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

<span class="kw">let </span><font color="Maroon" title="c1">T</font> be   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  <a href="pre_topc.html#NM1" title="PRE_TOPC:NM.1">TopSpace</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">  <a href="lattices.html#G3" title="LATTICES:aggr.3">LattStr</a>(# <span class="p1">(<span class="default"><a href="openlatt.html#K1" title="OPENLATT:func.1">Topology_of</a> <font color="Maroon" title="c1">T</font></span>)</span>,<span class="p1">(<span class="default"><a href="openlatt.html#K4" title="OPENLATT:func.4">Top_Union</a> <font color="Maroon" title="c1">T</font></span>)</span>,<span class="p1">(<span class="default"><a href="openlatt.html#K5" title="OPENLATT:func.5">Top_Meet</a> <font color="Maroon" title="c1">T</font></span>)</span> #) is   <a href="lattices.html#NM1" title="LATTICES:NM.1">Lattice</a></span><br/>

<span class="kw">set </span><font color="Maroon" title="c2">L</font> =  <a href="lattices.html#G3" title="LATTICES:aggr.3">LattStr</a>(# <span class="p1">(<span class="default"><a href="openlatt.html#K1" title="OPENLATT:func.1">Topology_of</a> <font color="Maroon" title="c1">T</font></span>)</span>,<span class="p1">(<span class="default"><a href="openlatt.html#K4" title="OPENLATT:func.4">Top_Union</a> <font color="Maroon" title="c1">T</font></span>)</span>,<span class="p1">(<span class="default"><a href="openlatt.html#K5" title="OPENLATT:func.5">Top_Meet</a> <font color="Maroon" title="c1">T</font></span>)</span> #);<br/>
<div><span class="lab"><font color="Green" title="E6">A1</font></span>: <a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="8_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">p</font>, <font color="Olive" title="b2">q</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="lattices.html#G3" title="LATTICES:aggr.3">LattStr</a>(# <span class="p1">(<span class="default"><a href="openlatt.html#K1" title="OPENLATT:func.1">Topology_of</a> <font color="Maroon" title="c1">T</font></span>)</span>,<span class="p1">(<span class="default"><a href="openlatt.html#K4" title="OPENLATT:func.4">Top_Union</a> <font color="Maroon" title="c1">T</font></span>)</span>,<span class="p1">(<span class="default"><a href="openlatt.html#K5" title="OPENLATT:func.5">Top_Meet</a> <font color="Maroon" title="c1">T</font></span>)</span> #) holds  <font color="Olive" title="b1">p</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Olive" title="b2">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">q</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Olive" title="b1">p</font></span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c3">p</font>, <font color="Maroon" title="c4">q</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="lattices.html#G3" title="LATTICES:aggr.3">LattStr</a>(# <span class="p1">(<span class="default"><a href="openlatt.html#K1" title="OPENLATT:func.1">Topology_of</a> <font color="Maroon" title="c1">T</font></span>)</span>,<span class="p1">(<span class="default"><a href="openlatt.html#K4" title="OPENLATT:func.4">Top_Union</a> <font color="Maroon" title="c1">T</font></span>)</span>,<span class="p1">(<span class="default"><a href="openlatt.html#K5" title="OPENLATT:func.5">Top_Meet</a> <font color="Maroon" title="c1">T</font></span>)</span> #); <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c3">p</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Maroon" title="c4">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">q</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Maroon" title="c3">p</font></span><br/><span class="kw">thus </span><font color="Maroon" title="c3">p</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Maroon" title="c4">q</font> = 
<font color="Maroon" title="c4">q</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c3">p</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="openlatt.html#D2" target="_self" onmouseover="rs('openlatt/D2')" onmouseout="rh()">Def2</a></span>
<br/>.= 
<font color="Maroon" title="c4">q</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Maroon" title="c3">p</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="openlatt.html#D2" target="_self" onmouseover="rs('openlatt/D2')" onmouseout="rh()">Def2</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>
