<?xml version="1.0"?>
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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">OU0</font> being   <a href="osalg_1.html#NM5" title="OSALG_1:NM.5">OSAlgebra</a> of <font color="Maroon" title="c1">S1</font><br/>  for <font color="Olive" title="b2">OU1</font> being   <a href="osalg_2.html#NM3" title="OSALG_2:NM.3">OSSubAlgebra</a> of <font color="Olive" title="b1">OU0</font> holds   <a href="osalg_2.html#K3" title="OSALG_2:func.3">OSConstants</a> <font color="Olive" title="b1">OU0</font> is    <a href="osalg_2.html#M2" title="OSALG_2:mode.2">OSSubset</a> of <font color="Olive" title="b2">OU1</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">OU0</font> be   <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">  for <font color="Olive" title="b1">OU1</font> being   <a href="osalg_2.html#NM3" title="OSALG_2:NM.3">OSSubAlgebra</a> of <font color="Maroon" title="c2">OU0</font> holds   <a href="osalg_2.html#K3" title="OSALG_2:func.3">OSConstants</a> <font color="Maroon" title="c2">OU0</font> is    <a href="osalg_2.html#M2" title="OSALG_2:mode.2">OSSubset</a> of <font color="Olive" title="b1">OU1</font></span><br/><span class="kw">let </span><font color="Maroon" title="c3">OU1</font> be   <a href="osalg_2.html#NM3" title="OSALG_2:NM.3">OSSubAlgebra</a> of <font color="Maroon" title="c2">OU0</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="osalg_2.html#K3" title="OSALG_2:func.3">OSConstants</a> <font color="Maroon" title="c2">OU0</font> is    <a href="osalg_2.html#M2" title="OSALG_2:mode.2">OSSubset</a> of <font color="Maroon" title="c3">OU1</font></span><br/>





<a NAME="E1:26"/>
 <a href="osalg_2.html#K3" title="OSALG_2:func.3">OSConstants</a> <font color="Maroon" title="c2">OU0</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a>  the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c3">OU1</font>
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="26_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c4">i</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> ; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="pboole.html#D2" onmouseover="rs('pboole/D2')" onmouseout="rh()">PBOOLE:def 2</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"> (  not <font color="Maroon" title="c4">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">S1</font> or <span class="p1">(<span class="default"><a href="osalg_2.html#K3" title="OSALG_2:func.3">OSConstants</a> <font color="Maroon" title="c2">OU0</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">i</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c3">OU1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">i</font> )</span><br/>

<span class="kw">assume </span><a NAME="E1:26_1"/>
<font color="Maroon" title="c4">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</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"> <span class="p1">(<span class="default"><a href="osalg_2.html#K3" title="OSALG_2:func.3">OSConstants</a> <font color="Maroon" title="c2">OU0</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">i</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c3">OU1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">i</font></span><br/>

<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c5">s</font> = <font color="Maroon" title="c4">i</font> as   <a href="osalg_1.html#NM1" title="OSALG_1:NM.1">SortSymbol</a> of <font color="Maroon" title="c1">S1</font> ;<br/>
<a NAME="E3:26_1"/>
 <a href="msualg_2.html#K2" title="MSUALG_2:func.2">Constants</a> <font color="Maroon" title="c2">OU0</font> is   <a href="msualg_2.html#NM1" title="MSUALG_2:NM.1">MSSubset</a> of <font color="Maroon" title="c3">OU1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="msualg_2.html#T10" onmouseover="rs('msualg_2/T10')" onmouseout="rh()">MSUALG_2:10</a></span>;<br/>
<a NAME="E4:26_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E16">A1</font></span>: 
 <a href="msualg_2.html#K2" title="MSUALG_2:func.2">Constants</a> <font color="Maroon" title="c2">OU0</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a>  the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c3">OU1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="pboole.html#D18" onmouseover="rs('pboole/D18')" onmouseout="rh()">PBOOLE:def 18</a></span>;<br/>
<a NAME="E5:26_1"/><span class="lab"><font color="Green" title="E17">A2</font></span>: 
 for <font color="Olive" title="b1">s2</font>, <font color="Olive" title="b2">s3</font> being   <a href="osalg_1.html#NM1" title="OSALG_1:NM.1">SortSymbol</a> of <font color="Maroon" title="c1">S1</font>  st <font color="Olive" title="b1">s2</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Olive" title="b2">s3</font> holds <br/><span class="p1">(<span class="default"><a href="msualg_2.html#K2" title="MSUALG_2:func.2">Constants</a> <font color="Maroon" title="c2">OU0</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">s2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c3">OU1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b2">s3</font>
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="26_1_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c6">s2</font>, <font color="Maroon" title="c7">s3</font> be   <a href="osalg_1.html#NM1" title="OSALG_1:NM.1">SortSymbol</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"> ( <font color="Maroon" title="c6">s2</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c7">s3</font> implies <span class="p1">(<span class="default"><a href="msualg_2.html#K2" title="MSUALG_2:func.2">Constants</a> <font color="Maroon" title="c2">OU0</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">s2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c3">OU1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">s3</font> )</span><br/>



