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<div class="add">

<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">A</font> being    <a href="osalg_2.html#M2" title="OSALG_2:mode.2">OSSubset</a> of <font color="Olive" title="b1">OU0</font> holds <br/> (  <a href="osalg_2.html#K10" title="OSALG_2:func.10">GenOSAlg</a> <font color="Olive" title="b2">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">OU0</font> <a href="msualg_2.html#K10" title="MSUALG_2:func.10">|</a> <span class="p1">(<span class="default"><a href="osalg_2.html#K9" title="OSALG_2:func.9">OSMSubSort</a> <font color="Olive" title="b2">A</font></span>)</span> &amp;  the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <span class="p1">(<span class="default"><a href="osalg_2.html#K10" title="OSALG_2:func.10">GenOSAlg</a> <font color="Olive" title="b2">A</font></span>)</span> <a href="pboole.html#R8" title="PBOOLE:pred.8">=</a>  <a href="osalg_2.html#K9" title="OSALG_2:func.9">OSMSubSort</a> <font color="Olive" title="b2">A</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">A</font> being    <a href="osalg_2.html#M2" title="OSALG_2:mode.2">OSSubset</a> of <font color="Maroon" title="c2">OU0</font> holds <br/> (  <a href="osalg_2.html#K10" title="OSALG_2:func.10">GenOSAlg</a> <font color="Olive" title="b1">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">OU0</font> <a href="msualg_2.html#K10" title="MSUALG_2:func.10">|</a> <span class="p1">(<span class="default"><a href="osalg_2.html#K9" title="OSALG_2:func.9">OSMSubSort</a> <font color="Olive" title="b1">A</font></span>)</span> &amp;  the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <span class="p1">(<span class="default"><a href="osalg_2.html#K10" title="OSALG_2:func.10">GenOSAlg</a> <font color="Olive" title="b1">A</font></span>)</span> <a href="pboole.html#R8" title="PBOOLE:pred.8">=</a>  <a href="osalg_2.html#K9" title="OSALG_2:func.9">OSMSubSort</a> <font color="Olive" title="b1">A</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c3">A</font> be    <a href="osalg_2.html#M2" title="OSALG_2:mode.2">OSSubset</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#K10" title="OSALG_2:func.10">GenOSAlg</a> <font color="Maroon" title="c3">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">OU0</font> <a href="msualg_2.html#K10" title="MSUALG_2:func.10">|</a> <span class="p1">(<span class="default"><a href="osalg_2.html#K9" title="OSALG_2:func.9">OSMSubSort</a> <font color="Maroon" title="c3">A</font></span>)</span> &amp;  the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <span class="p1">(<span class="default"><a href="osalg_2.html#K10" title="OSALG_2:func.10">GenOSAlg</a> <font color="Maroon" title="c3">A</font></span>)</span> <a href="pboole.html#R8" title="PBOOLE:pred.8">=</a>  <a href="osalg_2.html#K9" title="OSALG_2:func.9">OSMSubSort</a> <font color="Maroon" title="c3">A</font> )</span><br/>





<span class="kw">set </span><font color="Maroon" title="c4">a</font> =  <a href="osalg_2.html#K9" title="OSALG_2:func.9">OSMSubSort</a> <font color="Maroon" title="c3">A</font>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c5">u1</font> = <font color="Maroon" title="c2">OU0</font> <a href="msualg_2.html#K10" title="MSUALG_2:func.10">|</a> <span class="p1">(<span class="default"><a href="osalg_2.html#K9" title="OSALG_2:func.9">OSMSubSort</a> <font color="Maroon" title="c3">A</font></span>)</span> 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">OU0</font> ;<br/>
<a NAME="E2:57"/><span class="lab"><font color="Green" title="E34">A1</font></span>: 
<font color="Maroon" title="c5">u1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="msualg_1.html#G3" title="MSUALG_1:aggr.3">MSAlgebra</a>(# <span class="p1">(<span class="default"><a href="osalg_2.html#K9" title="OSALG_2:func.9">OSMSubSort</a> <font color="Maroon" title="c3">A</font></span>)</span>,<span class="p1">(<span class="default"><a href="msualg_2.html#K4" title="MSUALG_2:func.4">Opers</a> (<font color="Maroon" title="c2">OU0</font>,<span class="p2">(<span class="default"><a href="osalg_2.html#K9" title="OSALG_2:func.9">OSMSubSort</a> <font color="Maroon" title="c3">A</font></span>)</span>)</span>)</span> #)
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="msualg_2.html#D15" onmouseover="rs('msualg_2/D15')" onmouseout="rh()">MSUALG_2:def 15</a></span>;<br/>
<a NAME="E3:57"/><span class="lab"><font color="Green" title="E35">A2</font></span>: 
<font color="Maroon" title="c3">A</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a>  <a href="osalg_2.html#K9" title="OSALG_2:func.9">OSMSubSort</a> <font color="Maroon" title="c3">A</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="osalg_2.html#T29" target="_self" onmouseover="rs('osalg_2/T29')" onmouseout="rh()">Th29</a></span>;<br/>
<a NAME="E4:57"/><span class="lab"><font color="Green" title="E36">A3</font></span>: 
<font color="Maroon" title="c3">A</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/>
<a NAME="E5:57"/><span class="lab"><font color="Green" title="E37">A4</font></span>: 
( <font color="Maroon" title="c3">A</font> is    <a href="osalg_2.html#M2" title="OSALG_2:mode.2">OSSubset</a> of <font color="Maroon" title="c5">u1</font> &amp; (  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>  st <font color="Maroon" title="c3">A</font> is    <a href="osalg_2.html#M2" title="OSALG_2:mode.2">OSSubset</a> of <font color="Olive" title="b1">OU1</font> holds <br/><font color="Maroon" title="c5">u1</font> is   <a href="osalg_2.html#NM3" title="OSALG_2:NM.3">OSSubAlgebra</a> of <font color="Olive" title="b1">OU1</font> ) )
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="57_1"><span class="kw">proof </span></a><div class="add">

