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<span class="kw">let </span><font color="Maroon" title="c1">G</font> be   <a href="group_1.html#NM1" title="GROUP_1:NM.1">Group</a>; <a class="txt" 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="group_3.html#K1" title="GROUP_3:func.1">Subgroups</a> <font color="Maroon" title="c1">G</font></span>)</span>,<span class="p1">(<span class="default"><a href="group_4.html#K9" title="GROUP_4:func.9">SubJoin</a> <font color="Maroon" title="c1">G</font></span>)</span>,<span class="p1">(<span class="default"><a href="group_4.html#K10" title="GROUP_4:func.10">SubMeet</a> <font color="Maroon" title="c1">G</font></span>)</span> #) is   <a href="lattices.html#NM1" title="LATTICES:NM.1">Lattice</a> &amp;  <a href="lattices.html#G3" title="LATTICES:aggr.3">LattStr</a>(# <span class="p1">(<span class="default"><a href="group_3.html#K1" title="GROUP_3:func.1">Subgroups</a> <font color="Maroon" title="c1">G</font></span>)</span>,<span class="p1">(<span class="default"><a href="group_4.html#K9" title="GROUP_4:func.9">SubJoin</a> <font color="Maroon" title="c1">G</font></span>)</span>,<span class="p1">(<span class="default"><a href="group_4.html#K10" title="GROUP_4:func.10">SubMeet</a> <font color="Maroon" title="c1">G</font></span>)</span> #) is   <a href="lattices.html#NM4" title="LATTICES:NM.4">0_Lattice</a> &amp;  <a href="lattices.html#G3" title="LATTICES:aggr.3">LattStr</a>(# <span class="p1">(<span class="default"><a href="group_3.html#K1" title="GROUP_3:func.1">Subgroups</a> <font color="Maroon" title="c1">G</font></span>)</span>,<span class="p1">(<span class="default"><a href="group_4.html#K9" title="GROUP_4:func.9">SubJoin</a> <font color="Maroon" title="c1">G</font></span>)</span>,<span class="p1">(<span class="default"><a href="group_4.html#K10" title="GROUP_4:func.10">SubMeet</a> <font color="Maroon" title="c1">G</font></span>)</span> #) is   <a href="lattices.html#NM5" title="LATTICES:NM.5">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="group_3.html#K1" title="GROUP_3:func.1">Subgroups</a> <font color="Maroon" title="c1">G</font></span>)</span>,<span class="p1">(<span class="default"><a href="group_4.html#K9" title="GROUP_4:func.9">SubJoin</a> <font color="Maroon" title="c1">G</font></span>)</span>,<span class="p1">(<span class="default"><a href="group_4.html#K10" title="GROUP_4:func.10">SubMeet</a> <font color="Maroon" title="c1">G</font></span>)</span> #);<br/>
<div><span class="lab"><font color="Green" title="E43">A1</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="79_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c3">A</font>, <font color="Maroon" title="c4">B</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="group_3.html#K1" title="GROUP_3:func.1">Subgroups</a> <font color="Maroon" title="c1">G</font></span>)</span>,<span class="p1">(<span class="default"><a href="group_4.html#K9" title="GROUP_4:func.9">SubJoin</a> <font color="Maroon" title="c1">G</font></span>)</span>,<span class="p1">(<span class="default"><a href="group_4.html#K10" title="GROUP_4:func.10">SubMeet</a> <font color="Maroon" title="c1">G</font></span>)</span> #); <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">H1</font>, <font color="Olive" title="b2">H2</font> being   <a href="algstr_0.html#V15" title="ALGSTR_0:attr.15">strict</a>   <a href="group_2.html#M1" title="GROUP_2:mode.1">Subgroup</a> of <font color="Maroon" title="c1">G</font>  st <font color="Maroon" title="c3">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">H1</font> &amp; <font color="Maroon" title="c4">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">H2</font> holds <br/><font color="Maroon" title="c3">A</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Maroon" title="c4">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">H1</font> <a href="group_4.html#K8" title="GROUP_4:func.8">"\/"</a> <font color="Olive" title="b2">H2</font></span><br/><span class="kw">let </span><font color="Maroon" title="c5">H1</font>, <font color="Maroon" title="c6">H2</font> be   <a href="algstr_0.html#V15" title="ALGSTR_0:attr.15">strict</a>   <a href="group_2.html#M1" title="GROUP_2:mode.1">Subgroup</a> of <font color="Maroon" title="c1">G</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="c3">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">H1</font> &amp; <font color="Maroon" title="c4">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">H2</font> implies <font color="Maroon" title="c3">A</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Maroon" title="c4">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">H1</font> <a href="group_4.html#K8" title="GROUP_4:func.8">"\/"</a> <font color="Maroon" title="c6">H2</font> )</span><br/><span class="kw">assume </span><a NAME="E1:79_1"/><span class="lab"><font color="Green" title="E44">A2</font></span>: 