<div><span class="lab"><font color="Green" title="E7">A2</font></span>: <a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="8_2"><span class="kw">now </span> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">p</font>, <font color="Olive" title="b2">q</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="lattices.html#G3" title="LATTICES:aggr.3">LattStr</a>(# <span class="p1">(<span class="default"><a href="openlatt.html#K1" title="OPENLATT:func.1">Topology_of</a> <font color="Maroon" title="c1">T</font></span>)</span>,<span class="p1">(<span class="default"><a href="openlatt.html#K4" title="OPENLATT:func.4">Top_Union</a> <font color="Maroon" title="c1">T</font></span>)</span>,<span class="p1">(<span class="default"><a href="openlatt.html#K5" title="OPENLATT:func.5">Top_Meet</a> <font color="Maroon" title="c1">T</font></span>)</span> #) holds  <span class="p1">(<span class="default"><font color="Olive" title="b1">p</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Olive" title="b2">q</font></span>)</span> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Olive" title="b2">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">q</font></span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c3">p</font>, <font color="Maroon" title="c4">q</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="lattices.html#G3" title="LATTICES:aggr.3">LattStr</a>(# <span class="p1">(<span class="default"><a href="openlatt.html#K1" title="OPENLATT:func.1">Topology_of</a> <font color="Maroon" title="c1">T</font></span>)</span>,<span class="p1">(<span class="default"><a href="openlatt.html#K4" title="OPENLATT:func.4">Top_Union</a> <font color="Maroon" title="c1">T</font></span>)</span>,<span class="p1">(<span class="default"><a href="openlatt.html#K5" title="OPENLATT:func.5">Top_Meet</a> <font color="Maroon" title="c1">T</font></span>)</span> #); <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Maroon" title="c4">q</font></span>)</span> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Maroon" title="c4">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">q</font></span><br/><span class="kw">thus </span><span class="p1">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Maroon" title="c4">q</font></span>)</span> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Maroon" title="c4">q</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Maroon" title="c4">q</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c4">q</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="openlatt.html#D2" target="_self" onmouseover="rs('openlatt/D2')" onmouseout="rh()">Def2</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <font color="Maroon" title="c4">q</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c4">q</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="openlatt.html#D3" target="_self" onmouseover="rs('openlatt/D3')" onmouseout="rh()">Def3</a></span>
<br/>.= 
<font color="Maroon" title="c4">q</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_1.html#T22" onmouseover="rs('xboole_1/T22')" onmouseout="rh()">XBOOLE_1:22</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>
<div><span class="lab"><font color="Green" title="E8">A3</font></span>: <a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="8_3"><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">p</font>, <font color="Olive" title="b2">q</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="lattices.html#G3" title="LATTICES:aggr.3">LattStr</a>(# <span class="p1">(<span class="default"><a href="openlatt.html#K1" title="OPENLATT:func.1">Topology_of</a> <font color="Maroon" title="c1">T</font></span>)</span>,<span class="p1">(<span class="default"><a href="openlatt.html#K4" title="OPENLATT:func.4">Top_Union</a> <font color="Maroon" title="c1">T</font></span>)</span>,<span class="p1">(<span class="default"><a href="openlatt.html#K5" title="OPENLATT:func.5">Top_Meet</a> <font color="Maroon" title="c1">T</font></span>)</span> #) holds  <font color="Olive" title="b1">p</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">p</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Olive" title="b2">q</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">p</font></span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c3">p</font>, <font color="Maroon" title="c4">q</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="lattices.html#G3" title="LATTICES:aggr.3">LattStr</a>(# <span class="p1">(<span class="default"><a href="openlatt.html#K1" title="OPENLATT:func.1">Topology_of</a> <font