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<span class="kw">let </span><font color="Maroon" title="c1">S</font> be   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   non  <a href="struct_0.html#V11" title="STRUCT_0:attr.11">void</a>   <a href="msualg_1.html#L1" title="MSUALG_1:struct.1">ManySortedSign</a> ; <a class="txt" 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="msualg_1.html#L3" title="MSUALG_1:struct.3">MSAlgebra</a> of <font color="Maroon" title="c1">S</font><br/>  for <font color="Olive" title="b2">U1</font> being    <a href="msualg_2.html#M1" title="MSUALG_2:mode.1">MSSubAlgebra</a> of <font color="Olive" title="b1">U0</font><br/>  for <font color="Olive" title="b3">A</font>, <font color="Olive" title="b4">B</font> being   <a href="msualg_2.html#NM1" title="MSUALG_2:NM.1">MSSubset</a> of <font color="Olive" title="b1">U0</font>  st <font color="Olive" title="b4">B</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <font color="Olive" title="b3">A</font> <a href="pboole.html#K2" title="PBOOLE:func.2">\/</a>  the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Olive" title="b2">U1</font> holds <br/><span class="p1">(<span class="default"><a href="msualg_2.html#K12" title="MSUALG_2:func.12">GenMSAlg</a> <font color="Olive" title="b3">A</font></span>)</span> <a href="msualg_2.html#K13" title="MSUALG_2:func.13">"\/"</a> <font color="Olive" title="b2">U1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="msualg_2.html#K12" title="MSUALG_2:func.12">GenMSAlg</a> <font color="Olive" title="b4">B</font></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="msualg_1.html#L3" title="MSUALG_1:struct.3">MSAlgebra</a> of <font color="Maroon" title="c1">S</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">U1</font> being    <a href="msualg_2.html#M1" title="MSUALG_2:mode.1">MSSubAlgebra</a> of <font color="Maroon" title="c2">U0</font><br/>  for <font color="Olive" title="b2">A</font>, <font color="Olive" title="b3">B</font> being   <a href="msualg_2.html#NM1" title="MSUALG_2:NM.1">MSSubset</a> of <font color="Maroon" title="c2">U0</font>  st <font color="Olive" title="b3">B</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <font color="Olive" title="b2">A</font> <a href="pboole.html#K2" title="PBOOLE:func.2">\/</a>  the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Olive" title="b1">U1</font> holds <br/><span class="p1">(<span class="default"><a href="msualg_2.html#K12" title="MSUALG_2:func.12">GenMSAlg</a> <font color="Olive" title="b2">A</font></span>)</span> <a href="msualg_2.html#K13" title="MSUALG_2:func.13">"\/"</a> <font color="Olive" title="b1">U1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="msualg_2.html#K12" title="MSUALG_2:func.12">GenMSAlg</a> <font color="Olive" title="b3">B</font></span><br/><span class="kw">let </span><font color="Maroon" title="c3">U1</font> be    <a href="msualg_2.html#M1" title="MSUALG_2:mode.1">MSSubAlgebra</a> of <font color="Maroon" title="c2">U0</font>; <a class="txt" 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>, <font color="Olive" title="b2">B</font> being   <a href="msualg_2.html#NM1" title="MSUALG_2:NM.1">MSSubset</a> of <font color="Maroon" title="c2">U0</font>  st <font color="Olive" title="b2">B</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <font color="Olive" title="b1">A</font> <a href="pboole.html#K2" title="PBOOLE:func.2">\/</a>  the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c3">U1</font> holds <br/><span class="p1">(<span class="default"><a href="msualg_2.html#K12" title="MSUALG_2:func.12">GenMSAlg</a> <font color="Olive" title="b1">A</font></span>)</span> <a href="msualg_2.html#K13" title="MSUALG_2:func.13">"\/"</a> <font color="Maroon" title="c3">U1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="msualg_2.html#K12" title="MSUALG_2:func.12">GenMSAlg</a> <font color="Olive" title="b2">B</font></span><br/><span class="kw">let </span><font color="Maroon" title="c4">A</font>, <font color="Maroon" title="c5">B</font> be   <a href="msualg_2.html#NM1" title="MSUALG_2:NM.1">MSSubset</a> of <font color="Maroon" title="c2">U0</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c5">B</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <font color="Maroon" title="c4">A</font> <a href="pboole.html#K2" title="PBOOLE:func.2">\/</a>  the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c3">U1</font> implies <span class="p1">(<span class="default"><a href="msualg_2.html#K12" title="MSUALG_2:func.12">GenMSAlg</a> <font color="Maroon" title="c4">A</font></span>)</span> <a href="msualg_2.html#K13" title="MSUALG_2:func.13">"\/"</a> <font color="Maroon" title="c3">U1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="msualg_2.html#K12" title="MSUALG_2:func.12">GenMSAlg</a> <font color="Maroon" title="c5">B</font> )</span><br/>







<span class="kw">reconsider </span><font color="Maroon" title="c6">u1</font> =  the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c3">U1</font>, <font color="Maroon" title="c7">a</font> =  the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <span class="p1">(<span class="default"><a href="msualg_2.html#K12" title="MSUALG_2:func.12">GenMSAlg</a> <font color="Maroon" title="c4">A</font></span>)</span> as   <a href="msualg_2.html#NM1" title="MSUALG_2:NM.1">MSSubset</a> of <font color="Maroon" title="c2">U0</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="msualg_2.html#D9" target="_self" title="MSUALG_2:def.9">Def10</a></span>;<br/>
<a NAME="E2:56"/><span class="lab"><font color="Green" title="E40">A1</font></span>: 
 the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <span class="p1">(<span class="default"><a href="msualg_2.html#K12" title="MSUALG_2:func.12">GenMSAlg</a> <font color="Maroon" title="c4">A</font></span>)</span> <a href="pboole.html#K3" title="PBOOLE:func.3">/\</a>  the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <span class="p1">(<span class="default"><a href="msualg_2.html#K12" title="MSUALG_2:func.12">GenMSAlg</a> <font color="Maroon" title="c5">B</font></span>)</span> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a> <font color="Maroon" title="c7">a</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="pboole.html#T15" title="PBOOLE:th.15">PBOOLE:15</a></span>;<br/>
<a NAME="E3:56"/><span class="lab"><font color="Green" title="E41">A2</font></span>: 
 the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="msualg_2.html#K12" title="MSUALG_2:func.12">GenMSAlg</a> <font color="Maroon" title="c4">A</font></span>)</span> <a href="msualg_2.html#K11" title="MSUALG_2:func.11">/\</a> <span class="p2">(<span class="default"><a href="msualg_2.html#K12" title="MSUALG_2:func.12">GenMSAlg</a> <font color="Maroon" title="c5">B</font></span>)</span></span>)</span> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <span class="p1">(<span class="default"><a href="msualg_2.html#K12" title="MSUALG_2:func.12">GenMSAlg</a> <font color="Maroon" title="c4">A</font></span>)</span> <a href="pboole.html#K3" title="PBOOLE:func.3">/\</a>  the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <span class="p1">(<span class="default"><a href="msualg_2.html#K12" title="MSUALG_2:func.12">GenMSAlg</a> <font color="Maroon" title="c5">B</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="msualg_2.html#D16" target="_self" title="MSUALG_2:def.16">Def17</a></span>;<br/>
<a NAME="E4:56"/>
( <font color="Maroon" title="c7">a</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="c2">U0</font> &amp; <font color="Maroon" title="c6">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="c2">U0</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="pboole.html#D18" title="PBOOLE:def.18">PBOOLE:def 18</a></span>;<br/>
<a NAME="E5:56"/><span class="kw">then </span>
<font color="Maroon" title="c7">a</font> <a href="pboole.html#K2" title="PBOOLE:func.2">\/</a> <font color="Maroon" title="c6">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="c2">U0</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="pboole.html#T16" title="PBOOLE:th.16">PBOOLE:16</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">a</font> <a href="pboole.html#K2" title="PBOOLE:func.2">\/</a> <font color="Maroon" title="c6">u1</font> as   <a href="msualg_2.html#NM1" title="MSUALG_2:NM.1">MSSubset</a> of <font color="Maroon" title="c2">U0</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="pboole.html#D18" title="PBOOLE:def.18">PBOOLE:def 18</a></span>;<br/>