( <font color="Maroon" title="c3">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">H1</font> &amp; <font color="Maroon" title="c4">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">H2</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="c3">A</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Maroon" title="c4">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">H1</font> <a href="group_4.html#K8" title="GROUP_4:func.8">"\/"</a> <font color="Maroon" title="c6">H2</font></span><br/><span class="kw">thus </span><font color="Maroon" title="c3">A</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Maroon" title="c4">B</font> = 
<span class="p1">(<span class="default"><a href="group_4.html#K9" title="GROUP_4:func.9">SubJoin</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c3">A</font>,<font color="Maroon" title="c4">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/>.= 
<font color="Maroon" title="c5">H1</font> <a href="group_4.html#K8" title="GROUP_4:func.8">"\/"</a> <font color="Maroon" title="c6">H2</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:79_1"><span class="lab"><font color="Green" title="E44">A2</font></span></a>, <a class="ref" href="group_4.html#D10" target="_self" title="GROUP_4:def.10">Def11</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="E44">A3</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="79_2"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c3">A</font>, <font color="Maroon" title="c4">B</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="group_3.html#K1" title="GROUP_3:func.1">Subgroups</a> <font color="Maroon" title="c1">G</font></span>)</span>,<span class="p1">(<span class="default"><a href="group_4.html#K9" title="GROUP_4:func.9">SubJoin</a> <font color="Maroon" title="c1">G</font></span>)</span>,<span class="p1">(<span class="default"><a href="group_4.html#K10" title="GROUP_4:func.10">SubMeet</a> <font color="Maroon" title="c1">G</font></span>)</span> #); <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">H1</font>, <font color="Olive" title="b2">H2</font> being   <a href="algstr_0.html#V15" title="ALGSTR_0:attr.15">strict</a>   <a href="group_2.html#M1" title="GROUP_2:mode.1">Subgroup</a> of <font color="Maroon" title="c1">G</font>  st <font color="Maroon" title="c3">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">H1</font> &amp; <font color="Maroon" title="c4">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">H2</font> holds <br/><font color="Maroon" title="c3">A</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Maroon" title="c4">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">H1</font> <a href="group_2.html#K10" title="GROUP_2:func.10">/\</a> <font color="Olive" title="b2">H2</font></span><br/><span class="kw">let </span><font color="Maroon" title="c5">H1</font>, <font color="Maroon" title="c6">H2</font> be   <a href="algstr_0.html#V15" title="ALGSTR_0:attr.15">strict</a>   <a href="group_2.html#M1" title="GROUP_2:mode.1">Subgroup</a> of <font color="Maroon" title="c1">G</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="c3">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">H1</font> &amp; <font color="Maroon" title="c4">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">H2</font> implies <font color="Maroon" title="c3">A</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Maroon" title="c4">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">H1</font> <a href="group_2.html#K10" title="GROUP_2:func.10">/\</a> <font color="Maroon" title="c6">H2</font> )</span><br/><span class="kw">assume </span><a NAME="E1:79_2"/><span class="lab"><font color="Green" title="E45">A4</font></span>: 
( <font color="Maroon" title="c3">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">H1</font> &amp; <font color="Maroon" title="c4">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">H2</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="c3">A</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Maroon" title="c4">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">H1</font> <a href="group_2.html#K10" title="GROUP_2:func.10">/\</a> <font color="Maroon" title="c6">H2</font></span><br/><span class="kw">thus </span><font color="Maroon" title="c3">A</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Maroon" title="c4">B</font> = 
<span class="p1">(<span class="default"><a href="group_4.html#K10" title="GROUP_4:func.10">SubMeet</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c3">A</font>,<font color="Maroon" title="c4">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/>.= 