<a NAME="E1:57_1"/>
<font color="Maroon" title="c3">A</font> is   <a href="msualg_2.html#NM1" title="MSUALG_2:NM.1">MSSubset</a> of <font color="Maroon" title="c5">u1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:57"><span class="lab"><font color="Green" title="E35">A2</font></span></a>, <a class="txt" href="#E2:57"><span class="lab"><font color="Green" title="E34">A1</font></span></a>, <a class="ref" href="pboole.html#D18" onmouseover="rs('pboole/D18')" onmouseout="rh()">PBOOLE:def 18</a></span>;<br/>
<span class="kw">hence </span><a NAME="E2:57_1"/>
<font color="Maroon" title="c3">A</font> is    <a href="osalg_2.html#M2" title="OSALG_2:mode.2">OSSubset</a> of <font color="Maroon" title="c5">u1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:57"><span class="lab"><font color="Green" title="E36">A3</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">  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>  st <font color="Maroon" title="c3">A</font> is    <a href="osalg_2.html#M2" title="OSALG_2:mode.2">OSSubset</a> of <font color="Olive" title="b1">OU1</font> holds <br/><font color="Maroon" title="c5">u1</font> is   <a href="osalg_2.html#NM3" title="OSALG_2:NM.3">OSSubAlgebra</a> of <font color="Olive" title="b1">OU1</font></span><br/>

<span class="kw">let </span><font color="Maroon" title="c6">U2</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"> ( <font color="Maroon" title="c3">A</font> is    <a href="osalg_2.html#M2" title="OSALG_2:mode.2">OSSubset</a> of <font color="Maroon" title="c6">U2</font> implies <font color="Maroon" title="c5">u1</font> is   <a href="osalg_2.html#NM3" title="OSALG_2:NM.3">OSSubAlgebra</a> of <font color="Maroon" title="c6">U2</font> )</span><br/>

<span class="kw">reconsider </span><font color="Maroon" title="c7">B1</font> =  the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c6">U2</font> as   <a href="msualg_2.html#NM1" title="MSUALG_2:NM.1">MSSubset</a> of <font color="Maroon" title="c2">OU0</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="msualg_2.html#D9" onmouseover="rs('msualg_2/D9')" onmouseout="rh()">MSUALG_2:def 9</a></span>;<br/>
<a NAME="E4:57_1"/>
<font color="Maroon" title="c7">B1</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_1.html#T17" onmouseover="rs('osalg_1/T17')" onmouseout="rh()">OSALG_1:17</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c8">B</font> = <font color="Maroon" title="c7">B1</font> as    <a href="osalg_2.html#M2" title="OSALG_2:mode.2">OSSubset</a> of <font color="Maroon" title="c2">OU0</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">assume </span><a NAME="E6:57_1"/>
<font color="Maroon" title="c3">A</font> is    <a href="osalg_2.html#M2" title="OSALG_2:mode.2">OSSubset</a> of <font color="Maroon" title="c6">U2</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="c5">u1</font> is   <a href="osalg_2.html#NM3" title="OSALG_2:NM.3">OSSubAlgebra</a> of <font color="Maroon" title="c6">U2</font></span><br/>

