2"/><span class="lab"><font color="Green" title="E23">A12</font></span>: 
<font color="Maroon" title="c6">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c7">x1</font>,<font color="Maroon" title="c8">x2</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#D1" title="RELAT_1:def.1">RELAT_1:def 1</a></span>;<br/><a NAME="E4:24_1_1_2"/>
<font color="Maroon" title="c8">x2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">A</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:24_1_1_2"><span class="lab"><font color="Green" title="E22">A11</font></span></a>, <a class="txt" href="#E3:24_1_1_2"><span class="lab"><font color="Green" title="E23">A12</font></span></a>, <a class="ref" href="zfmisc_1.html#T87" title="ZFMISC_1:th.87">ZFMISC_1:87</a></span>;<br/><a NAME="E5:24_1_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c8">x2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"> { <span class="default"> <font color="Olive" title="b1">r</font> where <font color="Olive" title="b1">r</font> is   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a> : ( <font color="Maroon" title="c1">r1</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b1">r</font> &amp; <font color="Olive" title="b1">r</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c2">r2</font> ) </span> } </span> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="rcomp_1.html#D1" title="RCOMP_1:def.1">RCOMP_1:def 1</a></span>;<br/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c9">y2</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> <span class="kw"> such that </span><br/><a NAME="E7:24_1_1_2"/><span class="lab"><font color="Green" title="E24">A13</font></span>: 
<font color="Maroon" title="c8">x2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">y2</font>
 <span class="kw">and </span><br/><a NAME="E8:24_1_1_2"/><span class="lab"><font color="Green" title="E25">A14</font></span>: 
( <font color="Maroon" title="c1">r1</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c9">y2</font> &amp; <font color="Maroon" title="c9">y2</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c2">r2</font> )
 ;<br/><a NAME="E9:24_1_1_2"/>
<font color="Maroon" title="c7">x1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">A</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:24_1_1_2"><span class="lab"><font color="Green" title="E22">A11</font></span></a>, <a class="txt" href="#E3:24_1_1_2"><span class="lab"><font color="Green" title="E23">A12</font></span></a>, <a class="ref" href="zfmisc_1.html#T87" title="ZFMISC_1:th.87">ZFMISC_1:87</a></span>;<br/><a NAME="E10:24_1_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c7">x1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"> { <span class="default"> <font color="Olive" title="b1">r</font> where <font color="Olive" title="b1">r</font> is   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a> : ( <font color="Maroon" title="c1">r1</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b1">r</font> &amp; <font color="Olive" title="b1">r</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c2">r2</font> ) </span> } </span> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="rcomp_1.html#D1" title="RCOMP_1:def.1">RCOMP_1:def 1</a></span>;<br/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c10">y1</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> <span class="kw"> such that </span><br/><a NAME="E12:24_1_1_2"/><span class="lab"><font color="Green" title="E26">A15</font></span>: 
<font color="Maroon" title="c7">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">y1</font>
 <span class="kw">and </span><br/><a NAME="E13:24_1_1_2"/><span class="lab"><font color="Green" title="E27">A16</font></span>: 
( <font color="Maroon" title="c1">r1</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c10">y1</font> &amp; <font color="Maroon" title="c10">y1</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c2">r2</font> )
 ;<br/><font color="Maroon" title="c4">Ma</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">x</font> = 
<a href="real_lat.html#K2" title="REAL_LAT:func.2">maxreal</a> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c7">x1</font>,<font color="Maroon" title="c8">x2</font>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:24_1_1_2"><span class="lab"><font color="Green" title="E22">A11</font></span></a>, <a class="txt" href="#E3:24_1_1_2"><span class="lab"><font color="Green" title="E23">A12</font></span></a>, <a class="ref" href="funct_1.html#T49" title="FUNCT_1:th.49">FUNCT_1:49</a></span>
<br/>.= 
 <a href="xxreal_0.html#K4" title="XXREAL_0:func.4">max</a> (<font color="Maroon" title="c10">y1</font>,<font color="Maroon" title="c9">y2</font>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:24_1_1_2"><span class="lab"><font color="Green" title="E26">A15</font></span></a>, <a class="txt" href="#E7:24_1_1_2"><span class="lab"><font color="Green" title="E24">A13</font></span></a>, <a class="ref" href="real_lat.html#D2" title="REAL_LAT:def.2">REAL_LAT:def 2</a></span>
;<br/><a NAME="E15:24_1_1_2"/><span class="kw">then </span>