color="Maroon" title="c1">T</font></span>)</span>,<span class="p1">(<span class="default"><a href="openlatt.html#K4" title="OPENLATT:func.4">Top_Union</a> <font color="Maroon" title="c1">T</font></span>)</span>,<span class="p1">(<span class="default"><a href="openlatt.html#K5" title="OPENLATT:func.5">Top_Meet</a> <font color="Maroon" title="c1">T</font></span>)</span> #); <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c3">p</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Maroon" title="c4">q</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">p</font></span><br/><span class="kw">thus </span><font color="Maroon" title="c3">p</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Maroon" title="c4">q</font></span>)</span> = 
<font color="Maroon" title="c3">p</font> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Maroon" title="c4">q</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="openlatt.html#D3" target="_self" onmouseover="rs('openlatt/D3')" onmouseout="rh()">Def3</a></span>
<br/>.= 
<font color="Maroon" title="c3">p</font> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c4">q</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="openlatt.html#D2" target="_self" onmouseover="rs('openlatt/D2')" onmouseout="rh()">Def2</a></span>
<br/>.= 
<font color="Maroon" title="c3">p</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_1.html#T21" onmouseover="rs('xboole_1/T21')" onmouseout="rh()">XBOOLE_1:21</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>
<div><span class="lab"><font color="Green" title="E9">A4</font></span>: <a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="8_4"><span class="kw">now </span> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">p</font>, <font color="Olive" title="b2">q</font>, <font color="Olive" title="b3">r</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="lattices.html#G3" title="LATTICES:aggr.3">LattStr</a>(# <span class="p1">(<span class="default"><a href="openlatt.html#K1" title="OPENLATT:func.1">Topology_of</a> <font color="Maroon" title="c1">T</font></span>)</span>,<span class="p1">(<span class="default"><a href="openlatt.html#K4" title="OPENLATT:func.4">Top_Union</a> <font color="Maroon" title="c1">T</font></span>)</span>,<span class="p1">(<span class="default"><a href="openlatt.html#K5" title="OPENLATT:func.5">Top_Meet</a> <font color="Maroon" title="c1">T</font></span>)</span> #) holds  <font color="Olive" title="b1">p</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">q</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Olive" title="b3">r</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">p</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Olive" title="b2">q</font></span>)</span> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Olive" title="b3">r</font></span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c3">p</font>, <font color="Maroon" title="c4">q</font>, <font color="Maroon" title="c5">r</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="lattices.html#G3" title="LATTICES:aggr.3">LattStr</a>(# <span class="p1">(<span class="default"><a href="openlatt.html#K1" title="OPENLATT:func.1">Topology_of</a> <font color="Maroon" title="c1">T</font></span>)</span>,<span class="p1">(<span class="default"><a href="openlatt.html#K4" title="OPENLATT:func.4">Top_Union</a> <font color="Maroon" title="c1">T</font></span>)</span>,<span class="p1">(<span class="default"><a href="openlatt.html#K5" title="OPENLATT:func.5">Top_Meet</a> <font color="Maroon" title="c1">T</font></span>)</span> #); <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c3">p</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">q</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Maroon" title="c5">r</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Maroon" title="c4">q</font></span>)</span> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Maroon" title="c5">r</font></span><br/><span class="kw">thus </span><font color="Maroon" title="c3">p</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">q</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Maroon" title="c5">r</font></span>)</span> = 
<font color="Maroon" title="c3">p</font> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">q</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Maroon" title="c5">r</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="openlatt.html#D3" target="_self" onmouseover="rs('openlatt/D3')" onmouseout="rh()">Def3</a></span>