<span class="kw">assume </span><a NAME="E1:26_1_1"/>
<font color="Maroon" title="c6">s2</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c7">s3</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"> <span class="p1">(<span class="default"><a href="msualg_2.html#K2" title="MSUALG_2:func.2">Constants</a> <font color="Maroon" title="c2">OU0</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">s2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c3">OU1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">s3</font></span><br/>

<a NAME="E2:26_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E18">A3</font></span>: 
 the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c3">OU1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">s2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c3">OU1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">s3</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="osalg_1.html#D17" onmouseover="rs('osalg_1/D17')" onmouseout="rh()">OSALG_1:def 17</a></span>;<br/>
<a NAME="E3:26_1_1"/>
<span class="p1">(<span class="default"><a href="msualg_2.html#K2" title="MSUALG_2:func.2">Constants</a> <font color="Maroon" title="c2">OU0</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">s2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c3">OU1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">s2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:26_1"><span class="lab"><font color="Green" title="E16">A1</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:26_1_1"/>
<span class="p1">(<span class="default"><a href="msualg_2.html#K2" title="MSUALG_2:func.2">Constants</a> <font color="Maroon" title="c2">OU0</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">s2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c3">OU1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">s3</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:26_1_1"><span class="lab"><font color="Green" title="E18">A3</font></span></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="E6:26_1"/><span class="lab"><font color="Green" title="E18">A4</font></span>: 
 for <font color="Olive" title="b1">X</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>   st <font color="Olive" title="b1">X</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <span class="p1"> { <span class="default"> <span class="p2">(<span class="default"><a href="msualg_2.html#K1" title="MSUALG_2:func.1">Constants</a> (<font color="Maroon" title="c2">OU0</font>,<font color="Olive" title="b2">s1</font>)</span>)</span> where <font color="Olive" title="b2">s1</font> is   <a href="osalg_1.html#NM1" title="OSALG_1:NM.1">SortSymbol</a> of <font color="Maroon" title="c1">S1</font> : <font color="Olive" title="b2">s1</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c5">s</font> </span> } </span>  holds <br/><font color="Olive" title="b1">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c3">OU1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">s</font>
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="26_1_2"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c6">X</font> be    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</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"> ( <font color="Maroon" title="c6">X</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <span class="p1"> { <span class="default"> <span class="p2">(<span class="default"><a href="msualg_2.html#K1" title="MSUALG_2:func.1">Constants</a> (<font color="Maroon" title="c2">OU0</font>,<font color="Olive" title="b1">s1</font>)</span>)</span> where <font color="Olive" title="b1">s1</font> is   <a href="osalg_1.html#NM1" title="OSALG_1:NM.1">SortSymbol</a> of <font color="Maroon" title="c1">S1</font> : <font color="Olive" title="b1">s1</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c5">s</font> </span> } </span>  implies <font color="Maroon" title="c6">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c3">OU1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">s</font> )</span><br/>