( <font color="Maroon" title="c4">Ma</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">y1</font> or <font color="Maroon" title="c4">Ma</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">y2</font> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xxreal_0.html#T16" title="XXREAL_0:th.16">XXREAL_0:16</a></span>;<br/><a NAME="E16:24_1_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c4">Ma</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"> { <span class="default"> <font color="Olive" title="b1">r</font> where <font color="Olive" title="b1">r</font> is   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a> : ( <font color="Maroon" title="c1">r1</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b1">r</font> &amp; <font color="Olive" title="b1">r</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c2">r2</font> ) </span> } </span> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:24_1_1_2"><span class="lab"><font color="Green" title="E27">A16</font></span></a>, <a class="txt" href="#E8:24_1_1_2"><span class="lab"><font color="Green" title="E25">A14</font></span></a></span>;<br/><span class="kw">hence </span><a NAME="E17:24_1_1_2"/>
<font color="Maroon" title="c4">Ma</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">A</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="rcomp_1.html#D1" title="RCOMP_1:def.1">RCOMP_1:def 1</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">reconsider </span><font color="Maroon" title="c6">Mi</font> = <font color="Maroon" title="c5">Mi</font> as   <a href="binop_1.html#NM2" title="BINOP_1:NM.2">BinOp</a> of <font color="Maroon" title="c3">A</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:24_1_1"><span class="lab"><font color="Green" title="E19">A2</font></span></a>, <a class="txt" href="#E6:24_1_1"><span class="lab"><font color="Green" title="E20">A3</font></span></a>, <a class="ref" href="funct_2.html#T3" title="FUNCT_2:th.3">FUNCT_2:3</a></span>;<br/>
<a NAME="E9:24_1_1"/>
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c4">Ma</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Maroon" title="c3">A</font>,<font color="Maroon" title="c3">A</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 
<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/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c7">Ma</font> = <font color="Maroon" title="c4">Ma</font> as   <a href="binop_1.html#NM2" title="BINOP_1:NM.2">BinOp</a> of <font color="Maroon" title="c3">A</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:24_1_1"><span class="lab"><font color="Green" title="E21">A10</font></span></a>, <a class="ref" href="funct_2.html#T3" title="FUNCT_2:th.3">FUNCT_2:3</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c8">R</font> =  <a href="real_lat.html#K3" title="REAL_LAT:func.3">Real_Lattice</a> ;<br/>
<span class="kw">set </span><font color="Maroon" title="c9">L9</font> =  <a href="lattices.html#G3" title="LATTICES:aggr.3">LattStr</a>(# <font color="Maroon" title="c3">A</font>,<font color="Maroon" title="c7">Ma</font>,<font color="Maroon" title="c6">Mi</font> #);<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c10">L</font> =  <a href="lattices.html#G3" title="LATTICES:aggr.3">LattStr</a>(# <font color="Maroon" title="c3">A</font>,<font color="Maroon" title="c7">Ma</font>,<font color="Maroon" title="c6">Mi</font> #) as   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="lattices.html#L3" title="LATTICES:struct.3">LattStr</a>  ;<br/>
<div><span class="lab"><font color="Green" title="E22">A17</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="24_1_1_3"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c11">a</font>, <font color="Maroon" title="c12">b</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c10">L</font>; <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="c11">a</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Maroon" title="c12">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="real_lat.html#K2" title="REAL_LAT:func.2">maxreal</a> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c11">a</font>,<font color="Maroon" title="c12">b</font>) &amp; <font color="Maroon" title="c11">a</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Maroon" title="c12">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="real_lat.html#K1" title="REAL_LAT:func.1">minreal</a> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c11">a</font>,<font color="Maroon" title="c12">b</font>) )</span><br/><span class="kw">thus </span><font color="Maroon" title="c11">a</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Maroon" title="c12">b</font> = 
 the <a href="lattices.html#U2" title="LATTICES:sel.2">L_join</a> of <font color="Maroon" title="c10">L</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c11">a</font>,<font color="Maroon" title="c12">b</font>)
<span class="kw">by</span> <span class="lab"><a class="ref" href="lattices.html#D1" title="LATTICES:def.1">LATTICES:def 1</a></span>
<br/>.= 
<a href="real_lat.html#K2" title="REAL_LAT:func.2">maxreal</a> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c11">a</font>,<font color="Maroon" title="c12">b</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_1.html#T49" title="FUNCT_1:th.49">FUNCT_1:49</a></span>
