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<span class="kw">let </span><font color="Maroon" title="c1">U0</font> be   <a href="unialg_1.html#V3" title="UNIALG_1:attr.3">strict</a>   <a href="unialg_2.html#V2" title="UNIALG_2:attr.2">with_const_op</a>  <a href="unialg_1.html#NM2" title="UNIALG_1:NM.2">Universal_Algebra</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="lattices.html#K5" title="LATTICES:func.5">Bottom</a> <span class="p1">(<span class="default"><a href="unialg_2.html#K12" title="UNIALG_2:func.12">UnSubAlLattice</a> <font color="Maroon" title="c1">U0</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="unialg_2.html#K7" title="UNIALG_2:func.7">GenUnivAlg</a> <span class="p1">(<span class="default"><a href="unialg_2.html#K6" title="UNIALG_2:func.6">Constants</a> <font color="Maroon" title="c1">U0</font></span>)</span></span><br/>

<span class="kw">set </span><font color="Maroon" title="c2">L</font> =  <a href="unialg_2.html#K12" title="UNIALG_2:func.12">UnSubAlLattice</a> <font color="Maroon" title="c1">U0</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c3">C</font> =  <a href="unialg_2.html#K6" title="UNIALG_2:func.6">Constants</a> <font color="Maroon" title="c1">U0</font>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c4">G</font> =  <a href="unialg_2.html#K7" title="UNIALG_2:func.7">GenUnivAlg</a> <span class="p1">(<span class="default"><a href="unialg_2.html#K6" title="UNIALG_2:func.6">Constants</a> <font color="Maroon" title="c1">U0</font></span>)</span> as    <a href="unialg_3.html#M2" title="UNIALG_3:mode.2">Element</a> of  <a href="unialg_3.html#K1" title="UNIALG_3:func.1">Sub</a> <font color="Maroon" title="c1">U0</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="unialg_2.html#D15" title="UNIALG_2:def.15">UNIALG_2:def 15</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c5">l1</font> = <font color="Maroon" title="c4">G</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="unialg_2.html#K12" title="UNIALG_2:func.12">UnSubAlLattice</a> <font color="Maroon" title="c1">U0</font></span>)</span> ;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="30_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c6">l</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="unialg_2.html#K12" title="UNIALG_2:func.12">UnSubAlLattice</a> <font color="Maroon" title="c1">U0</font></span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c5">l1</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c6">l</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">l1</font> &amp; <font color="Maroon" title="c6">l</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c5">l1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">l1</font> )</span><br/><span class="kw">reconsider </span><font color="Maroon" title="c7">u1</font> = <font color="Maroon" title="c6">l</font> as    <a href="unialg_3.html#M2" title="UNIALG_3:mode.2">Element</a> of  <a href="unialg_3.html#K1" title="UNIALG_3:func.1">Sub</a> <font color="Maroon" title="c1">U0</font> ;<br/><span class="kw">reconsider </span><font color="Maroon" title="c8">U2</font> = <font color="Maroon" title="c7">u1</font> as   <a href="unialg_1.html#V3" title="UNIALG_1:attr.3">strict</a>   <a href="unialg_2.html#M3" title="UNIALG_2:mode.3">SubAlgebra</a> of <font color="Maroon" title="c1">U0</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="unialg_2.html#D15" title="UNIALG_2:def.15">UNIALG_2:def 15</a></span>;<br/><span class="kw">thus </span><font color="Maroon" title="c5">l1</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c6">l</font> = 
<span class="p1">(<span class="default"><a href="unialg_2.html#K7" title="UNIALG_2:func.7">GenUnivAlg</a> <span class="p2">(<span class="default"><a href="unialg_2.html#K6" title="UNIALG_2:func.6">Constants</a> <font color="Maroon" title="c1">U0</font></span>)</span></span>)</span> <a href="unialg_2.html#K5" title="UNIALG_2:func.5">/\</a> <font color="Maroon" title="c8">U2</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="unialg_2.html#D17" title="UNIALG_2:def.17">UNIALG_2:def 17</a></span>
<br/>.= 
<font color="Maroon" title="c5">l1</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="unialg_3.html#T20" target="_self" title="UNIALG_3:th.20">Th20</a></span>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c6">l</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c5">l1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">l1</font></span><br/><span class="kw">hence </span><a NAME="E4:30_1"/>
<font color="Maroon" title="c6">l</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c5">l1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">l1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E4:30"/>
 <a href="lattices.html#K5" title="LATTICES:func.5">Bottom</a> <span class="p1">(<span class="default"><a href="unialg_2.html#K12" title="UNIALG_2:func.12">UnSubAlLattice</a> <font color="Maroon" title="c1">U0</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="unialg_2.html#K7" title="UNIALG_2:func.7">GenUnivAlg</a> <span class="p1">(<span class="default"><a href="unialg_2.html#K6" title="UNIALG_2:func.6">Constants</a> <font color="Maroon" title="c1">U0</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="lattices.html#D16" title="LATTICES:def.16">LATTICES:def 16</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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