<span class="kw">assume </span><a NAME="E1:26_1_2"/>
<font color="Maroon" title="c6">X</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <span class="p1"> { <span class="default"> <span class="p2">(<span class="default"><a href="msualg_2.html#K1" title="MSUALG_2:func.1">Constants</a> (<font color="Maroon" title="c2">OU0</font>,<font color="Olive" title="b1">s1</font>)</span>)</span> where <font color="Olive" title="b1">s1</font> is   <a href="osalg_1.html#NM1" title="OSALG_1:NM.1">SortSymbol</a> of <font color="Maroon" title="c1">S1</font> : <font color="Olive" title="b1">s1</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c5">s</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">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c3">OU1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">s</font></span><br/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c7">s4</font> being   <a href="osalg_1.html#NM1" title="OSALG_1:NM.1">SortSymbol</a> of <font color="Maroon" title="c1">S1</font><span class="kw"> such that </span><br/><a NAME="E3:26_1_2"/><span class="lab"><font color="Green" title="E19">A5</font></span>: 
( <font color="Maroon" title="c6">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="msualg_2.html#K1" title="MSUALG_2:func.1">Constants</a> (<font color="Maroon" title="c2">OU0</font>,<font color="Maroon" title="c7">s4</font>) &amp; <font color="Maroon" title="c7">s4</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c5">s</font> )
 ;<br/>
<a NAME="E4:26_1_2"/>
 <a href="msualg_2.html#K1" title="MSUALG_2:func.1">Constants</a> (<font color="Maroon" title="c2">OU0</font>,<font color="Maroon" title="c7">s4</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="msualg_2.html#K2" title="MSUALG_2:func.2">Constants</a> <font color="Maroon" title="c2">OU0</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">s4</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="msualg_2.html#D4" onmouseover="rs('msualg_2/D4')" onmouseout="rh()">MSUALG_2:def 4</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:26_1_2"/>
<font color="Maroon" title="c6">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c3">OU1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">s</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:26_1"><span class="lab"><font color="Green" title="E17">A2</font></span></a>, <a class="txt" href="#E3:26_1_2"><span class="lab"><font color="Green" title="E19">A5</font></span></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>
<span class="p1">(<span class="default"><a href="osalg_2.html#K3" title="OSALG_2:func.3">OSConstants</a> <font color="Maroon" title="c2">OU0</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">i</font> = 
 <a href="osalg_2.html#K1" title="OSALG_2:func.1">OSConstants</a> (<font color="Maroon" title="c2">OU0</font>,<font color="Maroon" title="c5">s</font>)
<span class="kw">by</span> <span class="lab"><a class="ref" href="osalg_2.html#D5" target="_self" onmouseover="rs('osalg_2/D5')" onmouseout="rh()">Def5</a></span>
<br/>.= 
 <a href="tarski.html#K3" title="TARSKI:func.3">union</a> <span class="p1"> { <span class="default"> <span class="p2">(<span class="default"><a href="msualg_2.html#K1" title="MSUALG_2:func.1">Constants</a> (<font color="Maroon" title="c2">OU0</font>,<font color="Olive" title="b1">s1</font>)</span>)</span> where <font color="Olive" title="b1">s1</font> is   <a href="osalg_1.html#NM1" title="OSALG_1:NM.1">SortSymbol</a> of <font color="Maroon" title="c1">S1</font> : <font color="Olive" title="b1">s1</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c5">s</font> </span> } </span> 

;<br/>
<span class="kw">hence </span><a NAME="E8:26_1"/>
<span class="p1">(<span class="default"><a href="osalg_2.html#K3" title="OSALG_2:func.3">OSConstants</a> <font color="Maroon" title="c2">OU0</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">i</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c3">OU1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">i</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:26_1"><span class="lab"><font color="Green" title="E18">A4</font></span></a>, <a class="ref" href="zfmisc_1.html#T76" onmouseover="rs('zfmisc_1/T76')" onmouseout="rh()">ZFMISC_1:76</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="E2:26"/><span class="kw">then </span><span class="lab"><font color="Green" title="E16">A6</font></span>: 
 <a href="osalg_2.html#K3" title="OSALG_2:func.3">OSConstants</a> <font color="Maroon" title="c2">OU0</font> is    <a href="pboole.html#M3" title="PBOOLE:mode.3">ManySortedSubset</a> of  the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c3">OU1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="pboole.html#D18" onmouseover="rs('pboole/D18')" onmouseout="rh()">PBOOLE:def 18</a></span>;<br/>
<a NAME="E3:26"/>
 <a href="osalg_2.html#K3" title="OSALG_2:func.3">OSConstants</a> <font color="Maroon" title="c2">OU0</font> is   <a href="osalg_1.html#NM4" title="OSALG_1:NM.4">OrderSortedSet</a> of <font color="Maroon" title="c1">S1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="osalg_2.html#D2" target="_self" onmouseover="rs('osalg_2/D2')" onmouseout="rh()">Def2</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:26"/>
 <a href="osalg_2.html#K3" title="OSALG_2:func.3">OSConstants</a> <font color="Maroon" title="c2">OU0</font> is    <a href="osalg_2.html#M2" title="OSALG_2:mode.2">OSSubset</a> of <font color="Maroon" title="c3">OU1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:26"><span class="lab"><font color="Green" title="E16">A6</font></span></a>, <a class="ref" href="osalg_2.html#D2" target="_self" onmouseover="rs('osalg_2/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>