<font color="Maroon" title="c5">H1</font> <a href="group_2.html#K10" title="GROUP_2:func.10">/\</a> <font color="Maroon" title="c6">H2</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:79_2"><span class="lab"><font color="Green" title="E45">A4</font></span></a>, <a class="ref" href="group_4.html#D11" target="_self" title="GROUP_4:def.11">Def12</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="79_3"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c3">A</font>, <font color="Maroon" title="c4">B</font>, <font color="Maroon" title="c5">C</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="group_3.html#K1" title="GROUP_3:func.1">Subgroups</a> <font color="Maroon" title="c1">G</font></span>)</span>,<span class="p1">(<span class="default"><a href="group_4.html#K9" title="GROUP_4:func.9">SubJoin</a> <font color="Maroon" title="c1">G</font></span>)</span>,<span class="p1">(<span class="default"><a href="group_4.html#K10" title="GROUP_4:func.10">SubMeet</a> <font color="Maroon" title="c1">G</font></span>)</span> #); <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="c3">A</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Maroon" title="c4">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">B</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Maroon" title="c3">A</font> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Maroon" title="c4">B</font></span>)</span> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Maroon" title="c5">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">A</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">B</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Maroon" title="c5">C</font></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Maroon" title="c4">B</font></span>)</span> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Maroon" title="c4">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">B</font> &amp; <font color="Maroon" title="c3">A</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Maroon" title="c4">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">B</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Maroon" title="c3">A</font> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Maroon" title="c4">B</font></span>)</span> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Maroon" title="c5">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">A</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">B</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Maroon" title="c5">C</font></span>)</span> &amp; <font color="Maroon" title="c3">A</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Maroon" title="c4">B</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">A</font> )</span><br/><span class="kw">reconsider </span><font color="Maroon" title="c6">H1</font> = <font color="Maroon" title="c3">A</font>, <font color="Maroon" title="c7">H2</font> = <font color="Maroon" title="c4">B</font>, <font color="Maroon" title="c8">H3</font> = <font color="Maroon" title="c5">C</font> as   <a href="algstr_0.html#V15" title="ALGSTR_0:attr.15">strict</a>   <a href="group_2.html#M1" title="GROUP_2:mode.1">Subgroup</a> of <font color="Maroon" title="c1">G</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="group_3.html#D1" title="GROUP_3:def.1">GROUP_3:def 1</a></span>;<br/><a NAME="E2:79_3"/><span class="lab"><font color="Green" title="E45">A5</font></span>: 
<font color="Maroon" title="c7">H2</font> <a href="group_4.html#K8" title="GROUP_4:func.8">"\/"</a> <font color="Maroon" title="c8">H3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">B</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Maroon" title="c5">C</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:79"><span class="lab"><font color="Green" title="E43">A1</font></span></a></span>;<br/><span class="kw">thus </span><font color="Maroon" title="c3">A</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Maroon" title="c4">B</font> = 
<font color="Maroon" title="c6">H1</font> <a href="group_4.html#K8" title="GROUP_4:func.8">"\/"</a> <font color="Maroon" title="c7">H2</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:79"><span class="lab"><font color="Green" title="E43">A1</font></span></a></span>
<br/>.= 
<font color="Maroon" title="c7">H2</font> <a href="group_4.html#K8" title="GROUP_4:func.8">"\/"</a> <font color="Maroon" title="c6">H1</font>

<br/>.= 