<a NAME="E7:57_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E38">A5</font></span>: 
( <font color="Maroon" title="c8">B</font> is  <a href="msualg_2.html#V3" title="MSUALG_2:attr.3">opers_closed</a>  &amp; <font color="Maroon" title="c3">A</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a> <font color="Maroon" title="c8">B</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="msualg_2.html#D9" onmouseover="rs('msualg_2/D9')" onmouseout="rh()">MSUALG_2:def 9</a>, <a class="ref" href="pboole.html#D18" onmouseover="rs('pboole/D18')" onmouseout="rh()">PBOOLE:def 18</a></span>;<br/>
<a NAME="E8:57_1"/>
 <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="c6">U2</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="osalg_2.html#T13" target="_self" onmouseover="rs('osalg_2/T13')" onmouseout="rh()">Th13</a></span>;<br/>
<a NAME="E9:57_1"/><span class="kw">then </span>
 <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> <font color="Maroon" title="c8">B</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="E10:57_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E39">A6</font></span>: 
<font color="Maroon" title="c8">B</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="osalg_2.html#K5" title="OSALG_2:func.5">OSSubSort</a> <font color="Maroon" title="c3">A</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:57_1"><span class="lab"><font color="Green" title="E38">A5</font></span></a>, <a class="ref" href="osalg_2.html#T19" target="_self" onmouseover="rs('osalg_2/T19')" onmouseout="rh()">Th19</a></span>;<br/>
<a NAME="E11:57_1"/>
 the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c5">u1</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="c6">U2</font>
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="57_1_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c9">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="c9">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  the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c5">u1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">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="c6">U2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">i</font> )</span><br/>

<span class="kw">assume </span><a NAME="E1:57_1_1"/>
<font color="Maroon" title="c9">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">  the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c5">u1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">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="c6">U2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">i</font></span><br/>

<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c10">s</font> = <font color="Maroon" title="c9">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="E3:57_1_1"/>
(  the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c5">u1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="setfam_1.html#K1" title="SETFAM_1:func.1">meet</a> <span class="p1">(<span class="default"><a href="osalg_2.html#K8" title="OSALG_2:func.8">OSSubSort</a> (<font color="Maroon" title="c3">A</font>,<font color="Maroon" title="c10">s</font>)</span>)</span> &amp; <font color="Maroon" title="c8">B</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">s</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="osalg_2.html#K8" title="OSALG_2:func.8">OSSubSort</a> (<font color="Maroon" title="c3">A</font>,<font color="Maroon" title="c10">s</font>) )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:57"><span class="lab"><font color="Green" title="E34">A1</font></span></a>, <a class="txt" href="#E10:57_1"><span class="lab"><font color="Green" title="E39">A6</font></span></a>, <a class="ref" href="osalg_2.html#D10" target="_self" onmouseover="rs('osalg_2/D10')" onmouseout="rh()">Def10</a>, <a class="ref" href="osalg_2.html#D11" target="_self" onmouseover="rs('osalg_2/D11')" onmouseout="rh()">Def11</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:57_1_1"/>
 the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c5">u1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">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="c6">U2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">i</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="setfam_1.html#T3" onmouseover="rs('setfam_1/T3')" onmouseout="rh()">SETFAM_1:3</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="kw">hence </span><a NAME="E12:57_1"/>
<font color="Maroon" title="c5">u1</font> is   <a href="osalg_2.html#NM3" title="OSALG_2:NM.3">OSSubAlgebra</a> of <font color="Maroon" title="c6">U2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="msualg_2.html#T8" onmouseover="rs('msualg_2/T8')" onmouseout="rh()">MSUALG_2:8</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="kw">hence </span><a NAME="E6:57"/>
 <a href="osalg_2.html#K10" title="OSALG_2:func.10">GenOSAlg</a> <font color="Maroon" title="c3">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">OU0</font> <a href="msualg_2.html#K10" title="MSUALG_2:func.10">|</a> <span class="p1">(<span class="default"><a href="osalg_2.html#K9" title="OSALG_2:func.9">OSMSubSort</a> <font color="Maroon" title="c3">A</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="osalg_2.html#D12" target="_self" onmouseover="rs('osalg_2/D12')" onmouseout="rh()">Def12</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">  the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <span class="p1">(<span class="default"><a href="osalg_2.html#K10" title="OSALG_2:func.10">GenOSAlg</a> <font color="Maroon" title="c3">A</font></span>)</span> <a href="pboole.html#R8" title="PBOOLE:pred.8">=</a>  <a href="osalg_2.html#K9" title="OSALG_2:func.9">OSMSubSort</a> <font color="Maroon" title="c3">A</font></span><br/>

<span class="kw">thus </span><a NAME="E7:57"/>
 the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <span class="p1">(<span class="default"><a href="osalg_2.html#K10" title="OSALG_2:func.10">GenOSAlg</a> <font color="Maroon" title="c3">A</font></span>)</span> <a href="pboole.html#R8" title="PBOOLE:pred.8">=</a>  <a href="osalg_2.html#K9" title="OSALG_2:func.9">OSMSubSort</a> <font color="Maroon" title="c3">A</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:57"><span class="lab"><font color="Green" title="E34">A1</font></span></a>, <a class="txt" href="#E5:57"><span class="lab"><font color="Green" title="E37">A4</font></span></a>, <a class="ref" href="osalg_2.html#D12" target="_self" onmouseover="rs('osalg_2/D12')" onmouseout="rh()">Def12</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>
