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<b>let </b><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="msualg_1.html#V2" title="MSUALG_1:attr.2">void</a>  <a href="msualg_1.html#L1" title="MSUALG_1:struct.1">ManySortedSign</a> ;<br/><b>let </b><font color="Maroon" title="c2">U1</font> be    <a href="msualg_1.html#L3" title="MSUALG_1:struct.3">MSAlgebra</a> of <font color="Maroon" title="c1">S</font>;<br/><b>let </b><font color="Maroon" title="c3">U2</font> be    <a href="msualg_2.html#M1" title="MSUALG_2:mode.1">MSSubAlgebra</a> of <font color="Maroon" title="c2">U1</font>;<br/><b>let </b><font color="Maroon" title="c4">B1</font> be   <a href="msualg_2.html#NM1" title="MSUALG_2:NM.1">MSSubset</a> of <font color="Maroon" title="c2">U1</font>;<br/><b>let </b><font color="Maroon" title="c5">B2</font> be   <a href="msualg_2.html#NM1" title="MSUALG_2:NM.1">MSSubset</a> of <font color="Maroon" title="c3">U2</font>;<br/>









<b>assume </b><a NAME="E1:20"/><i><font color="Green" title="E6">A1</font></i>: 
<font color="Maroon" title="c4">B1</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <font color="Maroon" title="c5">B2</font>
 ;<br/>

<b>reconsider </b><font color="Maroon" title="c6">G</font> =  <a href="msualg_2.html#K12" title="MSUALG_2:func.12">GenMSAlg</a> <font color="Maroon" title="c5">B2</font> as    <a href="msualg_2.html#M1" title="MSUALG_2:mode.1">MSSubAlgebra</a> of <font color="Maroon" title="c2">U1</font> <b>by </b><i><a class="ref" href="msualg_2.html#T7" title="MSUALG_2:th.7">MSUALG_2:7</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c7">H</font> =  <a href="msualg_2.html#K12" title="MSUALG_2:func.12">GenMSAlg</a> <font color="Maroon" title="c4">B1</font> as    <a href="msualg_2.html#M1" title="MSUALG_2:mode.1">MSSubAlgebra</a> of <font color="Maroon" title="c3">U2</font> <b>by </b><i><a class="txt" href="extens_1.html#E1:20"><i><font color="Green" title="E6">A1</font></i></a>, <a class="ref" href="msualg_2.html#D18" title="MSUALG_2:def.18">MSUALG_2:def 18</a></i>;<br/>
<a NAME="E4:20"/>
<font color="Maroon" title="c4">B1</font> is   <a href="msualg_2.html#NM1" title="MSUALG_2:NM.1">MSSubset</a> of <font color="Maroon" title="c7">H</font>
 
<b>by </b><i><a class="ref" href="msualg_2.html#D18" title="MSUALG_2:def.18">MSUALG_2:def 18</a></i>;<br/>
<a NAME="E5:20"/><b>then </b><i><font color="Green" title="E7">A2</font></i>: 
 <a href="msualg_2.html#K12" title="MSUALG_2:func.12">GenMSAlg</a> <font color="Maroon" title="c5">B2</font> is    <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="c4">B1</font>
 
<b>by </b><i><a class="txt" href="extens_1.html#E1:20"><i><font color="Green" title="E6">A1</font></i></a>, <a class="ref" href="msualg_2.html#D18" title="MSUALG_2:def.18">MSUALG_2:def 18</a></i>;<br/>
<a NAME="E6:20"/>
<font color="Maroon" title="c4">B1</font> is   <a href="msualg_2.html#NM1" title="MSUALG_2:NM.1">MSSubset</a> of <font color="Maroon" title="c6">G</font>
 
<b>by </b><i><a class="txt" href="extens_1.html#E1:20"><i><font color="Green" title="E6">A1</font></i></a>, <a class="ref" href="msualg_2.html#D18" title="MSUALG_2:def.18">MSUALG_2:def 18</a></i>;<br/>
<a NAME="E7:20"/><b>then </b>
 <a href="msualg_2.html#K12" title="MSUALG_2:func.12">GenMSAlg</a> <font color="Maroon" title="c4">B1</font> is    <a href="msualg_2.html#M1" title="MSUALG_2:mode.1">MSSubAlgebra</a> of <font color="Maroon" title="c6">G</font>
 
<b>by </b><i><a class="ref" href="msualg_2.html#D18" title="MSUALG_2:def.18">MSUALG_2:def 18</a></i>;<br/>
<b>hence </b><a NAME="E8:20"/>
 <a href="msualg_2.html#K12" title="MSUALG_2:func.12">GenMSAlg</a> <font color="Maroon" title="c4">B1</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">B2</font>
 <b>by </b><i><a class="txt" href="extens_1.html#E5:20"><i><font color="Green" title="E7">A2</font></i></a>, <a class="ref" href="msualg_2.html#T8" title="MSUALG_2:th.8">MSUALG_2:8</a></i>;<br/>


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