<font color="Maroon" title="c4">B</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Maroon" title="c3">A</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:79"><span class="lab"><font color="Green" title="E43">A1</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"> ( <span class="p1">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Maroon" title="c4">B</font></span>)</span> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Maroon" title="c5">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">A</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">B</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Maroon" title="c5">C</font></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Maroon" title="c4">B</font></span>)</span> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Maroon" title="c4">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">B</font> &amp; <font color="Maroon" title="c3">A</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Maroon" title="c4">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">B</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Maroon" title="c3">A</font> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Maroon" title="c4">B</font></span>)</span> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Maroon" title="c5">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">A</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">B</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Maroon" title="c5">C</font></span>)</span> &amp; <font color="Maroon" title="c3">A</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Maroon" title="c4">B</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">A</font> )</span><br/><a NAME="E4:79_3"/><span class="lab"><font color="Green" title="E46">A6</font></span>: 
<font color="Maroon" title="c6">H1</font> <a href="group_4.html#K8" title="GROUP_4:func.8">"\/"</a> <font color="Maroon" title="c7">H2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">A</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Maroon" title="c4">B</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:79"><span class="lab"><font color="Green" title="E43">A1</font></span></a></span>;<br/><span class="kw">hence </span><span class="p1">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Maroon" title="c4">B</font></span>)</span> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Maroon" title="c5">C</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c6">H1</font> <a href="group_4.html#K8" title="GROUP_4:func.8">"\/"</a> <font color="Maroon" title="c7">H2</font></span>)</span> <a href="group_4.html#K8" title="GROUP_4:func.8">"\/"</a> <font color="Maroon" title="c8">H3</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:79"><span class="lab"><font color="Green" title="E43">A1</font></span></a></span>
<br/>.= 
<font color="Maroon" title="c6">H1</font> <a href="group_4.html#K8" title="GROUP_4:func.8">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">H2</font> <a href="group_4.html#K8" title="GROUP_4:func.8">"\/"</a> <font color="Maroon" title="c8">H3</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="group_4.html#T57" target="_self" title="GROUP_4:th.57">Th75</a></span>
<br/>.= 
<font color="Maroon" title="c3">A</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">B</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Maroon" title="c5">C</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:79"><span class="lab"><font color="Green" title="E43">A1</font></span></a>, <a class="txt" href="#E2:79_3"><span class="lab"><font color="Green" title="E45">A5</font></span></a></span>
;<br/> <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="c3">A</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Maroon" title="c4">B</font></span>)</span> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Maroon" title="c4">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">B</font> &amp; <font color="Maroon" title="c3">A</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Maroon" title="c4">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">B</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Maroon" title="c3">A</font> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Maroon" title="c4">B</font></span>)</span> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Maroon" title="c5">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">A</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">B</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Maroon" title="c5">C</font></span>)</span> &amp; <font color="Maroon" title="c3">A</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Maroon" title="c4">B</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">A</font> )</span><br/><a NAME="E6:79_3"/><span class="lab"><font color="Green" title="E47">A7</font></span>: 
