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<span class="kw">let </span><font color="Maroon" title="c1">S1</font> be   <a href="osalg_1.html#NM3" title="OSALG_1:NM.3">OrderSortedSign</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">U0</font> being   <a href="msualg_1.html#V4" title="MSUALG_1:attr.4">non-empty</a>  <a href="osalg_1.html#NM5" title="OSALG_1:NM.5">OSAlgebra</a> of <font color="Maroon" title="c1">S1</font> holds   <a href="lattices.html#K5" title="LATTICES:func.5">Bottom</a> <span class="p1">(<span class="default"><a href="osalg_2.html#K16" title="OSALG_2:func.16">OSSubAlLattice</a> <font color="Olive" title="b1">U0</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="osalg_2.html#K10" title="OSALG_2:func.10">GenOSAlg</a> <span class="p1">(<span class="default"><a href="osalg_2.html#K3" title="OSALG_2:func.3">OSConstants</a> <font color="Olive" title="b1">U0</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c2">U0</font> be   <a href="msualg_1.html#V4" title="MSUALG_1:attr.4">non-empty</a>  <a href="osalg_1.html#NM5" title="OSALG_1:NM.5">OSAlgebra</a> of <font color="Maroon" title="c1">S1</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="lattices.html#K5" title="LATTICES:func.5">Bottom</a> <span class="p1">(<span class="default"><a href="osalg_2.html#K16" title="OSALG_2:func.16">OSSubAlLattice</a> <font color="Maroon" title="c2">U0</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="osalg_2.html#K10" title="OSALG_2:func.10">GenOSAlg</a> <span class="p1">(<span class="default"><a href="osalg_2.html#K3" title="OSALG_2:func.3">OSConstants</a> <font color="Maroon" title="c2">U0</font></span>)</span></span><br/>



<span class="kw">set </span><font color="Maroon" title="c3">C</font> =  <a href="osalg_2.html#K3" title="OSALG_2:func.3">OSConstants</a> <font color="Maroon" title="c2">U0</font>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c4">G</font> =  <a href="osalg_2.html#K10" title="OSALG_2:func.10">GenOSAlg</a> <span class="p1">(<span class="default"><a href="osalg_2.html#K3" title="OSALG_2:func.3">OSConstants</a> <font color="Maroon" title="c2">U0</font></span>)</span> as    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="osalg_2.html#K13" title="OSALG_2:func.13">OSSub</a> <font color="Maroon" title="c2">U0</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="osalg_2.html#D14" target="_self" onmouseover="rs('osalg_2/D14')" onmouseout="rh()">Def14</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c5">L</font> =  <a href="osalg_2.html#K16" title="OSALG_2:func.16">OSSubAlLattice</a> <font color="Maroon" title="c2">U0</font>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c6">G1</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="osalg_2.html#K16" title="OSALG_2:func.16">OSSubAlLattice</a> <font color="Maroon" title="c2">U0</font></span>)</span> ;<br/>
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="83_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">a</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="osalg_2.html#K16" title="OSALG_2:func.16">OSSubAlLattice</a> <font color="Maroon" title="c2">U0</font></span>)</span> holds <br/> ( <font color="Maroon" title="c6">G1</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Olive" title="b1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">G1</font> &amp; <font color="Olive" title="b1">a</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c6">G1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">G1</font> )</span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c7">a</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="osalg_2.html#K16" title="OSALG_2:func.16">OSSubAlLattice</a> <font color="Maroon" title="c2">U0</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="c6">G1</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c7">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">G1</font> &amp; <font color="Maroon" title="c7">a</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c6">G1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">G1</font> )</span><br/><span class="kw">reconsider </span><font color="Maroon" title="c8">a1</font> = <font color="Maroon" title="c7">a</font> as    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="osalg_2.html#K13" title="OSALG_2:func.13">OSSub</a> <font color="Maroon" title="c2">U0</font> ;<br/><span class="kw">reconsider </span><font color="Maroon" title="c9">a2</font> = <font color="Maroon" title="c8">a1</font> as   <a href="msualg_1.html#V3" title="MSUALG_1:attr.3">strict</a>  <a href="osalg_2.html#NM3" title="OSALG_2:NM.3">OSSubAlgebra</a> of <font color="Maroon" title="c2">U0</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="osalg_2.html#D14" target="_self" onmouseover="rs('osalg_2/D14')" onmouseout="rh()">Def14</a></span>;<br/><span class="kw">thus </span><font color="Maroon" title="c6">G1</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c7">a</font> = 
<span class="p1">(<span class="default"><a href="osalg_2.html#K10" title="OSALG_2:func.10">GenOSAlg</a> <span class="p2">(<span class="default"><a href="osalg_2.html#K3" title="OSALG_2:func.3">OSConstants</a> <font color="Maroon" title="c2">U0</font></span>)</span></span>)</span> <a href="msualg_2.html#K11" title="MSUALG_2:func.11">/\</a> <font color="Maroon" title="c9">a2</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="osalg_2.html#D16" target="_self" onmouseover="rs('osalg_2/D16')" onmouseout="rh()">Def16</a></span>
<br/>.= 
<font color="Maroon" title="c6">G1</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="osalg_2.html#T36" target="_self" onmouseover="rs('osalg_2/T36')" onmouseout="rh()">Th36</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"> <font color="Maroon" title="c7">a</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c6">G1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">G1</font></span><br/><span class="kw">hence </span><a NAME="E4:83_1"/>
<font color="Maroon" title="c7">a</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c6">G1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">G1</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E4:83"/>
 <a href="lattices.html#K5" title="LATTICES:func.5">Bottom</a> <span class="p1">(<span class="default"><a href="osalg_2.html#K16" title="OSALG_2:func.16">OSSubAlLattice</a> <font color="Maroon" title="c2">U0</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="osalg_2.html#K10" title="OSALG_2:func.10">GenOSAlg</a> <span class="p1">(<span class="default"><a href="osalg_2.html#K3" title="OSALG_2:func.3">OSConstants</a> <font color="Maroon" title="c2">U0</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="lattices.html#D16" onmouseover="rs('lattices/D16')" onmouseout="rh()">LATTICES:def 16</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/>


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