<br/>.= 
<font color="Maroon" title="c3">p</font> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">q</font> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <font color="Maroon" title="c5">r</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="openlatt.html#D3" target="_self" onmouseover="rs('openlatt/D3')" onmouseout="rh()">Def3</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <font color="Maroon" title="c4">q</font></span>)</span> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <font color="Maroon" title="c5">r</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_1.html#T16" onmouseover="rs('xboole_1/T16')" onmouseout="rh()">XBOOLE_1:16</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Maroon" title="c4">q</font></span>)</span> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <font color="Maroon" title="c5">r</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="openlatt.html#D3" target="_self" onmouseover="rs('openlatt/D3')" onmouseout="rh()">Def3</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Maroon" title="c4">q</font></span>)</span> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Maroon" title="c5">r</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="openlatt.html#D3" target="_self" onmouseover="rs('openlatt/D3')" onmouseout="rh()">Def3</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>
<div><span class="lab"><font color="Green" title="E10">A5</font></span>: <a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="8_5"><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">p</font>, <font color="Olive" title="b2">q</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="lattices.html#G3" title="LATTICES:aggr.3">LattStr</a>(# <span class="p1">(<span class="default"><a href="openlatt.html#K1" title="OPENLATT:func.1">Topology_of</a> <font color="Maroon" title="c1">T</font></span>)</span>,<span class="p1">(<span class="default"><a href="openlatt.html#K4" title="OPENLATT:func.4">Top_Union</a> <font color="Maroon" title="c1">T</font></span>)</span>,<span class="p1">(<span class="default"><a href="openlatt.html#K5" title="OPENLATT:func.5">Top_Meet</a> <font color="Maroon" title="c1">T</font></span>)</span> #) holds  <font color="Olive" title="b1">p</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Olive" title="b2">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">q</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Olive" title="b1">p</font></span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c3">p</font>, <font color="Maroon" title="c4">q</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="lattices.html#G3" title="LATTICES:aggr.3">LattStr</a>(# <span class="p1">(<span class="default"><a href="openlatt.html#K1" title="OPENLATT:func.1">Topology_of</a> <font color="Maroon" title="c1">T</font></span>)</span>,<span class="p1">(<span class="default"><a href="openlatt.html#K4" title="OPENLATT:func.4">Top_Union</a> <font color="Maroon" title="c1">T</font></span>)</span>,<span class="p1">(<span class="default"><a href="openlatt.html#K5" title="OPENLATT:func.5">Top_Meet</a> <font color="Maroon" title="c1">T</font></span>)</span> #); <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c3">p</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Maroon" title="c4">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">q</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Maroon" title="c3">p</font></span><br/><span class="kw">thus </span><font color="Maroon" title="c3">p</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Maroon" title="c4">q</font> = 
<font color="Maroon" title="c4">q</font> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <font color="Maroon" title="c3">p</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="openlatt.html#D3" target="_self" onmouseover="rs('openlatt/D3')" onmouseout="rh()">Def3</a></span>
<br/>.= 
<font color="Maroon" title="c4">q</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Maroon" title="c3">p</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="openlatt.html#D3" target="_self" onmouseover="rs('openlatt/D3')" onmouseout="rh()">Def3</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>