<br/>.= 
<a href="real_lat.html#K2" title="REAL_LAT:func.2">maxreal</a> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c11">a</font>,<font color="Maroon" title="c12">b</font>)

; <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="c11">a</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Maroon" title="c12">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="real_lat.html#K1" title="REAL_LAT:func.1">minreal</a> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c11">a</font>,<font color="Maroon" title="c12">b</font>)</span><br/><span class="kw">thus </span><font color="Maroon" title="c11">a</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Maroon" title="c12">b</font> = 
 the <a href="lattices.html#U1" title="LATTICES:sel.1">L_meet</a> of <font color="Maroon" title="c10">L</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c11">a</font>,<font color="Maroon" title="c12">b</font>)
<span class="kw">by</span> <span class="lab"><a class="ref" href="lattices.html#D2" title="LATTICES:def.2">LATTICES:def 2</a></span>
<br/>.= 
<a href="real_lat.html#K1" title="REAL_LAT:func.1">minreal</a> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c11">a</font>,<font color="Maroon" title="c12">b</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_1.html#T49" title="FUNCT_1:th.49">FUNCT_1:49</a></span>
<br/>.= 
<a href="real_lat.html#K1" title="REAL_LAT:func.1">minreal</a> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c11">a</font>,<font color="Maroon" title="c12">b</font>)

; <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>
<div><span class="lab"><font color="Green" title="E23">A18</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="24_1_1_4"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c11">x</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c3">A</font>; <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="c11">x</font> is   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="real_lat.html#K3" title="REAL_LAT:func.3">Real_Lattice</a></span><br/><a NAME="E1:24_1_1_4"/>
<font color="Maroon" title="c11">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">A</font>
 ;<br/><a NAME="E2:24_1_1_4"/><span class="kw">then </span>
<font color="Maroon" title="c11">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"> { <span class="default"> <font color="Olive" title="b1">r</font> where <font color="Olive" title="b1">r</font> is   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a> : ( <font color="Maroon" title="c1">r1</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b1">r</font> &amp; <font color="Olive" title="b1">r</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c2">r2</font> ) </span> } </span> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="rcomp_1.html#D1" title="RCOMP_1:def.1">RCOMP_1:def 1</a></span>;<br/><a NAME="E3:24_1_1_4"/><span class="kw">then </span>
 ex <font color="Olive" title="b1">y</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>  st <br/>( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">y</font> &amp; <font color="Maroon" title="c1">r1</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b1">y</font> &amp; <font color="Olive" title="b1">y</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c2">r2</font> )
 ;<br/><span class="kw">hence </span><a NAME="E4:24_1_1_4"/>
<font color="Maroon" title="c11">x</font> is   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="real_lat.html#K3" title="REAL_LAT:func.3">Real_Lattice</a>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="real_lat.html#D3" title="REAL_LAT:def.3">REAL_LAT:def 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><span class="kw">end;</span></div>
<div><span class="lab"><font color="Green" title="E24">A19</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="24_1_1_5"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c11">p</font>, <font color="Maroon" title="c12">q</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c10">L</font>; <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="c11">p</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Maroon" title="c12">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">q</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Maroon" title="c11">p</font></span><br/><span class="kw">reconsider </span><font color="Maroon" title="c13">p9</font> = <font color="Maroon" title="c11">p</font>, <font color="Maroon" title="c14">q9</font> = <font color="Maroon" title="c12">q</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="real_lat.html#K3" title="REAL_LAT:func.3">Real_Lattice</a> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:24_1_1"><span class="lab"><font color="Green" title="E23">A18</font></span></a></span>;<br/><span class="kw">thus </span><font color="Maroon" title="c11">p</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Maroon" title="c12">q</font> = 
