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

<b>let </b><font color="Maroon" title="c1">S1</font> be   <a href="osalg_1.html#NM3" title="OSALG_1:NM.3">OrderSortedSign</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">U0</font> being <a href="msualg_1.html#V4" title="MSUALG_1:attr.4">strict</a> <a href="msualg_1.html#V5" title="MSUALG_1:attr.5">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#K6" title="LATTICES:func.6">Top</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> <font color="Olive" title="b1">U0</font></span><br/><b>let </b><font color="Maroon" title="c2">U0</font> be  <a href="msualg_1.html#V4" title="MSUALG_1:attr.4">strict</a> <a href="msualg_1.html#V5" title="MSUALG_1:attr.5">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" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="lattices.html#K6" title="LATTICES:func.6">Top</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> <font color="Maroon" title="c2">U0</font></span><br/>



<b>reconsider </b><font color="Maroon" title="c3">B</font> = the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <font color="Maroon" title="c2">U0</font> as   <a href="msualg_2.html#NM1" title="MSUALG_2:NM.1">MSSubset</a> of <font color="Maroon" title="c2">U0</font> <b>by </b><i><a class="ref" href="pboole.html#D23" title="PBOOLE:def.23">PBOOLE:def 23</a></i>;<br/>
<a NAME="E2:85"/>
<font color="Maroon" title="c3">B</font> is   <a href="osalg_1.html#NM4" title="OSALG_1:NM.4">OrderSortedSet</a> of <font color="Maroon" title="c1">S1</font>
 
<b>by </b><i><a class="ref" href="osalg_1.html#T17" title="OSALG_1:th.17">OSALG_1:17</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c4">B</font> = the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <font color="Maroon" title="c2">U0</font> as    <a href="osalg_2.html#M2" title="OSALG_2:mode.2">OSSubset</a> of <font color="Maroon" title="c2">U0</font> <b>by </b><i><a class="ref" href="osalg_2.html#D2" target="_self" title="OSALG_2:def.2">Def2</a></i>;<br/>
<b>thus </b> <a href="lattices.html#K6" title="LATTICES:func.6">Top</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="osalg_2.html#K10" title="OSALG_2:func.10">GenOSAlg</a> <font color="Maroon" title="c4">B</font>
<b>by </b><i><a class="ref" href="osalg_2.html#T55" target="_self" title="OSALG_2:th.55">Th55</a></i>
<br/>.= 
<font color="Maroon" title="c2">U0</font>
<b>by </b><i><a class="ref" href="osalg_2.html#T39" target="_self" title="OSALG_2:th.39">Th39</a></i>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