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="8_6"><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">p</font>, <font color="Olive" title="b2">q</font>, <font color="Olive" title="b3">r</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="lattices.html#G3" title="LATTICES:aggr.3">LattStr</a>(# <span class="p1">(<span class="default"><a href="openlatt.html#K1" title="OPENLATT:func.1">Topology_of</a> <font color="Maroon" title="c1">T</font></span>)</span>,<span class="p1">(<span class="default"><a href="openlatt.html#K4" title="OPENLATT:func.4">Top_Union</a> <font color="Maroon" title="c1">T</font></span>)</span>,<span class="p1">(<span class="default"><a href="openlatt.html#K5" title="OPENLATT:func.5">Top_Meet</a> <font color="Maroon" title="c1">T</font></span>)</span> #) holds  <font color="Olive" title="b1">p</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">q</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Olive" title="b3">r</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">p</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Olive" title="b2">q</font></span>)</span> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Olive" title="b3">r</font></span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c3">p</font>, <font color="Maroon" title="c4">q</font>, <font color="Maroon" title="c5">r</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="lattices.html#G3" title="LATTICES:aggr.3">LattStr</a>(# <span class="p1">(<span class="default"><a href="openlatt.html#K1" title="OPENLATT:func.1">Topology_of</a> <font color="Maroon" title="c1">T</font></span>)</span>,<span class="p1">(<span class="default"><a href="openlatt.html#K4" title="OPENLATT:func.4">Top_Union</a> <font color="Maroon" title="c1">T</font></span>)</span>,<span class="p1">(<span class="default"><a href="openlatt.html#K5" title="OPENLATT:func.5">Top_Meet</a> <font color="Maroon" title="c1">T</font></span>)</span> #); <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c3">p</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">q</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Maroon" title="c5">r</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Maroon" title="c4">q</font></span>)</span> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Maroon" title="c5">r</font></span><br/><span class="kw">thus </span><font color="Maroon" title="c3">p</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">q</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Maroon" title="c5">r</font></span>)</span> = 
<font color="Maroon" title="c3">p</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">q</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Maroon" title="c5">r</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="openlatt.html#D2" target="_self" onmouseover="rs('openlatt/D2')" onmouseout="rh()">Def2</a></span>
<br/>.= 
<font color="Maroon" title="c3">p</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">q</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c5">r</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="openlatt.html#D2" target="_self" onmouseover="rs('openlatt/D2')" onmouseout="rh()">Def2</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c4">q</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c5">r</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_1.html#T4" onmouseover="rs('xboole_1/T4')" onmouseout="rh()">XBOOLE_1:4</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Maroon" title="c4">q</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c5">r</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="openlatt.html#D2" target="_self" onmouseover="rs('openlatt/D2')" onmouseout="rh()">Def2</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Maroon" title="c4">q</font></span>)</span> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Maroon" title="c5">r</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="openlatt.html#D2" target="_self" onmouseover="rs('openlatt/D2')" onmouseout="rh()">Def2</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="E7:8"/><span class="kw">then </span>