<a href="real_lat.html#K2" title="REAL_LAT:func.2">maxreal</a> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c11">p</font>,<font color="Maroon" title="c12">q</font>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:24_1_1"><span class="lab"><font color="Green" title="E22">A17</font></span></a></span>
<br/>.= 
<a href="real_lat.html#K2" title="REAL_LAT:func.2">maxreal</a> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c14">q9</font>,<font color="Maroon" title="c13">p9</font>)
<span class="kw">by</span> <span class="lab"><a class="ref" href="real_lat.html#T1" title="REAL_LAT:th.1">REAL_LAT:1</a></span>
<br/>.= 
<font color="Maroon" title="c12">q</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Maroon" title="c11">p</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:24_1_1"><span class="lab"><font color="Green" title="E22">A17</font></span></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>
<div><span class="lab"><font color="Green" title="E25">A20</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="24_1_1_6"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c11">p</font>, <font color="Maroon" title="c12">q</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c10">L</font>; <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="c11">p</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c11">p</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Maroon" title="c12">q</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">p</font></span><br/><span class="kw">reconsider </span><font color="Maroon" title="c13">p9</font> = <font color="Maroon" title="c11">p</font>, <font color="Maroon" title="c14">q9</font> = <font color="Maroon" title="c12">q</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="real_lat.html#K3" title="REAL_LAT:func.3">Real_Lattice</a> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:24_1_1"><span class="lab"><font color="Green" title="E23">A18</font></span></a></span>;<br/><span class="kw">thus </span><font color="Maroon" title="c11">p</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c11">p</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Maroon" title="c12">q</font></span>)</span> = 
<a href="real_lat.html#K1" title="REAL_LAT:func.1">minreal</a> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c11">p</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c11">p</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Maroon" title="c12">q</font></span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:24_1_1"><span class="lab"><font color="Green" title="E22">A17</font></span></a></span>
<br/>.= 
<a href="real_lat.html#K1" title="REAL_LAT:func.1">minreal</a> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c13">p9</font>,<span class="p1">(<span class="default"><a href="real_lat.html#K2" title="REAL_LAT:func.2">maxreal</a> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c13">p9</font>,<font color="Maroon" title="c14">q9</font>)</span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:24_1_1"><span class="lab"><font color="Green" title="E22">A17</font></span></a></span>
<br/>.= 
<font color="Maroon" title="c11">p</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="real_lat.html#T6" title="REAL_LAT:th.6">REAL_LAT:6</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>
<div><span class="lab"><font color="Green" title="E26">A21</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="24_1_1_7"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c11">p</font>, <font color="Maroon" title="c12">q</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c10">L</font>; <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="c11">p</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Maroon" title="c12">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">q</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Maroon" title="c11">p</font></span><br/><span class="kw">reconsider </span><font color="Maroon" title="c13">p9</font> = <font color="Maroon" title="c11">p</font>, <font color="Maroon" title="c14">q9</font> = <font color="Maroon" title="c12">q</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="real_lat.html#K3" title="REAL_LAT:func.3">Real_Lattice</a> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:24_1_1"><span class="lab"><font color="Green" title="E23">A18</font></span></a></span>;<br/><span class="kw">thus </span><font color="Maroon" title="c11">p</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Maroon" title="c12">q</font> = 
<a href="real_lat.html#K1" title="REAL_LAT:func.1">minreal</a> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c11">p</font>,<font color="Maroon" title="c12">q</font>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:24_1_1"><span class="lab"><font color="Green" title="E22">A17</font></span></a></span>
<br/>.= 
<a href="real_lat.html#K1" title="REAL_LAT:func.1">minreal</a> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c14">q9</font>,<font color="Maroon" title="c13">p9</font>)
<span class="kw">by</span> <span class="lab"><a class="ref" href="real_lat.html#T2" title="REAL_LAT:th.2">REAL_LAT:2</a></span>
<br/>.= 
