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<span class="kw">let </span><font color="Maroon" title="c1">H</font> be   non  <a href="struct_0.html#V7" title="STRUCT_0:attr.7">trivial</a>  <a href="lattice2.html#NM2" title="LATTICE2:NM.2">H_Lattice</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">p9</font>, <font color="Olive" title="b2">q9</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">H</font> holds  <span class="p1">(<span class="default"><a href="openlatt.html#K18" title="OPENLATT:func.18">StoneH</a> <font color="Maroon" title="c1">H</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">p9</font> <a href="filter_0.html#K4" title="FILTER_0:func.4">=&gt;</a> <font color="Olive" title="b2">q9</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"><a href="openlatt.html#K18" title="OPENLATT:func.18">StoneH</a> <font color="Maroon" title="c1">H</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">p9</font></span>)</span> <a href="filter_0.html#K4" title="FILTER_0:func.4">=&gt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="openlatt.html#K18" title="OPENLATT:func.18">StoneH</a> <font color="Maroon" title="c1">H</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b2">q9</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c2">p9</font>, <font color="Maroon" title="c3">q9</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">H</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="openlatt.html#K18" title="OPENLATT:func.18">StoneH</a> <font color="Maroon" title="c1">H</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p9</font> <a href="filter_0.html#K4" title="FILTER_0:func.4">=&gt;</a> <font color="Maroon" title="c3">q9</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"><a href="openlatt.html#K18" title="OPENLATT:func.18">StoneH</a> <font color="Maroon" title="c1">H</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">p9</font></span>)</span> <a href="filter_0.html#K4" title="FILTER_0:func.4">=&gt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="openlatt.html#K18" title="OPENLATT:func.18">StoneH</a> <font color="Maroon" title="c1">H</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">q9</font></span>)</span></span><br/>





<a NAME="E1:54"/><span class="lab"><font color="Green" title="E34">A1</font></span>: 
 the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="openlatt.html#K6" title="OPENLATT:func.6">Open_setLatt</a> <span class="p2">(<span class="default"><a href="openlatt.html#K17" title="OPENLATT:func.17">HTopSpace</a> <font color="Maroon" title="c1">H</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"><a href="tarski.html#K3" title="TARSKI:func.3">union</a> <font color="Olive" title="b1">A</font></span>)</span> where <font color="Olive" title="b1">A</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="openlatt.html#K9" title="OPENLATT:func.9">StoneS</a> <font color="Maroon" title="c1">H</font></span>)</span> : verum </span> } </span> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="openlatt.html#D12" target="_self" onmouseover="rs('openlatt/D12')" onmouseout="rh()">Def12</a></span>;<br/>
<div><span class="lab"><font color="Green" title="E35">A2</font></span>: <a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="54_1"><span class="kw">now </span> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">r</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="openlatt.html#K6" title="OPENLATT:func.6">Open_setLatt</a> <span class="p2">(<span class="default"><a href="openlatt.html#K17" title="OPENLATT:func.17">HTopSpace</a> <font color="Maroon" title="c1">H</font></span>)</span></span>)</span>  st <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="openlatt.html#K18" title="OPENLATT:func.18">StoneH</a> <font color="Maroon" title="c1">H</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">p9</font></span>)</span> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Olive" title="b1">r</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <span class="p1">(<span class="default"><a href="openlatt.html#K18" title="OPENLATT:func.18">StoneH</a> <font color="Maroon" title="c1">H</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">q9</font> holds <br/><font color="Olive" title="b1">r</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <span class="p1">(<span class="default"><a href="openlatt.html#K18" title="OPENLATT:func.18">StoneH</a> <font color="Maroon" title="c1">H</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p9</font> <a href="filter_0.html#K4" title="FILTER_0:func.4">=&gt;</a> <font color="Maroon" title="c3">q9</font></span>)</span></span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c4">r</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="openlatt.html#K6" title="OPENLATT:func.6">Open_setLatt</a> <span