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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="Red">::  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> holds  <span class="p1">(<span class="default"><a href="msualg_2.html#K12" title="MSUALG_2:func.12">GenMSAlg</a> <span class="p2">(<span class="default"><a href="msualg_2.html#K2" title="MSUALG_2:func.2">Constants</a> <font color="Olive" title="b1">U0</font></span>)</span></span>)</span> <a href="msualg_2.html#K11" title="MSUALG_2:func.11">/\</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> <span class="p1">(<span class="default"><a href="msualg_2.html#K2" title="MSUALG_2:func.2">Constants</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="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="Red">::  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> holds  <span class="p1">(<span class="default"><a href="msualg_2.html#K12" title="MSUALG_2:func.12">GenMSAlg</a> <span class="p2">(<span class="default"><a href="msualg_2.html#K2" title="MSUALG_2:func.2">Constants</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="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> <span class="p1">(<span class="default"><a href="msualg_2.html#K2" title="MSUALG_2:func.2">Constants</a> <font color="Maroon" title="c2">U0</font></span>)</span></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="Red">::  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> <span class="p2">(<span class="default"><a href="msualg_2.html#K2" title="MSUALG_2:func.2">Constants</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="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> <span class="p1">(<span class="default"><a href="msualg_2.html#K2" title="MSUALG_2:func.2">Constants</a> <font color="Maroon" title="c2">U0</font></span>)</span></span><br/>





<span class="kw">set </span><font color="Maroon" title="c4">C</font> =  <a href="msualg_2.html#K2" title="MSUALG_2:func.2">Constants</a> <font color="Maroon" title="c2">U0</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c5">G</font> =  <a href="msualg_2.html#K12" title="MSUALG_2:func.12">GenMSAlg</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">U0</font></span>)</span>;<br/>
<a NAME="E1:55"/>
 <a href="msualg_2.html#K2" title="MSUALG_2:func.2">Constants</a> <font color="Maroon" title="c2">U0</font> is   <a href="msualg_2.html#NM1" title="MSUALG_2:NM.1">MSSubset</a> of <font color="Maroon" title="c3">U1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="msualg_2.html#T11" target="_self" title="MSUALG_2:th.11">Th11</a></span>;<br/>
<a NAME="E2:55"/><span class="kw">then </span>
 <a href="msualg_2.html#K12" title="MSUALG_2:func.12">GenMSAlg</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">U0</font></span>)</span> 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 <font color="Maroon" title="c3">U1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="msualg_2.html#D18" target="_self" title="MSUALG_2:def.18">Def18</a></span>;<br/>
<a NAME="E3:55"/><span class="kw">then </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> <span class="p2">(<span class="default"><a href="msualg_2.html#K2" title="MSUALG_2:func.2">Constants</a> <font color="Maroon" title="c2">U0</font></span>)</span></span>)</span> is   <a href="msualg_2.html#NM1" title="MSUALG_2:NM.1">MSSubset</a> of <font color="Maroon" title="c3">U1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="msualg_2.html#D10" target="_self" title="MSUALG_2:def.10">Def10</a></span>;<br/>
<a NAME="E4:55"/><span class="kw">then </span><span class="lab"><font color="Green" title="E38">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> <span class="p2">(<span class="default"><a href="msualg_2.html#K2" title="MSUALG_2:func.2">Constants</a> <font color="Maroon" title="c2">U0</font></span>)</span></span>)</span> <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">U1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="pboole.html#D23" title="PBOOLE:def.23">PBOOLE:def 23</a></span>;<br/>
<a NAME="E5:55"/>
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> <span class="p3">(<span class="default"><a href="msualg_2.html#K2" title="MSUALG_2:func.2">Constants</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="c3">U1</font></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> <span class="p2">(<span class="default"><a href="msualg_2.html#K2" title="MSUALG_2:func.2">Constants</a> <font color="Maroon" title="c2">U0</font></span>)</span></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 <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">Def17</a></span>;<br/>
<a NAME="E6:55"/><span class="kw">then </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> <span class="p3">(<span class="default"><a href="msualg_2.html#K2" title="MSUALG_2:func.2">Constants</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="c3">U1</font></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> <span class="p2">(<span class="default"><a href="msualg_2.html#K2" title="MSUALG_2:func.2">Constants</a> <font color="Maroon" title="c2">U0</font></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:55"><span class="lab"><font color="Green" title="E38">A1</font></span></a>, <a class="ref" href="pboole.html#T25" title="PBOOLE:th.25">PBOOLE:25</a></span>;<br/>
<span class="kw">hence </span><a NAME="E7:55"/>
<span class="p1">(<span class="default"><a href="msualg_2.html#K12" title="MSUALG_2:func.12">GenMSAlg</a> <span class="p2">(<span class="default"><a href="msualg_2.html#K2" title="MSUALG_2:func.2">Constants</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="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> <span class="p1">(<span class="default"><a href="msualg_2.html#K2" title="MSUALG_2:func.2">Constants</a> <font color="Maroon" title="c2">U0</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="msualg_2.html#T10" target="_self" title="MSUALG_2:th.10">Th10</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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