<font color="Maroon" title="c12">q</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Maroon" title="c11">p</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:24_1_1"><span class="lab"><font color="Green" title="E22">A17</font></span></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>
<div><span class="lab"><font color="Green" title="E27">A22</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="24_1_1_8"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c11">p</font>, <font color="Maroon" title="c12">q</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c10">L</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"><font color="Maroon" title="c11">p</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Maroon" title="c12">q</font></span>)</span> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Maroon" title="c12">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">q</font></span><br/><span class="kw">reconsider </span><font color="Maroon" title="c13">p9</font> = <font color="Maroon" title="c11">p</font>, <font color="Maroon" title="c14">q9</font> = <font color="Maroon" title="c12">q</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="real_lat.html#K3" title="REAL_LAT:func.3">Real_Lattice</a> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:24_1_1"><span class="lab"><font color="Green" title="E23">A18</font></span></a></span>;<br/><span class="kw">thus </span><span class="p1">(<span class="default"><font color="Maroon" title="c11">p</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Maroon" title="c12">q</font></span>)</span> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Maroon" title="c12">q</font> = 
<a href="real_lat.html#K2" title="REAL_LAT:func.2">maxreal</a> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c11">p</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Maroon" title="c12">q</font></span>)</span>,<font color="Maroon" title="c12">q</font>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:24_1_1"><span class="lab"><font color="Green" title="E22">A17</font></span></a></span>
<br/>.= 
<a href="real_lat.html#K2" title="REAL_LAT:func.2">maxreal</a> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<span class="p1">(<span class="default"><a href="real_lat.html#K1" title="REAL_LAT:func.1">minreal</a> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c13">p9</font>,<font color="Maroon" title="c14">q9</font>)</span>)</span>,<font color="Maroon" title="c14">q9</font>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:24_1_1"><span class="lab"><font color="Green" title="E22">A17</font></span></a></span>
<br/>.= 
<font color="Maroon" title="c12">q</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="real_lat.html#T5" title="REAL_LAT:th.5">REAL_LAT:5</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>
<div><span class="lab"><font color="Green" title="E28">A23</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="24_1_1_9"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c11">p</font>, <font color="Maroon" title="c12">q</font>, <font color="Maroon" title="c13">r</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c10">L</font>; <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="c11">p</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">q</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Maroon" title="c13">r</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c11">p</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Maroon" title="c12">q</font></span>)</span> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Maroon" title="c13">r</font></span><br/><span class="kw">reconsider </span><font color="Maroon" title="c14">p9</font> = <font color="Maroon" title="c11">p</font>, <font color="Maroon" title="c15">q9</font> = <font color="Maroon" title="c12">q</font>, <font color="Maroon" title="c16">r9</font> = <font color="Maroon" title="c13">r</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="real_lat.html#K3" title="REAL_LAT:func.3">Real_Lattice</a> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:24_1_1"><span class="lab"><font color="Green" title="E23">A18</font></span></a></span>;<br/><span class="kw">thus </span><font color="Maroon" title="c11">p</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">q</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Maroon" title="c13">r</font></span>)</span> = 
<a href="real_lat.html#K1" title="REAL_LAT:func.1">minreal</a> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c11">p</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c12">q</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Maroon" title="c13">r</font></span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:24_1_1"><span class="lab"><font color="Green" title="E22">A17</font></span></a></span>
<br/>.= 
<a href="real_lat.html#K1" title="REAL_LAT:func.1">minreal</a> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c11">p</font>,<span class="p1">(<span class="default"><a href="real_lat.html#K1" title="REAL_LAT:func.1">minreal</a> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c12">q</font>,<font color="Maroon" title="c13">r</font>)</span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:24_1_1"><span class="lab"><font color="Green" title="E22">A17</font></span></a></span>