class="p2">(<span class="default"><a href="openlatt.html#K17" title="OPENLATT:func.17">HTopSpace</a> <font color="Maroon" title="c1">H</font></span>)</span></span>)</span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="openlatt.html#K18" title="OPENLATT:func.18">StoneH</a> <font color="Maroon" title="c1">H</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">p9</font></span>)</span> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c4">r</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <span class="p1">(<span class="default"><a href="openlatt.html#K18" title="OPENLATT:func.18">StoneH</a> <font color="Maroon" title="c1">H</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">q9</font> implies <font color="Maroon" title="c4">r</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <span class="p1">(<span class="default"><a href="openlatt.html#K18" title="OPENLATT:func.18">StoneH</a> <font color="Maroon" title="c1">H</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p9</font> <a href="filter_0.html#K4" title="FILTER_0:func.4">=&gt;</a> <font color="Maroon" title="c3">q9</font></span>)</span> )</span><br/><a NAME="E1:54_1"/>
<font color="Maroon" title="c4">r</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="openlatt.html#K6" title="OPENLATT:func.6">Open_setLatt</a> <span class="p2">(<span class="default"><a href="openlatt.html#K17" title="OPENLATT:func.17">HTopSpace</a> <font color="Maroon" title="c1">H</font></span>)</span></span>)</span>
 ;<br/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c5">A</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="openlatt.html#K9" title="OPENLATT:func.9">StoneS</a> <font color="Maroon" title="c1">H</font></span>)</span><span class="kw"> such that </span><br/><a NAME="E3:54_1"/><span class="lab"><font color="Green" title="E36">A3</font></span>: 
<font color="Maroon" title="c4">r</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="tarski.html#K3" title="TARSKI:func.3">union</a> <font color="Maroon" title="c5">A</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:54"><span class="lab"><font color="Green" title="E34">A1</font></span></a></span>;<br/><span class="kw">assume </span><a NAME="E4:54_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="openlatt.html#K18" title="OPENLATT:func.18">StoneH</a> <font color="Maroon" title="c1">H</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">p9</font></span>)</span> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c4">r</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <span class="p1">(<span class="default"><a href="openlatt.html#K18" title="OPENLATT:func.18">StoneH</a> <font color="Maroon" title="c1">H</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">q9</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c4">r</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <span class="p1">(<span class="default"><a href="openlatt.html#K18" title="OPENLATT:func.18">StoneH</a> <font color="Maroon" title="c1">H</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p9</font> <a href="filter_0.html#K4" title="FILTER_0:func.4">=&gt;</a> <font color="Maroon" title="c3">q9</font></span>)</span></span><br/><a NAME="E5:54_1"/><span class="kw">then </span>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="openlatt.html#K18" title="OPENLATT:func.18">StoneH</a> <font color="Maroon" title="c1">H</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">p9</font></span>)</span> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c4">r</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="openlatt.html#K18" title="OPENLATT:func.18">StoneH</a> <font color="Maroon" title="c1">H</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">q9</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="openlatt.html#T6" target="_self" onmouseover="rs('openlatt/T6')" onmouseout="rh()">Th6</a></span>;<br/><a NAME="E6:54_1"/><span class="kw">then </span>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="openlatt.html#K18" title="OPENLATT:func.18">StoneH</a> <font color="Maroon" title="c1">H</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">p9</font></span>)</span> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <span class="p1">(<span class="default"><a href="tarski.html#K3" title="TARSKI:func.3">union</a> <font color="Maroon" title="c5">A</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="openlatt.html#K18" title="OPENLATT:func.18">StoneH</a> <font color="Maroon" title="c1">H</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">q9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:54_1"><span class="lab"><font color="Green" title="E36">A3</font></span></a>, <a class="ref" href="openlatt.html#D3" target="_self" onmouseover="rs('openlatt/D3')" onmouseout="rh()">Def3</a></span>;<br/><a NAME="E7:54_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E37">A4</font></span>: 