<font color="Maroon" title="c6">H1</font> <a href="group_2.html#K10" title="GROUP_2:func.10">/\</a> <font color="Maroon" title="c7">H2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">A</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Maroon" title="c4">B</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:79"><span class="lab"><font color="Green" title="E44">A3</font></span></a></span>;<br/><span class="kw">hence </span><span class="p1">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Maroon" title="c4">B</font></span>)</span> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Maroon" title="c4">B</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c6">H1</font> <a href="group_2.html#K10" title="GROUP_2:func.10">/\</a> <font color="Maroon" title="c7">H2</font></span>)</span> <a href="group_4.html#K8" title="GROUP_4:func.8">"\/"</a> <font color="Maroon" title="c7">H2</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:79"><span class="lab"><font color="Green" title="E43">A1</font></span></a></span>
<br/>.= 
<font color="Maroon" title="c4">B</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="group_4.html#T66" target="_self" title="GROUP_4:th.66">Th84</a></span>
;<br/> <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="c3">A</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Maroon" title="c4">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">B</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Maroon" title="c3">A</font> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Maroon" title="c4">B</font></span>)</span> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Maroon" title="c5">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">A</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">B</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Maroon" title="c5">C</font></span>)</span> &amp; <font color="Maroon" title="c3">A</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Maroon" title="c4">B</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">A</font> )</span><br/><a NAME="E8:79_3"/><span class="lab"><font color="Green" title="E48">A8</font></span>: 
<font color="Maroon" title="c7">H2</font> <a href="group_2.html#K10" title="GROUP_2:func.10">/\</a> <font color="Maroon" title="c8">H3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">B</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Maroon" title="c5">C</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:79"><span class="lab"><font color="Green" title="E44">A3</font></span></a></span>;<br/><span class="kw">thus </span><font color="Maroon" title="c3">A</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Maroon" title="c4">B</font> = 
<font color="Maroon" title="c7">H2</font> <a href="group_2.html#K10" title="GROUP_2:func.10">/\</a> <font color="Maroon" title="c6">H1</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:79"><span class="lab"><font color="Green" title="E44">A3</font></span></a></span>
<br/>.= 
<font color="Maroon" title="c4">B</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Maroon" title="c3">A</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:79"><span class="lab"><font color="Green" title="E44">A3</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"> ( <span class="p1">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Maroon" title="c4">B</font></span>)</span> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Maroon" title="c5">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">A</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">B</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Maroon" title="c5">C</font></span>)</span> &amp; <font color="Maroon" title="c3">A</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Maroon" title="c4">B</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">A</font> )</span><br/><span class="kw">thus </span><span class="p1">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Maroon" title="c4">B</font></span>)</span> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Maroon" title="c5">C</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c6">H1</font> <a href="group_2.html#K10" title="GROUP_2:func.10">/\</a> <font color="Maroon" title="c7">H2</font></span>)</span> <a href="group_2.html#K10" title="GROUP_2:func.10">/\</a> <font color="Maroon" title="c8">H3</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:79"><span class="lab"><font color="Green" title="E44">A3</font></span></a>, <a class="txt" href="#E6:79_3"><span class="lab"><font color="Green" title="E47">A7</font></span></a></span>
<br/>.= 
<font color="Maroon" title="c6">H1</font> <a href="group_2.html#K10" title="GROUP_2:func.10">/\</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">H2</font> <a href="group_2.html#K10" title="GROUP_2:func.10">/\</a> <font color="Maroon" title="c8">H3</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="group_2.html#T84" title="GROUP_2:th.84">GROUP_2:84</a></span>
<br/>.= 