<a NAME="E7:56"/><span class="lab"><font color="Green" title="E42">A3</font></span>: 
<span class="p1">(<span class="default"><a href="msualg_2.html#K12" title="MSUALG_2:func.12">GenMSAlg</a> <font color="Maroon" title="c4">A</font></span>)</span> <a href="msualg_2.html#K13" title="MSUALG_2:func.13">"\/"</a> <font color="Maroon" title="c3">U1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="msualg_2.html#K12" title="MSUALG_2:func.12">GenMSAlg</a> <font color="Maroon" title="c8">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="msualg_2.html#D18" target="_self" title="MSUALG_2:def.18">Def19</a></span>;<br/>
<a NAME="E8:56"/><span class="kw">then </span>
<font color="Maroon" title="c7">a</font> <a href="pboole.html#K2" title="PBOOLE:func.2">\/</a> <font color="Maroon" title="c6">u1</font> is   <a href="msualg_2.html#NM1" title="MSUALG_2:NM.1">MSSubset</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="msualg_2.html#K12" title="MSUALG_2:func.12">GenMSAlg</a> <font color="Maroon" title="c4">A</font></span>)</span> <a href="msualg_2.html#K13" title="MSUALG_2:func.13">"\/"</a> <font color="Maroon" title="c3">U1</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="msualg_2.html#D17" target="_self" title="MSUALG_2:def.17">Def18</a></span>;<br/>
<a NAME="E9:56"/><span class="kw">then </span><span class="lab"><font color="Green" title="E43">A4</font></span>: 
<font color="Maroon" title="c7">a</font> <a href="pboole.html#K2" title="PBOOLE:func.2">\/</a> <font color="Maroon" title="c6">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 <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="msualg_2.html#K12" title="MSUALG_2:func.12">GenMSAlg</a> <font color="Maroon" title="c4">A</font></span>)</span> <a href="msualg_2.html#K13" title="MSUALG_2:func.13">"\/"</a> <font color="Maroon" title="c3">U1</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="pboole.html#D18" title="PBOOLE:def.18">PBOOLE:def 18</a></span>;<br/>
<a NAME="E10:56"/>
<font color="Maroon" title="c4">A</font> is   <a href="msualg_2.html#NM1" title="MSUALG_2:NM.1">MSSubset</a> of <span class="p1">(<span class="default"><a href="msualg_2.html#K12" title="MSUALG_2:func.12">GenMSAlg</a> <font color="Maroon" title="c4">A</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="msualg_2.html#D17" target="_self" title="MSUALG_2:def.17">Def18</a></span>;<br/>
<a NAME="E11:56"/><span class="kw">then </span><span class="lab"><font color="Green" title="E44">A5</font></span>: 
<font color="Maroon" title="c4">A</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 <span class="p1">(<span class="default"><a href="msualg_2.html#K12" title="MSUALG_2:func.12">GenMSAlg</a> <font color="Maroon" title="c4">A</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="pboole.html#D18" title="PBOOLE:def.18">PBOOLE:def 18</a></span>;<br/>
<a NAME="E12:56"/>
<font color="Maroon" title="c5">B</font> is   <a href="msualg_2.html#NM1" title="MSUALG_2:NM.1">MSSubset</a> of <span class="p1">(<span class="default"><a href="msualg_2.html#K12" title="MSUALG_2:func.12">GenMSAlg</a> <font color="Maroon" title="c5">B</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="msualg_2.html#D17" target="_self" title="MSUALG_2:def.17">Def18</a></span>;<br/>
<a NAME="E13:56"/><span class="kw">then </span><span class="lab"><font color="Green" title="E45">A6</font></span>: 
<font color="Maroon" title="c5">B</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 <span class="p1">(<span class="default"><a href="msualg_2.html#K12" title="MSUALG_2:func.12">GenMSAlg</a> <font color="Maroon" title="c5">B</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="pboole.html#D18" title="PBOOLE:def.18">PBOOLE:def 18</a></span>;<br/>