 <a href="tarski.html#K3" title="TARSKI:func.3">union</a> <span class="p1">(<span class="default"><a href="setfam_1.html#K3" title="SETFAM_1:func.3">INTERSECTION</a> (<span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="openlatt.html#K18" title="OPENLATT:func.18">StoneH</a> <font color="Maroon" title="c1">H</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">p9</font></span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<font color="Maroon" title="c5">A</font>)</span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="openlatt.html#K18" title="OPENLATT:func.18">StoneH</a> <font color="Maroon" title="c1">H</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">q9</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="setfam_1.html#T25" onmouseover="rs('setfam_1/T25')" onmouseout="rh()">SETFAM_1:25</a></span>;<br/><div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="54_1_1"><span class="kw">now </span> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">x</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>   st <font color="Olive" title="b1">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c5">A</font> holds <br/><font color="Olive" title="b1">x</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="openlatt.html#K18" title="OPENLATT:func.18">StoneH</a> <font color="Maroon" title="c1">H</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p9</font> <a href="filter_0.html#K4" title="FILTER_0:func.4">=&gt;</a> <font color="Maroon" title="c3">q9</font></span>)</span></span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c6">x</font> be    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c6">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c5">A</font> implies <font color="Maroon" title="c6">x</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="openlatt.html#K18" title="OPENLATT:func.18">StoneH</a> <font color="Maroon" title="c1">H</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p9</font> <a href="filter_0.html#K4" title="FILTER_0:func.4">=&gt;</a> <font color="Maroon" title="c3">q9</font></span>)</span> )</span><br/><span class="kw">assume </span><a NAME="E1:54_1_1"/><span class="lab"><font color="Green" title="E38">A5</font></span>: 
<font color="Maroon" title="c6">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c5">A</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c6">x</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="openlatt.html#K18" title="OPENLATT:func.18">StoneH</a> <font color="Maroon" title="c1">H</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p9</font> <a href="filter_0.html#K4" title="FILTER_0:func.4">=&gt;</a> <font color="Maroon" title="c3">q9</font></span>)</span></span><br/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c7">x9</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">H</font><span class="kw"> such that </span><br/><a NAME="E3:54_1_1"/><span class="lab"><font color="Green" title="E39">A6</font></span>: 
<font color="Maroon" title="c6">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="openlatt.html#K18" title="OPENLATT:func.18">StoneH</a> <font color="Maroon" title="c1">H</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">x9</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="openlatt.html#T13" target="_self" onmouseover="rs('openlatt/T13')" onmouseout="rh()">Th13</a></span>;<br/><a NAME="E4:54_1_1"/>
<span class="p1">(<span class="default"><a href="openlatt.html#K18" title="OPENLATT:func.18">StoneH</a> <font color="Maroon" title="c1">H</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">p9</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="openlatt.html#K18" title="OPENLATT:func.18">StoneH</a> <font color="Maroon" title="c1">H</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">p9</font></span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D1" onmouseover="rs('tarski/D1')" onmouseout="rh()">TARSKI:def 1</a></span>;<br/><a NAME="E5:54_1_1"/><span class="kw">then </span>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="openlatt.html#K18" title="OPENLATT:func.18">StoneH</a> <font color="Maroon" title="c1">H</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">p9</font></span>)</span> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <font color="Maroon" title="c6">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="setfam_1.html#K3" title="SETFAM_1:func.3">INTERSECTION</a> (<span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="openlatt.html#K18" title="OPENLATT:func.18">StoneH</a> <font color="Maroon" title="c1">H</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">p9</font></span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<font