<font color="Maroon" title="c3">A</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">B</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Maroon" title="c5">C</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:79"><span class="lab"><font color="Green" title="E44">A3</font></span></a>, <a class="txt" href="#E8:79_3"><span class="lab"><font color="Green" title="E48">A8</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"> <font color="Maroon" title="c3">A</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Maroon" title="c4">B</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">A</font></span><br/><span class="kw">thus </span><font color="Maroon" title="c3">A</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Maroon" title="c4">B</font></span>)</span> = 
<font color="Maroon" title="c6">H1</font> <a href="group_2.html#K10" title="GROUP_2:func.10">/\</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">H1</font> <a href="group_4.html#K8" title="GROUP_4:func.8">"\/"</a> <font color="Maroon" title="c7">H2</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:79"><span class="lab"><font color="Green" title="E44">A3</font></span></a>, <a class="txt" href="#E4:79_3"><span class="lab"><font color="Green" title="E46">A6</font></span></a></span>
<br/>.= 
<font color="Maroon" title="c3">A</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="group_4.html#T67" target="_self" title="GROUP_4:th.67">Th85</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="E4:79"/><span class="kw">then </span><span class="lab"><font color="Green" title="E45">A9</font></span>: 
(  <a href="lattices.html#G3" title="LATTICES:aggr.3">LattStr</a>(# <span class="p1">(<span class="default"><a href="group_3.html#K1" title="GROUP_3:func.1">Subgroups</a> <font color="Maroon" title="c1">G</font></span>)</span>,<span class="p1">(<span class="default"><a href="group_4.html#K9" title="GROUP_4:func.9">SubJoin</a> <font color="Maroon" title="c1">G</font></span>)</span>,<span class="p1">(<span class="default"><a href="group_4.html#K10" title="GROUP_4:func.10">SubMeet</a> <font color="Maroon" title="c1">G</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="group_3.html#K1" title="GROUP_3:func.1">Subgroups</a> <font color="Maroon" title="c1">G</font></span>)</span>,<span class="p1">(<span class="default"><a href="group_4.html#K9" title="GROUP_4:func.9">SubJoin</a> <font color="Maroon" title="c1">G</font></span>)</span>,<span class="p1">(<span class="default"><a href="group_4.html#K10" title="GROUP_4:func.10">SubMeet</a> <font color="Maroon" title="c1">G</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="group_3.html#K1" title="GROUP_3:func.1">Subgroups</a> <font color="Maroon" title="c1">G</font></span>)</span>,<span class="p1">(<span class="default"><a href="group_4.html#K9" title="GROUP_4:func.9">SubJoin</a> <font color="Maroon" title="c1">G</font></span>)</span>,<span class="p1">(<span class="default"><a href="group_4.html#K10" title="GROUP_4:func.10">SubMeet</a> <font color="Maroon" title="c1">G</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="group_3.html#K1" title="GROUP_3:func.1">Subgroups</a> <font color="Maroon" title="c1">G</font></span>)</span>,<span class="p1">(<span class="default"><a href="group_4.html#K9" title="GROUP_4:func.9">SubJoin</a> <font color="Maroon" title="c1">G</font></span>)</span>,<span class="p1">(<span class="default"><a href="group_4.html#K10" title="GROUP_4:func.10">SubMeet</a> <font color="Maroon" title="c1">G</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="group_3.html#K1" title="GROUP_3:func.1">Subgroups</a> <font color="Maroon" title="c1">G</font></span>)</span>,<span class="p1">(<span class="default"><a href="group_4.html#K9" title="GROUP_4:func.9">SubJoin</a> <font color="Maroon" title="c1">G</font></span>)</span>,<span class="p1">(<span class="default"><a href="group_4.html#K10" title="GROUP_4:func.10">SubMeet</a> <font color="Maroon" title="c1">G</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="group_3.html#K1" title="GROUP_3:func.1">Subgroups</a> <font color="Maroon" title="c1">G</font></span>)</span>,<span class="p1">(<span class="default"><a href="group_4.html#K9" title="GROUP_4:func.9">SubJoin</a> <font color="Maroon" title="c1">G</font></span>)</span>,<span class="p1">(<span class="default"><a href="group_4.html#K10" title="GROUP_4:func.10">SubMeet</a> <font color="Maroon" title="c1">G</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="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">hence </span><a NAME="E5:79"/>