<span class="kw">assume </span><a NAME="E14:56"/><span class="lab"><font color="Green" title="E46">A7</font></span>: 
<font color="Maroon" title="c5">B</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <font color="Maroon" title="c4">A</font> <a href="pboole.html#K2" title="PBOOLE:func.2">\/</a>  the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c3">U1</font>
 ; <a class="txt" 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#K12" title="MSUALG_2:func.12">GenMSAlg</a> <font color="Maroon" title="c4">A</font></span>)</span> <a href="msualg_2.html#K13" title="MSUALG_2:func.13">"\/"</a> <font color="Maroon" title="c3">U1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="msualg_2.html#K12" title="MSUALG_2:func.12">GenMSAlg</a> <font color="Maroon" title="c5">B</font></span><br/>

<a NAME="E15:56"/><span class="kw">then </span>
<font color="Maroon" title="c4">A</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a> <font color="Maroon" title="c5">B</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="pboole.html#T14" title="PBOOLE:th.14">PBOOLE:14</a></span>;<br/>
<a NAME="E16:56"/><span class="kw">then </span>
<font color="Maroon" title="c4">A</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 <span class="p1">(<span class="default"><a href="msualg_2.html#K12" title="MSUALG_2:func.12">GenMSAlg</a> <font color="Maroon" title="c5">B</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:56"><span class="lab"><font color="Green" title="E45">A6</font></span></a>, <a class="ref" href="pboole.html#T13" title="PBOOLE:th.13">PBOOLE:13</a></span>;<br/>
<a NAME="E17:56"/><span class="kw">then </span>
<font color="Maroon" title="c4">A</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 <span class="p1">(<span class="default"><a href="msualg_2.html#K12" title="MSUALG_2:func.12">GenMSAlg</a> <font color="Maroon" title="c4">A</font></span>)</span> <a href="pboole.html#K3" title="PBOOLE:func.3">/\</a>  the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <span class="p1">(<span class="default"><a href="msualg_2.html#K12" title="MSUALG_2:func.12">GenMSAlg</a> <font color="Maroon" title="c5">B</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:56"><span class="lab"><font color="Green" title="E44">A5</font></span></a>, <a class="ref" href="pboole.html#T17" title="PBOOLE:th.17">PBOOLE:17</a></span>;<br/>
<a NAME="E18:56"/><span class="kw">then </span>
<font color="Maroon" title="c4">A</font> is   <a href="msualg_2.html#NM1" title="MSUALG_2:NM.1">MSSubset</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="msualg_2.html#K12" title="MSUALG_2:func.12">GenMSAlg</a> <font color="Maroon" title="c4">A</font></span>)</span> <a href="msualg_2.html#K11" title="MSUALG_2:func.11">/\</a> <span class="p2">(<span class="default"><a href="msualg_2.html#K12" title="MSUALG_2:func.12">GenMSAlg</a> <font color="Maroon" title="c5">B</font></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:56"><span class="lab"><font color="Green" title="E41">A2</font></span></a>, <a class="ref" href="pboole.html#D18" title="PBOOLE:def.18">PBOOLE:def 18</a></span>;<br/>
<a NAME="E19:56"/><span class="kw">then </span>
 <a href="msualg_2.html#K12" title="MSUALG_2:func.12">GenMSAlg</a> <font color="Maroon" title="c4">A</font> is    <a href="msualg_2.html#M1" title="MSUALG_2:mode.1">MSSubAlgebra</a> of <span class="p1">(<span class="default"><a href="msualg_2.html#K12" title="MSUALG_2:func.12">GenMSAlg</a> <font color="Maroon" title="c4">A</font></span>)</span> <a href="msualg_2.html#K11" title="MSUALG_2:func.11">/\</a> <span class="p1">(<span class="default"><a href="msualg_2.html#K12" title="MSUALG_2:func.12">GenMSAlg</a> <font color="Maroon" title="c5">B</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="msualg_2.html#D17" target="_self" title="MSUALG_2:def.17">Def18</a></span>;<br/>
<a NAME="E20:56"/><span class="kw">then </span>
