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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> <a href="realset2.html#V3">trivial</a> non <a href="msualg_1.html#V2">void</a> <a href="msualg_1.html#V6">segmental</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#V5">non-empty</a>  <a href="msualg_1.html#L3">MSAlgebra</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>



<b>assume </b><a NAME="E1:27"/><i><font color="Green">E22</font></i>: 
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default">0</span><a href="tarski.html#K1">}</a></span>
 ;<br/>

<a NAME="E2:27"/><b>then </b>
 <a href="msualg_1.html#K7">MSSign</a> <span class="p1">(<span class="default"><a href="msualg_1.html#K13">1-Alg</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="msualg_1.html#G1">ManySortedSign</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>,the <a href="msualg_1.html#U1">OperSymbols</a> of <font color="Maroon">c<sub>1</sub></font>,the <a href="msualg_1.html#U2">Arity</a> of <font color="Maroon">c<sub>1</sub></font>,the <a href="msualg_1.html#U3">ResultSort</a> of <font color="Maroon">c<sub>1</sub></font> #)
 
<b>by </b><i><a class="ref" href="mssublat.html#T23" target="_self">Th23</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">c<sub>3</sub></font> =  <a href="msualg_1.html#K10">MSAlg</a> <span class="p1">(<span class="default"><a href="msualg_1.html#K13">1-Alg</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> as  <a href="msualg_1.html#V4">strict</a>  <a href="msualg_1.html#L3">MSAlgebra</a> of <font color="Maroon">c<sub>1</sub></font> ;<br/>
<a NAME="E4:27"/>
the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> the <a href="msualg_1.html#U4">Sorts</a> of <span class="p1">(<span class="default"><a href="msualg_1.html#K10">MSAlg</a> <span class="p2">(<span class="default"><a href="msualg_1.html#K13">1-Alg</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>
 
;<br/>
<b>then reconsider </b><font color="Maroon">c<sub>4</sub></font> = <font color="Maroon">c<sub>3</sub></font> as  <a href="msualg_1.html#V4">strict</a> <a href="msualg_1.html#V5">non-empty</a>  <a href="msualg_1.html#L3">MSAlgebra</a> of <font color="Maroon">c<sub>1</sub></font> <b>by </b><i><a class="ref" href="msualg_1.html#D8">MSUALG_1:def 8</a></i>;<br/>
<a NAME="E6:27"/><i><font color="Green">E23</font></i>: 
 <a href="msualg_1.html#K13">1-Alg</a> <span class="p1">(<span class="default"><a href="msualg_1.html#K10">MSAlg</a> <span class="p2">(<span class="default"><a href="msualg_1.html#K13">1-Alg</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="unialg_1.html#G1">UAStr</a>(# <span class="p1">(<span class="default"><a href="msualg_1.html#K11">the_sort_of</a> <span class="p2">(<span class="default"><a href="msualg_1.html#K10">MSAlg</a> <span class="p3">(<span class="default"><a href="msualg_1.html#K13">1-Alg</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="msualg_1.html#K12">the_charact_of</a> <span class="p2">(<span class="default"><a href="msualg_1.html#K10">MSAlg</a> <span class="p3">(<span class="default"><a href="msualg_1.html#K13">1-Alg</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> #)
 
<b>by </b><i><a class="ref" href="msualg_1.html#D19">MSUALG_1:def 19</a></i>;<br/>
<a NAME="E7:27"/><i><font color="Green">E24</font></i>: 
 <a href="msualg_1.html#K13">1-Alg</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a>  <a href="unialg_1.html#G1">UAStr</a>(# <span class="p1">(<span class="default"><a href="msualg_1.html#K11">the_sort_of</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="msualg_1.html#K12">the_charact_of</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> #)
 
<b>by </b><i><a class="ref" href="msualg_1.html#D19">MSUALG_1:def 19</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>5</sub></font> =  <a href="msualg_1.html#K11">the_sort_of</a> <span class="p1">(<span class="default"><a href="msualg_1.html#K10">MSAlg</a> <span class="p2">(<span class="default"><a href="msualg_1.html#K13">1-Alg</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> as   <a href="pboole.html#NM3">Component</a> of the <a href="msualg_1.html#U4">Sorts</a> of <span class="p1">(<span class="default"><a href="msualg_1.html#K10">MSAlg</a> <span class="p2">(<span class="default"><a href="msualg_1.html#K13">1-Alg</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <b>by </b><i><a class="ref" href="msualg_1.html#D17">MSUALG_1:def 17</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>6</sub></font> = <font color="Maroon">c<sub>5</sub></font> as   <a href="pboole.html#NM3">Component</a> of the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">c<sub>4</sub></font> ;<br/>
<a NAME="E10:27"/>
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a>  <a href="msualg_1.html#K11">the_sort_of</a> <font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="ref" href="msualg_1.html#D17">MSUALG_1:def 17</a></i>;<br/>
<a NAME="E11:27"/><b>then </b><i><font color="Green">E25</font></i>: 
the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="msualg_1.html#K13">1-Alg</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="msualg_1.html#K13">1-Alg</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="mssublat.html#E6:27"><i><font color="Green">E23</font></i></a>, <a class="txt" href="mssublat.html#E7:27"><i><font color="Green">E24</font></i></a>, <a class="ref" href="msualg_1.html#T15">MSUALG_1:15</a></i>;<br/>
the <a href="unialg_1.html#U1">charact</a> of <span class="p1">(<span class="default"><a href="msualg_1.html#K13">1-Alg</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> = 
 <a href="msualg_1.html#K12">the_charact_of</a> <span class="p1">(<span class="default"><a href="msualg_1.html#K10">MSAlg</a> <span class="p2">(<span class="default"><a href="msualg_1.html#K13">1-Alg</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="mssublat.html#E6:27"><i><font color="Green">E23</font></i></a>, <a class="ref" href="msualg_1.html#T15">MSUALG_1:15</a></i>
<br/>.= 
the <a href="msualg_1.html#U5">Charact</a> of <font color="Maroon">c<sub>4</sub></font>
<b>by </b><i><a class="ref" href="msualg_1.html#D18">MSUALG_1:def 18</a></i>
<br/>.= 
the <a href="unialg_1.html#U1">charact</a> of <span class="p1">(<span class="default"><a href="msualg_1.html#K13">1-Alg</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="mssublat.html#E7:27"><i><font color="Green">E24</font></i></a>, <a class="ref" href="msualg_1.html#D18">MSUALG_1:def 18</a></i>
;<br/>
<b>hence </b> <a href="msualg_1.html#G3">MSAlgebra</a>(# the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">c<sub>2</sub></font>,the <a href="msualg_1.html#U5">Charact</a> of <font color="Maroon">c<sub>2</sub></font> #) = 
 <a href="msualg_1.html#G3">MSAlgebra</a>(# the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">c<sub>4</sub></font>,the <a href="msualg_1.html#U5">Charact</a> of <font color="Maroon">c<sub>4</sub></font> #)
<b>by </b><i><a class="txt" href="mssublat.html#E1:27"><i><font color="Green">E22</font></i></a>, <a class="txt" href="mssublat.html#E11:27"><i><font color="Green">E25</font></i></a>, <a class="ref" href="mssublat.html#T24" target="_self">Th24</a></i>
<br/>.= 
 <a href="msualg_1.html#K10">MSAlg</a> <span class="p1">(<span class="default"><a href="msualg_1.html#K13">1-Alg</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>

;<br/><br/>


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