color="Maroon" title="c5">A</font>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:54_1_1"><span class="lab"><font color="Green" title="E38">A5</font></span></a>, <a class="ref" href="setfam_1.html#D5" onmouseover="rs('setfam_1/D5')" onmouseout="rh()">SETFAM_1:def 5</a></span>;<br/><a NAME="E6:54_1_1"/><span class="kw">then </span>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="openlatt.html#K18" title="OPENLATT:func.18">StoneH</a> <font color="Maroon" title="c1">H</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">p9</font></span>)</span> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="openlatt.html#K18" title="OPENLATT:func.18">StoneH</a> <font color="Maroon" title="c1">H</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">x9</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="openlatt.html#K18" title="OPENLATT:func.18">StoneH</a> <font color="Maroon" title="c1">H</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">q9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:54_1"><span class="lab"><font color="Green" title="E37">A4</font></span></a>, <a class="txt" href="#E3:54_1_1"><span class="lab"><font color="Green" title="E39">A6</font></span></a>, <a class="ref" href="setfam_1.html#T41" onmouseover="rs('setfam_1/T41')" onmouseout="rh()">SETFAM_1:41</a></span>;<br/><a NAME="E7:54_1_1"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="openlatt.html#K18" title="OPENLATT:func.18">StoneH</a> <font color="Maroon" title="c1">H</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p9</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c7">x9</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="openlatt.html#K18" title="OPENLATT:func.18">StoneH</a> <font color="Maroon" title="c1">H</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">q9</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="openlatt.html#T15" target="_self" onmouseover="rs('openlatt/T15')" onmouseout="rh()">Th15</a></span>;<br/><a NAME="E8:54_1_1"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="openlatt.html#K18" title="OPENLATT:func.18">StoneH</a> <font color="Maroon" title="c1">H</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p9</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c7">x9</font></span>)</span> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <span class="p1">(<span class="default"><a href="openlatt.html#K18" title="OPENLATT:func.18">StoneH</a> <font color="Maroon" title="c1">H</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">q9</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="openlatt.html#T6" target="_self" onmouseover="rs('openlatt/T6')" onmouseout="rh()">Th6</a></span>;<br/><a NAME="E9:54_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c2">p9</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c7">x9</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <font color="Maroon" title="c3">q9</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="lattice4.html#T5" onmouseover="rs('lattice4/T5')" onmouseout="rh()">LATTICE4:5</a></span>;<br/><a NAME="E10:54_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c7">x9</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <font color="Maroon" title="c2">p9</font> <a href="filter_0.html#K4" title="FILTER_0:func.4">=&gt;</a> <font color="Maroon" title="c3">q9</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="filter_0.html#D7" onmouseover="rs('filter_0/D7')" onmouseout="rh()">FILTER_0:def 7</a></span>;<br/><a NAME="E11:54_1_1"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="openlatt.html#K18" title="OPENLATT:func.18">StoneH</a> <font color="Maroon" title="c1">H</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">x9</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <span class="p1">(<span class="default"><a href="openlatt.html#K18" title="OPENLATT:func.18">StoneH</a> <font color="Maroon" title="c1">H</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p9</font> <a href="filter_0.html#K4" title="FILTER_0:func.4">=&gt;</a> <font color="Maroon" title="c3">q9</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="lattice4.html#T4" onmouseover="rs('lattice4/T4')" onmouseout="rh()">LATTICE4:4</a></span>;<br/><span class="kw">hence </span><a NAME="E12:54_1_1"/>
<font color="Maroon" title="c6">x</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="openlatt.html#K18" title="OPENLATT:func.18">StoneH</a> <font color="Maroon" title="c1">H</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p9</font> <a href="filter_0.html#K4" title="FILTER_0:func.4">=&gt;</a> <font color="Maroon" title="c3">q9</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:54_1_1"><span class="lab"><font color="Green" title="E39">A6</font></span></a>, <a class="ref" href="openlatt.html#T6" target="_self" onmouseover="rs('openlatt/T6')" onmouseout="rh()">Th6</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><a NAME="E9:54_1"/><span class="kw">then </span>