<br/>.= 
<a href="real_lat.html#K1" title="REAL_LAT:func.1">minreal</a> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<span class="p1">(<span class="default"><a href="real_lat.html#K1" title="REAL_LAT:func.1">minreal</a> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c14">p9</font>,<font color="Maroon" title="c15">q9</font>)</span>)</span>,<font color="Maroon" title="c16">r9</font>)
<span class="kw">by</span> <span class="lab"><a class="ref" href="real_lat.html#T4" title="REAL_LAT:th.4">REAL_LAT:4</a></span>
<br/>.= 
<a href="real_lat.html#K1" title="REAL_LAT:func.1">minreal</a> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c11">p</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Maroon" title="c12">q</font></span>)</span>,<font color="Maroon" title="c13">r</font>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:24_1_1"><span class="lab"><font color="Green" title="E22">A17</font></span></a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c11">p</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Maroon" title="c12">q</font></span>)</span> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Maroon" title="c13">r</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:24_1_1"><span class="lab"><font color="Green" title="E22">A17</font></span></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>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="24_1_1_10"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c11">p</font>, <font color="Maroon" title="c12">q</font>, <font color="Maroon" title="c13">r</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c10">L</font>; <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="c11">p</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">q</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Maroon" title="c13">r</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c11">p</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Maroon" title="c12">q</font></span>)</span> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Maroon" title="c13">r</font></span><br/><span class="kw">reconsider </span><font color="Maroon" title="c14">p9</font> = <font color="Maroon" title="c11">p</font>, <font color="Maroon" title="c15">q9</font> = <font color="Maroon" title="c12">q</font>, <font color="Maroon" title="c16">r9</font> = <font color="Maroon" title="c13">r</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="real_lat.html#K3" title="REAL_LAT:func.3">Real_Lattice</a> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:24_1_1"><span class="lab"><font color="Green" title="E23">A18</font></span></a></span>;<br/><span class="kw">thus </span><font color="Maroon" title="c11">p</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">q</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Maroon" title="c13">r</font></span>)</span> = 
<a href="real_lat.html#K2" title="REAL_LAT:func.2">maxreal</a> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c11">p</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c12">q</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Maroon" title="c13">r</font></span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:24_1_1"><span class="lab"><font color="Green" title="E22">A17</font></span></a></span>
<br/>.= 
<a href="real_lat.html#K2" title="REAL_LAT:func.2">maxreal</a> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c11">p</font>,<span class="p1">(<span class="default"><a href="real_lat.html#K2" title="REAL_LAT:func.2">maxreal</a> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c12">q</font>,<font color="Maroon" title="c13">r</font>)</span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:24_1_1"><span class="lab"><font color="Green" title="E22">A17</font></span></a></span>
<br/>.= 
<a href="real_lat.html#K2" title="REAL_LAT:func.2">maxreal</a> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<span class="p1">(<span class="default"><a href="real_lat.html#K2" title="REAL_LAT:func.2">maxreal</a> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c14">p9</font>,<font color="Maroon" title="c15">q9</font>)</span>)</span>,<font color="Maroon" title="c16">r9</font>)
<span class="kw">by</span> <span class="lab"><a class="ref" href="real_lat.html#T3" title="REAL_LAT:th.3">REAL_LAT:3</a></span>
<br/>.= 
<a href="real_lat.html#K2" title="REAL_LAT:func.2">maxreal</a> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c11">p</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Maroon" title="c12">q</font></span>)</span>,<font color="Maroon" title="c13">r</font>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:24_1_1"><span class="lab"><font color="Green" title="E22">A17</font></span></a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c11">p</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Maroon" title="c12">q</font></span>)</span> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Maroon" title="c13">r</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:24_1_1"><span class="lab"><font color="Green" title="E22">A17</font></span></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>