 <a href="lattices.html#G3" title="LATTICES:aggr.3">LattStr</a>(# <span class="p1">(<span class="default"><a href="group_3.html#K1" title="GROUP_3:func.1">Subgroups</a> <font color="Maroon" title="c1">G</font></span>)</span>,<span class="p1">(<span class="default"><a href="group_4.html#K9" title="GROUP_4:func.9">SubJoin</a> <font color="Maroon" title="c1">G</font></span>)</span>,<span class="p1">(<span class="default"><a href="group_4.html#K10" title="GROUP_4:func.10">SubMeet</a> <font color="Maroon" title="c1">G</font></span>)</span> #) is   <a href="lattices.html#NM1" title="LATTICES:NM.1">Lattice</a>
 ; <a class="txt" 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="group_3.html#K1" title="GROUP_3:func.1">Subgroups</a> <font color="Maroon" title="c1">G</font></span>)</span>,<span class="p1">(<span class="default"><a href="group_4.html#K9" title="GROUP_4:func.9">SubJoin</a> <font color="Maroon" title="c1">G</font></span>)</span>,<span class="p1">(<span class="default"><a href="group_4.html#K10" title="GROUP_4:func.10">SubMeet</a> <font color="Maroon" title="c1">G</font></span>)</span> #) is   <a href="lattices.html#NM4" title="LATTICES:NM.4">0_Lattice</a> &amp;  <a href="lattices.html#G3" title="LATTICES:aggr.3">LattStr</a>(# <span class="p1">(<span class="default"><a href="group_3.html#K1" title="GROUP_3:func.1">Subgroups</a> <font color="Maroon" title="c1">G</font></span>)</span>,<span class="p1">(<span class="default"><a href="group_4.html#K9" title="GROUP_4:func.9">SubJoin</a> <font color="Maroon" title="c1">G</font></span>)</span>,<span class="p1">(<span class="default"><a href="group_4.html#K10" title="GROUP_4:func.10">SubMeet</a> <font color="Maroon" title="c1">G</font></span>)</span> #) is   <a href="lattices.html#NM5" title="LATTICES:NM.5">1_Lattice</a> )</span><br/>

<span class="kw">reconsider </span><font color="Maroon" title="c3">L</font> =  <a href="lattices.html#G3" title="LATTICES:aggr.3">LattStr</a>(# <span class="p1">(<span class="default"><a href="group_3.html#K1" title="GROUP_3:func.1">Subgroups</a> <font color="Maroon" title="c1">G</font></span>)</span>,<span class="p1">(<span class="default"><a href="group_4.html#K9" title="GROUP_4:func.9">SubJoin</a> <font color="Maroon" title="c1">G</font></span>)</span>,<span class="p1">(<span class="default"><a href="group_4.html#K10" title="GROUP_4:func.10">SubMeet</a> <font color="Maroon" title="c1">G</font></span>)</span> #) as   <a href="lattices.html#NM1" title="LATTICES:NM.1">Lattice</a> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:79"><span class="lab"><font color="Green" title="E45">A9</font></span></a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c4">E</font> =  <a href="group_2.html#K6" title="GROUP_2:func.6">(1).</a> <font color="Maroon" title="c1">G</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c3">L</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="group_3.html#D1" title="GROUP_3:def.1">GROUP_3:def 1</a></span>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="79_4"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c5">A</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c3">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="c4">E</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c5">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">E</font> &amp; <font color="Maroon" title="c5">A</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c4">E</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">E</font> )</span><br/><span class="kw">reconsider </span><font color="Maroon" title="c6">H</font> = <font color="Maroon" title="c5">A</font> as   <a href="algstr_0.html#V15" title="ALGSTR_0:attr.15">strict</a>   <a href="group_2.html#M1" title="GROUP_2:mode.1">Subgroup</a> of <font color="Maroon" title="c1">G</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="group_3.html#D1" title="GROUP_3:def.1">GROUP_3:def 1</a></span>;<br/><span class="kw">thus </span><font color="Maroon" title="c4">E</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c5">A</font> = 
<span class="p1">(<span class="default"><a href="group_2.html#K6" title="GROUP_2:func.6">(1).</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="group_2.html#K10" title="GROUP_2:func.10">/\</a> <font color="Maroon" title="c6">H</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:79"><span class="lab"><font color="Green" title="E44">A3</font></span></a></span>
<br/>.= 
<font color="Maroon" title="c4">E</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="group_2.html#T85" title="GROUP_2:th.85">GROUP_2:85</a></span>
; <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">A</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c4">E</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">E</font></span><br/><span class="kw">hence </span><a NAME="E3:79_4"/>