 <a href="tarski.html#K3" title="TARSKI:func.3">union</a> <font color="Maroon" title="c5">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="openlatt.html#K18" title="OPENLATT:func.18">StoneH</a> <font color="Maroon" title="c1">H</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p9</font> <a href="filter_0.html#K4" title="FILTER_0:func.4">=&gt;</a> <font color="Maroon" title="c3">q9</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="zfmisc_1.html#T76" onmouseover="rs('zfmisc_1/T76')" onmouseout="rh()">ZFMISC_1:76</a></span>;<br/><span class="kw">hence </span><a NAME="E10:54_1"/>
<font color="Maroon" title="c4">r</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <span class="p1">(<span class="default"><a href="openlatt.html#K18" title="OPENLATT:func.18">StoneH</a> <font color="Maroon" title="c1">H</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p9</font> <a href="filter_0.html#K4" title="FILTER_0:func.4">=&gt;</a> <font color="Maroon" title="c3">q9</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:54_1"><span class="lab"><font color="Green" title="E36">A3</font></span></a>, <a class="ref" href="openlatt.html#T6" target="_self" onmouseover="rs('openlatt/T6')" onmouseout="rh()">Th6</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<a NAME="E3:54"/>
<font color="Maroon" title="c2">p9</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p9</font> <a href="filter_0.html#K4" title="FILTER_0:func.4">=&gt;</a> <font color="Maroon" title="c3">q9</font></span>)</span> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <font color="Maroon" title="c3">q9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="filter_0.html#D7" onmouseover="rs('filter_0/D7')" onmouseout="rh()">FILTER_0:def 7</a></span>;<br/>
<a NAME="E4:54"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="openlatt.html#K18" title="OPENLATT:func.18">StoneH</a> <font color="Maroon" title="c1">H</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p9</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">p9</font> <a href="filter_0.html#K4" title="FILTER_0:func.4">=&gt;</a> <font color="Maroon" title="c3">q9</font></span>)</span></span>)</span> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <span class="p1">(<span class="default"><a href="openlatt.html#K18" title="OPENLATT:func.18">StoneH</a> <font color="Maroon" title="c1">H</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">q9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="lattice4.html#T4" onmouseover="rs('lattice4/T4')" onmouseout="rh()">LATTICE4:4</a></span>;<br/>
<a NAME="E5:54"/><span class="kw">then </span>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="openlatt.html#K18" title="OPENLATT:func.18">StoneH</a> <font color="Maroon" title="c1">H</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">p9</font></span>)</span> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="openlatt.html#K18" title="OPENLATT:func.18">StoneH</a> <font color="Maroon" title="c1">H</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">p9</font> <a href="filter_0.html#K4" title="FILTER_0:func.4">=&gt;</a> <font color="Maroon" title="c3">q9</font></span>)</span></span>)</span> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <span class="p1">(<span class="default"><a href="openlatt.html#K18" title="OPENLATT:func.18">StoneH</a> <font color="Maroon" title="c1">H</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">q9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="lattice4.html#D2" onmouseover="rs('lattice4/D2')" onmouseout="rh()">LATTICE4:def 2</a></span>;<br/>
<span class="kw">hence </span><a NAME="E6:54"/>
<span class="p1">(<span class="default"><a href="openlatt.html#K18" title="OPENLATT:func.18">StoneH</a> <font color="Maroon" title="c1">H</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p9</font> <a href="filter_0.html#K4" title="FILTER_0:func.4">=&gt;</a> <font color="Maroon" title="c3">q9</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"><a href="openlatt.html#K18" title="OPENLATT:func.18">StoneH</a> <font color="Maroon" title="c1">H</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">p9</font></span>)</span> <a href="filter_0.html#K4" title="FILTER_0:func.4">=&gt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="openlatt.html#K18" title="OPENLATT:func.18">StoneH</a> <font color="Maroon" title="c1">H</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">q9</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:54"><span class="lab"><font color="Green" title="E35">A2</font></span></a>, <a class="ref" href="filter_0.html#D7" onmouseover="rs('filter_0/D7')" onmouseout="rh()">FILTER_0:def 7</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