<font color="Maroon" title="c7">a</font> is   <a href="msualg_2.html#NM1" title="MSUALG_2:NM.1">MSSubset</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="msualg_2.html#K12" title="MSUALG_2:func.12">GenMSAlg</a> <font color="Maroon" title="c4">A</font></span>)</span> <a href="msualg_2.html#K11" title="MSUALG_2:func.11">/\</a> <span class="p2">(<span class="default"><a href="msualg_2.html#K12" title="MSUALG_2:func.12">GenMSAlg</a> <font color="Maroon" title="c5">B</font></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="msualg_2.html#D9" target="_self" title="MSUALG_2:def.9">Def10</a></span>;<br/>
<a NAME="E21:56"/><span class="kw">then </span>
<font color="Maroon" title="c7">a</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 <span class="p1">(<span class="default"><a href="msualg_2.html#K12" title="MSUALG_2:func.12">GenMSAlg</a> <font color="Maroon" title="c4">A</font></span>)</span> <a href="pboole.html#K3" title="PBOOLE:func.3">/\</a>  the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <span class="p1">(<span class="default"><a href="msualg_2.html#K12" title="MSUALG_2:func.12">GenMSAlg</a> <font color="Maroon" title="c5">B</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:56"><span class="lab"><font color="Green" title="E41">A2</font></span></a>, <a class="ref" href="pboole.html#D18" title="PBOOLE:def.18">PBOOLE:def 18</a></span>;<br/>
<a NAME="E22:56"/><span class="kw">then </span>
<font color="Maroon" title="c7">a</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <span class="p1">(<span class="default"><a href="msualg_2.html#K12" title="MSUALG_2:func.12">GenMSAlg</a> <font color="Maroon" title="c4">A</font></span>)</span> <a href="pboole.html#K3" title="PBOOLE:func.3">/\</a>  the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <span class="p1">(<span class="default"><a href="msualg_2.html#K12" title="MSUALG_2:func.12">GenMSAlg</a> <font color="Maroon" title="c5">B</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:56"><span class="lab"><font color="Green" title="E40">A1</font></span></a>, <a class="ref" href="pboole.html#D10" title="PBOOLE:def.10">PBOOLE:def 10</a></span>;<br/>
<a NAME="E23:56"/><span class="kw">then </span><span class="lab"><font color="Green" title="E47">A8</font></span>: 
<font color="Maroon" title="c7">a</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 <span class="p1">(<span class="default"><a href="msualg_2.html#K12" title="MSUALG_2:func.12">GenMSAlg</a> <font color="Maroon" title="c5">B</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="pboole.html#T15" title="PBOOLE:th.15">PBOOLE:15</a></span>;<br/>
<a NAME="E24:56"/>
<font color="Maroon" title="c6">u1</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a> <font color="Maroon" title="c5">B</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:56"><span class="lab"><font color="Green" title="E46">A7</font></span></a>, <a class="ref" href="pboole.html#T14" title="PBOOLE:th.14">PBOOLE:14</a></span>;<br/>
<a NAME="E25:56"/><span class="kw">then </span>
<font color="Maroon" title="c6">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 <span class="p1">(<span class="default"><a href="msualg_2.html#K12" title="MSUALG_2:func.12">GenMSAlg</a> <font color="Maroon" title="c5">B</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:56"><span class="lab"><font color="Green" title="E45">A6</font></span></a>, <a class="ref" href="pboole.html#T13" title="PBOOLE:th.13">PBOOLE:13</a></span>;<br/>
<a NAME="E26:56"/><span class="kw">then </span>
<font color="Maroon" title="c8">b</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 <span class="p1">(<span class="default"><a href="msualg_2.html#K12" title="MSUALG_2:func.12">GenMSAlg</a> <font color="Maroon" title="c5">B</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E23:56"><span class="lab"><font color="Green" title="E47">A8</font></span></a>, <a class="ref" href="pboole.html#T16" title="PBOOLE:th.16">PBOOLE:16</a></span>;<br/>
<a NAME="E27:56"/><span class="kw">then </span>
<font color="Maroon" title="c8">b</font> is   <a href="msualg_2.html#NM1" title="MSUALG_2:NM.1">MSSubset</a> of <span class="p1">(<span class="default"><a href="msualg_2.html#K12" title="MSUALG_2:func.12">GenMSAlg</a> <font color="Maroon" title="c5">B</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="pboole.html#D18" title="PBOOLE:def.18">PBOOLE:def 18</a></span>;<br/>