<font color="Maroon" title="c5">A</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c4">E</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">E</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>
<span class="kw">hence </span><a NAME="E9:79"/>
 <a href="lattices.html#G3" title="LATTICES:aggr.3">LattStr</a>(# <span class="p1">(<span class="default"><a href="group_3.html#K1" title="GROUP_3:func.1">Subgroups</a> <font color="Maroon" title="c1">G</font></span>)</span>,<span class="p1">(<span class="default"><a href="group_4.html#K9" title="GROUP_4:func.9">SubJoin</a> <font color="Maroon" title="c1">G</font></span>)</span>,<span class="p1">(<span class="default"><a href="group_4.html#K10" title="GROUP_4:func.10">SubMeet</a> <font color="Maroon" title="c1">G</font></span>)</span> #) is   <a href="lattices.html#NM4" title="LATTICES:NM.4">0_Lattice</a>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="lattices.html#D13" title="LATTICES:def.13">LATTICES:def 13</a></span>; <a class="txt" 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="group_3.html#K1" title="GROUP_3:func.1">Subgroups</a> <font color="Maroon" title="c1">G</font></span>)</span>,<span class="p1">(<span class="default"><a href="group_4.html#K9" title="GROUP_4:func.9">SubJoin</a> <font color="Maroon" title="c1">G</font></span>)</span>,<span class="p1">(<span class="default"><a href="group_4.html#K10" title="GROUP_4:func.10">SubMeet</a> <font color="Maroon" title="c1">G</font></span>)</span> #) is   <a href="lattices.html#NM5" title="LATTICES:NM.5">1_Lattice</a></span><br/>

<span class="kw">reconsider </span><font color="Maroon" title="c5">F</font> =  <a href="group_2.html#K7" title="GROUP_2:func.7">(Omega).</a> <font color="Maroon" title="c1">G</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c3">L</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="group_3.html#D1" title="GROUP_3:def.1">GROUP_3:def 1</a></span>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="79_5"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c6">A</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c3">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="c5">F</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c6">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">F</font> &amp; <font color="Maroon" title="c6">A</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c5">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">F</font> )</span><br/><span class="kw">reconsider </span><font color="Maroon" title="c7">H</font> = <font color="Maroon" title="c6">A</font> as   <a href="algstr_0.html#V15" title="ALGSTR_0:attr.15">strict</a>   <a href="group_2.html#M1" title="GROUP_2:mode.1">Subgroup</a> of <font color="Maroon" title="c1">G</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="group_3.html#D1" title="GROUP_3:def.1">GROUP_3:def 1</a></span>;<br/><span class="kw">thus </span><font color="Maroon" title="c5">F</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c6">A</font> = 
<span class="p1">(<span class="default"><a href="group_2.html#K7" title="GROUP_2:func.7">(Omega).</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="group_4.html#K8" title="GROUP_4:func.8">"\/"</a> <font color="Maroon" title="c7">H</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:79"><span class="lab"><font color="Green" title="E43">A1</font></span></a></span>
<br/>.= 
<font color="Maroon" title="c5">F</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="group_4.html#T59" target="_self" title="GROUP_4:th.59">Th77</a></span>
; <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">A</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c5">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">F</font></span><br/><span class="kw">hence </span><a NAME="E3:79_5"/>
<font color="Maroon" title="c6">A</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c5">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">F</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>
<span class="kw">hence </span><a NAME="E12:79"/>
 <a href="lattices.html#G3" title="LATTICES:aggr.3">LattStr</a>(# <span class="p1">(<span class="default"><a href="group_3.html#K1" title="GROUP_3:func.1">Subgroups</a> <font color="Maroon" title="c1">G</font></span>)</span>,<span class="p1">(<span class="default"><a href="group_4.html#K9" title="GROUP_4:func.9">SubJoin</a> <font color="Maroon" title="c1">G</font></span>)</span>,<span class="p1">(<span class="default"><a href="group_4.html#K10" title="GROUP_4:func.10">SubMeet</a> <font color="Maroon" title="c1">G</font></span>)</span> #) is   <a href="lattices.html#NM5" title="LATTICES:NM.5">1_Lattice</a>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="lattices.html#D14" title="LATTICES:def.14">LATTICES:def 14</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>