(  <a href="lattices.html#G3" title="LATTICES:aggr.3">LattStr</a>(# <span class="p1">(<span class="default"><a href="openlatt.html#K1" title="OPENLATT:func.1">Topology_of</a> <font color="Maroon" title="c1">T</font></span>)</span>,<span class="p1">(<span class="default"><a href="openlatt.html#K4" title="OPENLATT:func.4">Top_Union</a> <font color="Maroon" title="c1">T</font></span>)</span>,<span class="p1">(<span class="default"><a href="openlatt.html#K5" title="OPENLATT:func.5">Top_Meet</a> <font color="Maroon" title="c1">T</font></span>)</span> #) is  <a href="lattices.html#V4" title="LATTICES:attr.4">join-commutative</a>  &amp;  <a href="lattices.html#G3" title="LATTICES:aggr.3">LattStr</a>(# <span class="p1">(<span class="default"><a href="openlatt.html#K1" title="OPENLATT:func.1">Topology_of</a> <font color="Maroon" title="c1">T</font></span>)</span>,<span class="p1">(<span class="default"><a href="openlatt.html#K4" title="OPENLATT:func.4">Top_Union</a> <font color="Maroon" title="c1">T</font></span>)</span>,<span class="p1">(<span class="default"><a href="openlatt.html#K5" title="OPENLATT:func.5">Top_Meet</a> <font color="Maroon" title="c1">T</font></span>)</span> #) is  <a href="lattices.html#V5" title="LATTICES:attr.5">join-associative</a>  &amp;  <a href="lattices.html#G3" title="LATTICES:aggr.3">LattStr</a>(# <span class="p1">(<span class="default"><a href="openlatt.html#K1" title="OPENLATT:func.1">Topology_of</a> <font color="Maroon" title="c1">T</font></span>)</span>,<span class="p1">(<span class="default"><a href="openlatt.html#K4" title="OPENLATT:func.4">Top_Union</a> <font color="Maroon" title="c1">T</font></span>)</span>,<span class="p1">(<span class="default"><a href="openlatt.html#K5" title="OPENLATT:func.5">Top_Meet</a> <font color="Maroon" title="c1">T</font></span>)</span> #) is  <a href="lattices.html#V8" title="LATTICES:attr.8">meet-absorbing</a>  &amp;  <a href="lattices.html#G3" title="LATTICES:aggr.3">LattStr</a>(# <span class="p1">(<span class="default"><a href="openlatt.html#K1" title="OPENLATT:func.1">Topology_of</a> <font color="Maroon" title="c1">T</font></span>)</span>,<span class="p1">(<span class="default"><a href="openlatt.html#K4" title="OPENLATT:func.4">Top_Union</a> <font color="Maroon" title="c1">T</font></span>)</span>,<span class="p1">(<span class="default"><a href="openlatt.html#K5" title="OPENLATT:func.5">Top_Meet</a> <font color="Maroon" title="c1">T</font></span>)</span> #) is  <a href="lattices.html#V6" title="LATTICES:attr.6">meet-commutative</a>  &amp;  <a href="lattices.html#G3" title="LATTICES:aggr.3">LattStr</a>(# <span class="p1">(<span class="default"><a href="openlatt.html#K1" title="OPENLATT:func.1">Topology_of</a> <font color="Maroon" title="c1">T</font></span>)</span>,<span class="p1">(<span class="default"><a href="openlatt.html#K4" title="OPENLATT:func.4">Top_Union</a> <font color="Maroon" title="c1">T</font></span>)</span>,<span class="p1">(<span class="default"><a href="openlatt.html#K5" title="OPENLATT:func.5">Top_Meet</a> <font color="Maroon" title="c1">T</font></span>)</span> #) is  <a href="lattices.html#V7" title="LATTICES:attr.7">meet-associative</a>  &amp;  <a href="lattices.html#G3" title="LATTICES:aggr.3">LattStr</a>(# <span class="p1">(<span class="default"><a href="openlatt.html#K1" title="OPENLATT:func.1">Topology_of</a> <font color="Maroon" title="c1">T</font></span>)</span>,<span class="p1">(<span class="default"><a href="openlatt.html#K4" title="OPENLATT:func.4">Top_Union</a> <font color="Maroon" title="c1">T</font></span>)</span>,<span class="p1">(<span class="default"><a href="openlatt.html#K5" title="OPENLATT:func.5">Top_Meet</a> <font color="Maroon" title="c1">T</font></span>)</span> #) 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="#E1:8"><span class="lab"><font color="Green" title="E6">A1</font></span></a>, <a class="txt" href="#E2:8"><span class="lab"><font color="Green" title="E7">A2</font></span></a>, <a class="txt" href="#E5:8"><span class="lab"><font color="Green" title="E10">A5</font></span></a>, <a class="txt" href="#E4:8"><span class="lab"><font color="Green" title="E9">A4</font></span></a>, <a class="txt" href="#E3:8"><span class="lab"><font color="Green" title="E8">A3</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E8:8"/>
 <a href="lattices.html#G3" title="LATTICES:aggr.3">LattStr</a>(# <span class="p1">(<span class="default"><a href="openlatt.html#K1" title="OPENLATT:func.1">Topology_of</a> <font color="Maroon" title="c1">T</font></span>)</span>,<span class="p1">(<span class="default"><a href="openlatt.html#K4" title="OPENLATT:func.4">Top_Union</a> <font color="Maroon" title="c1">T</font></span>)</span>,<span class="p1">(<span class="default"><a href="openlatt.html#K5" title="OPENLATT:func.5">Top_Meet</a> <font color="Maroon" title="c1">T</font></span>)</span> #) is   <a href="lattices.html#NM1" title="LATTICES:NM.1">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"> verum</span><br/>


</div>