<a NAME="E20:24_1_1"/><span class="kw">then </span>
( <font color="Maroon" title="c10">L</font> is  <a href="lattices.html#V4" title="LATTICES:attr.4">join-commutative</a>  &amp; <font color="Maroon" title="c10">L</font> is  <a href="lattices.html#V5" title="LATTICES:attr.5">join-associative</a>  &amp; <font color="Maroon" title="c10">L</font> is  <a href="lattices.html#V8" title="LATTICES:attr.8">meet-absorbing</a>  &amp; <font color="Maroon" title="c10">L</font> is  <a href="lattices.html#V6" title="LATTICES:attr.6">meet-commutative</a>  &amp; <font color="Maroon" title="c10">L</font> is  <a href="lattices.html#V7" title="LATTICES:attr.7">meet-associative</a>  &amp; <font color="Maroon" title="c10">L</font> is  <a href="lattices.html#V9" title="LATTICES:attr.9">join-absorbing</a>  )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:24_1_1"><span class="lab"><font color="Green" title="E24">A19</font></span></a>, <a class="txt" href="#E17:24_1_1"><span class="lab"><font color="Green" title="E27">A22</font></span></a>, <a class="txt" href="#E16:24_1_1"><span class="lab"><font color="Green" title="E26">A21</font></span></a>, <a class="txt" href="#E18:24_1_1"><span class="lab"><font color="Green" title="E28">A23</font></span></a>, <a class="txt" href="#E15:24_1_1"><span class="lab"><font color="Green" title="E25">A20</font></span></a>, <a class="ref" href="lattices.html#D4" title="LATTICES:def.4">LATTICES:def 4</a>, <a class="ref" href="lattices.html#D5" title="LATTICES:def.5">LATTICES:def 5</a>, <a class="ref" href="lattices.html#D6" title="LATTICES:def.6">LATTICES:def 6</a>, <a class="ref" href="lattices.html#D7" title="LATTICES:def.7">LATTICES:def 7</a>, <a class="ref" href="lattices.html#D8" title="LATTICES:def.8">LATTICES:def 8</a>, <a class="ref" href="lattices.html#D9" title="LATTICES:def.9">LATTICES:def 9</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c11">L9</font> =  <a href="lattices.html#G3" title="LATTICES:aggr.3">LattStr</a>(# <font color="Maroon" title="c3">A</font>,<font color="Maroon" title="c7">Ma</font>,<font color="Maroon" title="c6">Mi</font> #) as   <a href="lattices.html#V3" title="LATTICES:attr.3">strict</a>  <a href="lattices.html#NM1" title="LATTICES:NM.1">Lattice</a> ;<br/>
<span class="kw">take </span>
<font color="Maroon" title="c11">L9</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="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c11">L9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><font color="Maroon" title="c1">r1</font>,<font color="Maroon" title="c2">r2</font></span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span> &amp;  the <a href="lattices.html#U2" title="LATTICES:sel.2">L_join</a> of <font color="Maroon" title="c11">L9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="real_lat.html#K2" title="REAL_LAT:func.2">maxreal</a> <a href="realset1.html#K1" title="REALSET1:func.1">||</a> <span class="p1"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><font color="Maroon" title="c1">r1</font>,<font color="Maroon" title="c2">r2</font></span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span> &amp;  the <a href="lattices.html#U1" title="LATTICES:sel.1">L_meet</a> of <font color="Maroon" title="c11">L9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="real_lat.html#K1" title="REAL_LAT:func.1">minreal</a> <a href="realset1.html#K1" title="REALSET1:func.1">||</a> <span class="p1"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><font color="Maroon" title="c1">r1</font>,<font color="Maroon" title="c2">r2</font></span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span> )</span><br/>

<span class="kw">thus </span><a NAME="E22:24_1_1"/>
(  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c11">L9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><font color="Maroon" title="c1">r1</font>,<font color="Maroon" title="c2">r2</font></span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span> &amp;  the <a href="lattices.html#U2" title="LATTICES:sel.2">L_join</a> of <font color="Maroon" title="c11">L9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="real_lat.html#K2" title="REAL_LAT:func.2">maxreal</a> <a href="realset1.html#K1" title="REALSET1:func.1">||</a> <span class="p1"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><font color="Maroon" title="c1">r1</font>,<font color="Maroon" title="c2">r2</font></span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span> &amp;  the <a href="lattices.html#U1" title="LATTICES:sel.1">L_meet</a> of <font color="Maroon" title="c11">L9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="real_lat.html#K1" title="REAL_LAT:func.1">minreal</a> <a href="realset1.html#K1" title="REALSET1:func.1">||</a> <span class="p1"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><font color="Maroon" title="c1">r1</font>,<font color="Maroon" title="c2">r2</font></span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</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/>


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