<a NAME="E28:56"/><span class="kw">then </span><span class="lab"><font color="Green" title="E48">A9</font></span>: 
 <a href="msualg_2.html#K12" title="MSUALG_2:func.12">GenMSAlg</a> <font color="Maroon" title="c8">b</font> is   <a href="msualg_1.html#V3" title="MSUALG_1:attr.3">strict</a>   <a href="msualg_2.html#M1" title="MSUALG_2:mode.1">MSSubAlgebra</a> of  <a href="msualg_2.html#K12" title="MSUALG_2:func.12">GenMSAlg</a> <font color="Maroon" title="c5">B</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="msualg_2.html#D17" target="_self" title="MSUALG_2:def.17">Def18</a></span>;<br/>
<a NAME="E29:56"/>
<font color="Maroon" title="c4">A</font> <a href="pboole.html#K2" title="PBOOLE:func.2">\/</a> <font color="Maroon" title="c6">u1</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a> <font color="Maroon" title="c7">a</font> <a href="pboole.html#K2" title="PBOOLE:func.2">\/</a> <font color="Maroon" title="c6">u1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:56"><span class="lab"><font color="Green" title="E44">A5</font></span></a>, <a class="ref" href="pboole.html#T20" title="PBOOLE:th.20">PBOOLE:20</a></span>;<br/>
<a NAME="E30:56"/><span class="kw">then </span>
<font color="Maroon" title="c5">B</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 <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="msualg_2.html#K12" title="MSUALG_2:func.12">GenMSAlg</a> <font color="Maroon" title="c4">A</font></span>)</span> <a href="msualg_2.html#K13" title="MSUALG_2:func.13">"\/"</a> <font color="Maroon" title="c3">U1</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:56"><span class="lab"><font color="Green" title="E46">A7</font></span></a>, <a class="txt" href="#E9:56"><span class="lab"><font color="Green" title="E43">A4</font></span></a>, <a class="ref" href="pboole.html#T13" title="PBOOLE:th.13">PBOOLE:13</a></span>;<br/>
<a NAME="E31:56"/><span class="kw">then </span>
<font color="Maroon" title="c5">B</font> is   <a href="msualg_2.html#NM1" title="MSUALG_2:NM.1">MSSubset</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="msualg_2.html#K12" title="MSUALG_2:func.12">GenMSAlg</a> <font color="Maroon" title="c4">A</font></span>)</span> <a href="msualg_2.html#K13" title="MSUALG_2:func.13">"\/"</a> <font color="Maroon" title="c3">U1</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="pboole.html#D18" title="PBOOLE:def.18">PBOOLE:def 18</a></span>;<br/>
<a NAME="E32:56"/><span class="kw">then </span>
 <a href="msualg_2.html#K12" title="MSUALG_2:func.12">GenMSAlg</a> <font color="Maroon" title="c5">B</font> is   <a href="msualg_1.html#V3" title="MSUALG_1:attr.3">strict</a>   <a href="msualg_2.html#M1" title="MSUALG_2:mode.1">MSSubAlgebra</a> of <span class="p1">(<span class="default"><a href="msualg_2.html#K12" title="MSUALG_2:func.12">GenMSAlg</a> <font color="Maroon" title="c4">A</font></span>)</span> <a href="msualg_2.html#K13" title="MSUALG_2:func.13">"\/"</a> <font color="Maroon" title="c3">U1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="msualg_2.html#D17" target="_self" title="MSUALG_2:def.17">Def18</a></span>;<br/>
<span class="kw">hence </span><a NAME="E33:56"/>
<span class="p1">(<span class="default"><a href="msualg_2.html#K12" title="MSUALG_2:func.12">GenMSAlg</a> <font color="Maroon" title="c4">A</font></span>)</span> <a href="msualg_2.html#K13" title="MSUALG_2:func.13">"\/"</a> <font color="Maroon" title="c3">U1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="msualg_2.html#K12" title="MSUALG_2:func.12">GenMSAlg</a> <font color="Maroon" title="c5">B</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:56"><span class="lab"><font color="Green" title="E42">A3</font></span></a>, <a class="txt" href="#E28:56"><span class="lab"><font color="Green" title="E48">A9</font></span></a>, <a class="ref" href="msualg_2.html#T7" target="_self" title="MSUALG_2:th.7">Th8</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
