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<b>let </b><font color="Maroon">c<sub>1</sub></font> be  non <a href="struct_0.html#V3">empty</a> non <a href="msualg_1.html#V2">void</a>  <a href="msualg_1.html#L1">ManySortedSign</a> ;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be    <a href="msualg_1.html#L3">MSAlgebra</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be    <a href="msualg_2.html#M1">MSSubAlgebra</a> of <font color="Maroon">c<sub>2</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>4</sub></font> be   <a href="msualg_2.html#NM1">MSSubset</a> of <font color="Maroon">c<sub>2</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>5</sub></font> be   <a href="msualg_2.html#NM1">MSSubset</a> of <font color="Maroon">c<sub>3</sub></font>;<br/>









<b>assume </b><a NAME="E1:21"/><i><font color="Green">E7</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="pboole.html#R6">=</a> <font color="Maroon">c<sub>5</sub></font>
 ;<br/>

<b>reconsider </b><font color="Maroon">c<sub>6</sub></font> =  <a href="msualg_2.html#K12">GenMSAlg</a> <font color="Maroon">c<sub>5</sub></font> as    <a href="msualg_2.html#M1">MSSubAlgebra</a> of <font color="Maroon">c<sub>2</sub></font> <b>by </b><i><a class="ref" href="msualg_2.html#T7">MSUALG_2:7</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>7</sub></font> =  <a href="msualg_2.html#K12">GenMSAlg</a> <font color="Maroon">c<sub>4</sub></font> as    <a href="msualg_2.html#M1">MSSubAlgebra</a> of <font color="Maroon">c<sub>3</sub></font> <b>by </b><i><a class="txt" href="extens_1.html#E1:21"><i><font color="Green">E7</font></i></a>, <a class="ref" href="msualg_2.html#D18">MSUALG_2:def 18</a></i>;<br/>
<a NAME="E4:21"/>
<font color="Maroon">c<sub>4</sub></font> is   <a href="msualg_2.html#NM1">MSSubset</a> of <font color="Maroon">c<sub>7</sub></font>
 
<b>by </b><i><a class="ref" href="msualg_2.html#D18">MSUALG_2:def 18</a></i>;<br/>
<a NAME="E5:21"/><b>then </b><i><font color="Green">E8</font></i>: 
 <a href="msualg_2.html#K12">GenMSAlg</a> <font color="Maroon">c<sub>5</sub></font> is    <a href="msualg_2.html#M1">MSSubAlgebra</a> of  <a href="msualg_2.html#K12">GenMSAlg</a> <font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="txt" href="extens_1.html#E1:21"><i><font color="Green">E7</font></i></a>, <a class="ref" href="msualg_2.html#D18">MSUALG_2:def 18</a></i>;<br/>
<a NAME="E6:21"/>
<font color="Maroon">c<sub>4</sub></font> is   <a href="msualg_2.html#NM1">MSSubset</a> of <font color="Maroon">c<sub>6</sub></font>
 
<b>by </b><i><a class="txt" href="extens_1.html#E1:21"><i><font color="Green">E7</font></i></a>, <a class="ref" href="msualg_2.html#D18">MSUALG_2:def 18</a></i>;<br/>
<a NAME="E7:21"/><b>then </b>
 <a href="msualg_2.html#K12">GenMSAlg</a> <font color="Maroon">c<sub>4</sub></font> is    <a href="msualg_2.html#M1">MSSubAlgebra</a> of <font color="Maroon">c<sub>6</sub></font>
 
<b>by </b><i><a class="ref" href="msualg_2.html#D18">MSUALG_2:def 18</a></i>;<br/>
<b>hence </b><a NAME="E8:21"/>
 <a href="msualg_2.html#K12">GenMSAlg</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a>  <a href="msualg_2.html#K12">GenMSAlg</a> <font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="txt" href="extens_1.html#E5:21"><i><font color="Green">E8</font></i></a>, <a class="ref" href="msualg_2.html#T8">MSUALG_2:8</a></i>;<br/>


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